%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV419-1.010 : TPTP v9.0.0. Released v3.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 11.09s 11.30s
% Output : Proof 11.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV419-1.010 : TPTP v9.0.0. Released v3.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n016.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Fri Jun 20 09:47:17 EDT 2025
% 0.11/0.34 % CPUTime :
% 11.09/11.30 % SZS status Unsatisfiable
% 11.09/11.30 % SZS output start Proof
% 11.09/11.30 tff(node22_type, type, (
% 11.09/11.30 node22: ( $i * $i * $i * $i ) > $o)).
% 11.09/11.30 tff(s2_type, type, (
% 11.09/11.30 s2: $i)).
% 11.09/11.30 tff(s1_type, type, (
% 11.09/11.30 s1: $i)).
% 11.09/11.30 tff(c_l_type, type, (
% 11.09/11.30 c_l: $i)).
% 11.09/11.30 tff(c_e_h_1_type, type, (
% 11.09/11.30 c_e_h_1: $i)).
% 11.09/11.30 tff(node21_type, type, (
% 11.09/11.30 node21: ( $i * $i * $i * $i ) > $o)).
% 11.09/11.30 tff(node20_type, type, (
% 11.09/11.30 node20: ( $i * $i * $i ) > $o)).
% 11.09/11.30 tff(m_and_h_gate_v_in2_type, type, (
% 11.09/11.30 m_and_h_gate_v_in2: ( $i * $i * $i ) > $o)).
% 11.09/11.30 tff(m_and_h_gate_h_init_v_out_type, type, (
% 11.09/11.30 m_and_h_gate_h_init_v_out: ( $i * $i * $i ) > $o)).
% 11.09/11.30 tff(c_m_type, type, (
% 11.09/11.30 c_m: $i)).
% 11.09/11.30 tff(node11_type, type, (
% 11.09/11.30 node11: ( $i * $i * $i * $i ) > $o)).
% 11.09/11.30 tff(s0_type, type, (
% 11.09/11.30 s0: $i)).
% 11.09/11.30 tff(node10_type, type, (
% 11.09/11.30 node10: ( $i * $i * $i * $i ) > $o)).
% 11.09/11.30 tff(node9_type, type, (
% 11.09/11.30 node9: ( $i * $i * $i ) > $o)).
% 11.09/11.30 tff(m_and_h_gate_h_init_v_in2_type, type, (
% 11.09/11.30 m_and_h_gate_h_init_v_in2: ( $i * $i * $i ) > $o)).
% 11.09/11.30 tff(c_n_type, type, (
% 11.09/11.30 c_n: $i)).
% 11.09/11.30 tff(m_and_h_gate_h_init_v_init_h_out_type, type, (
% 11.09/11.30 m_and_h_gate_h_init_v_init_h_out: ( $i * $i * $i ) > $o)).
% 11.09/11.30 tff(m_cell_v_token_type, type, (
% 11.09/11.30 m_cell_v_token: ( $i * $i ) > $o)).
% 11.09/11.30 tff(trans_type, type, (
% 11.09/11.30 trans: ( $i * $i ) > $o)).
% 11.09/11.30 tff(succ_type, type, (
% 11.09/11.30 succ: ( $i * $i ) > $o)).
% 11.09/11.30 tff(m_and_h_gate_v_out_type, type, (
% 11.09/11.30 m_and_h_gate_v_out: ( $i * $i * $i ) > $o)).
% 11.09/11.30 tff(m_or_h_gate_v_in1_type, type, (
% 11.09/11.30 m_or_h_gate_v_in1: ( $i * $i * $i ) > $o)).
% 11.09/11.30 tff(c_j_type, type, (
% 11.09/11.30 c_j: $i)).
% 11.09/11.30 tff(m_or_h_gate_v_out_type, type, (
% 11.09/11.30 m_or_h_gate_v_out: ( $i * $i * $i ) > $o)).
% 11.09/11.30 tff(s3_type, type, (
% 11.09/11.30 s3: $i)).
% 11.09/11.30 tff(m_c_h_element_v_in2_type, type, (
% 11.09/11.30 m_c_h_element_v_in2: ( $i * $i * $i ) > $o)).
% 11.09/11.30 tff(c_h_type, type, (
% 11.09/11.30 c_h: $i)).
% 11.09/11.30 tff(m_c_h_element_v_out_type, type, (
% 11.09/11.30 m_c_h_element_v_out: ( $i * $i * $i ) > $o)).
% 11.09/11.30 tff(s4_type, type, (
% 11.09/11.30 s4: $i)).
% 11.09/11.30 tff(m_and_h_gate_v_in1_type, type, (
% 11.09/11.30 m_and_h_gate_v_in1: ( $i * $i * $i ) > $o)).
% 11.09/11.30 tff(c_i_type, type, (
% 11.09/11.30 c_i: $i)).
% 11.09/11.30 tff(s5_type, type, (
% 11.09/11.30 s5: $i)).
% 11.09/11.30 tff(c_e_type, type, (
% 11.09/11.30 c_e: $i)).
% 11.09/11.30 tff(s6_type, type, (
% 11.09/11.30 s6: $i)).
% 11.09/11.30 tff(m_and_h_gate_h_init_v_in1_type, type, (
% 11.09/11.30 m_and_h_gate_h_init_v_in1: ( $i * $i * $i ) > $o)).
% 11.09/11.30 tff(s7_type, type, (
% 11.09/11.30 s7: $i)).
% 11.09/11.30 tff(s8_type, type, (
% 11.09/11.30 s8: $i)).
% 11.09/11.30 tff(c_r_type, type, (
% 11.09/11.30 c_r: $i)).
% 11.09/11.30 tff(s9_type, type, (
% 11.09/11.30 s9: $i)).
% 11.09/11.30 tff(m_user_v_ack_type, type, (
% 11.09/11.30 m_user_v_ack: ( $i * $i * $i ) > $o)).
% 11.09/11.30 tff(c_u_type, type, (
% 11.09/11.30 c_u: $i)).
% 11.09/11.30 tff(c_e_h_3_type, type, (
% 11.09/11.30 c_e_h_3: $i)).
% 11.09/11.30 tff(m_or_h_gate_v_in2_type, type, (
% 11.09/11.30 m_or_h_gate_v_in2: ( $i * $i * $i ) > $o)).
% 11.09/11.30 tff(m_cell_v_ack_type, type, (
% 11.09/11.30 m_cell_v_ack: ( $i * $i ) > $o)).
% 11.09/11.30 tff(c_q_type, type, (
% 11.09/11.30 c_q: $i)).
% 11.09/11.30 tff(c_e_h_2_type, type, (
% 11.09/11.30 c_e_h_2: $i)).
% 11.09/11.30 tff(c_f_type, type, (
% 11.09/11.30 c_f: $i)).
% 11.09/11.30 tff(node14_type, type, (
% 11.09/11.30 node14: ( $i * $i * $i * $i ) > $o)).
% 11.09/11.30 tff(node16_type, type, (
% 11.09/11.30 node16: ( $i * $i * $i ) > $o)).
% 11.09/11.30 tff(m_c_h_element_v_in1_type, type, (
% 11.09/11.30 m_c_h_element_v_in1: ( $i * $i * $i ) > $o)).
% 11.09/11.30 tff(node17_type, type, (
% 11.09/11.30 node17: ( $i * $i * $i ) > $o)).
% 11.09/11.30 tff(node18_type, type, (
% 11.09/11.30 node18: ( $i * $i * $i * $i ) > $o)).
% 11.09/11.30 tff(node19_type, type, (
% 11.09/11.30 node19: ( $i * $i * $i * $i ) > $o)).
% 11.09/11.30 tff(node15_type, type, (
% 11.09/11.30 node15: ( $i * $i * $i * $i ) > $o)).
% 11.09/11.30 tff(node3_type, type, (
% 11.09/11.30 node3: ( $i * $i * $i ) > $o)).
% 11.09/11.30 tff(m_cell_v_left_type, type, (
% 11.09/11.30 m_cell_v_left: ( $i * $i ) > $o)).
% 11.09/11.30 tff(c_k_type, type, (
% 11.09/11.30 c_k: $i)).
% 11.09/11.30 tff(c_g_type, type, (
% 11.09/11.30 c_g: $i)).
% 11.09/11.30 tff(node6_type, type, (
% 11.09/11.30 node6: ( $i * $i * $i * $i ) > $o)).
% 11.09/11.30 tff(node5_type, type, (
% 11.09/11.30 node5: ( $i * $i * $i * $i ) > $o)).
% 11.09/11.30 tff(c_d_type, type, (
% 11.09/11.30 c_d: $i)).
% 11.09/11.30 tff(c_c_type, type, (
% 11.09/11.30 c_c: $i)).
% 11.09/11.30 tff(m_mutex_h_half_v_out_type, type, (
% 11.09/11.30 m_mutex_h_half_v_out: ( $i * $i * $i ) > $o)).
% 11.09/11.30 tff(c_b_type, type, (
% 11.09/11.30 c_b: $i)).
% 11.09/11.30 tff(c_a_type, type, (
% 11.09/11.30 c_a: $i)).
% 11.09/11.30 tff(node23_type, type, (
% 11.09/11.30 node23: $i > $o)).
% 11.09/11.30 tff(node24_type, type, (
% 11.09/11.30 node24: $i > $o)).
% 11.09/11.30 tff(node25_type, type, (
% 11.09/11.30 node25: $i > $o)).
% 11.09/11.30 tff(node26_type, type, (
% 11.09/11.30 node26: $i > $o)).
% 11.09/11.30 tff(xuntil28_type, type, (
% 11.09/11.30 xuntil28: $i > $o)).
% 11.09/11.30 tff(until27_type, type, (
% 11.09/11.30 until27: $i > $o)).
% 11.09/11.30 tff(until2p29_type, type, (
% 11.09/11.30 until2p29: $i > $o)).
% 11.09/11.30 tff(xuntil2p30_type, type, (
% 11.09/11.31 xuntil2p30: $i > $o)).
% 11.09/11.31 tff(last_type, type, (
% 11.09/11.31 last: $i > $o)).
% 11.09/11.31 tff(loop_type, type, (
% 11.09/11.31 loop: $o)).
% 11.09/11.31 tff(1,assumption,(node21(c_e_h_1, c_l, s1, s2)), introduced(assumption)).
% 11.09/11.31 tff(2,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)), introduced(assumption)).
% 11.09/11.31 tff(3,assumption,(node10(c_e_h_1, c_m, s0, s1)), introduced(assumption)).
% 11.09/11.31 tff(4,assumption,(m_cell_v_token(c_e_h_1, s0)), introduced(assumption)).
% 11.09/11.31 tff(5,plain,
% 11.09/11.31 (^[X: $i] : refl((~m_cell_v_token(c_e_h_1, X)) <=> (~m_cell_v_token(c_e_h_1, X)))),
% 11.09/11.31 inference(bind,[status(th)],[])).
% 11.09/11.31 tff(6,plain,
% 11.09/11.31 (![X: $i] : (~m_cell_v_token(c_e_h_1, X)) <=> ![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 11.09/11.31 inference(quant_intro,[status(thm)],[5])).
% 11.09/11.31 tff(7,plain,
% 11.09/11.31 (![X: $i] : (~m_cell_v_token(c_e_h_1, X)) <=> ![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(8,axiom,(![X: $i] : (~m_cell_v_token(c_e_h_1, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_3')).
% 11.09/11.31 tff(9,plain,
% 11.09/11.31 (![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[8, 7])).
% 11.09/11.31 tff(10,plain,(
% 11.09/11.31 ![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 11.09/11.31 inference(skolemize,[status(sab)],[9])).
% 11.09/11.31 tff(11,plain,
% 11.09/11.31 (![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[10, 6])).
% 11.09/11.31 tff(12,plain,
% 11.09/11.31 ((~![X: $i] : (~m_cell_v_token(c_e_h_1, X))) | (~m_cell_v_token(c_e_h_1, s0))),
% 11.09/11.31 inference(quant_inst,[status(thm)],[])).
% 11.09/11.31 tff(13,plain,
% 11.09/11.31 ($false),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[12, 11, 4])).
% 11.09/11.31 tff(14,plain,(~m_cell_v_token(c_e_h_1, s0)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.31 tff(15,plain,
% 11.09/11.31 (^[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)))),
% 11.09/11.31 inference(bind,[status(th)],[])).
% 11.09/11.31 tff(16,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(quant_intro,[status(thm)],[15])).
% 11.09/11.31 tff(17,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(18,plain,
% 11.09/11.31 (^[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)))),
% 11.09/11.31 inference(bind,[status(th)],[])).
% 11.09/11.31 tff(19,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(quant_intro,[status(thm)],[18])).
% 11.09/11.31 tff(20,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')).
% 11.09/11.31 tff(21,plain,
% 11.09/11.31 (![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[20, 19])).
% 11.09/11.31 tff(22,plain,
% 11.09/11.31 (![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[21, 17])).
% 11.09/11.31 tff(23,plain,(
% 11.09/11.31 ![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 11.09/11.31 inference(skolemize,[status(sab)],[22])).
% 11.09/11.31 tff(24,plain,
% 11.09/11.31 (![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[23, 16])).
% 11.09/11.31 tff(25,plain,
% 11.09/11.31 (((~![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))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(26,plain,
% 11.09/11.31 ((~![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))),
% 11.09/11.31 inference(quant_inst,[status(thm)],[])).
% 11.09/11.31 tff(27,plain,
% 11.09/11.31 ((~![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)),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[26, 25])).
% 11.09/11.31 tff(28,plain,
% 11.09/11.31 (m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0)),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 11.09/11.31 tff(29,plain,
% 11.09/11.31 (^[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)))),
% 11.09/11.31 inference(bind,[status(th)],[])).
% 11.09/11.31 tff(30,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(quant_intro,[status(thm)],[29])).
% 11.09/11.31 tff(31,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(32,plain,
% 11.09/11.31 (^[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)))),
% 11.09/11.31 inference(bind,[status(th)],[])).
% 11.09/11.31 tff(33,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(quant_intro,[status(thm)],[32])).
% 11.09/11.31 tff(34,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')).
% 11.09/11.31 tff(35,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[34, 33])).
% 11.09/11.31 tff(36,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[35, 31])).
% 11.09/11.31 tff(37,plain,(
% 11.09/11.31 ![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))),
% 11.09/11.31 inference(skolemize,[status(sab)],[36])).
% 11.09/11.31 tff(38,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[37, 30])).
% 11.09/11.31 tff(39,plain,
% 11.09/11.31 (((~![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))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(40,plain,
% 11.09/11.31 ((~![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))),
% 11.09/11.31 inference(quant_inst,[status(thm)],[])).
% 11.09/11.31 tff(41,plain,
% 11.09/11.31 ((~![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)),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[40, 39])).
% 11.09/11.31 tff(42,plain,
% 11.09/11.31 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[41, 38, 28])).
% 11.09/11.31 tff(43,plain,
% 11.09/11.31 (^[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))))),
% 11.09/11.31 inference(bind,[status(th)],[])).
% 11.09/11.31 tff(44,plain,
% 11.09/11.31 (![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)))),
% 11.09/11.31 inference(quant_intro,[status(thm)],[43])).
% 11.09/11.31 tff(45,plain,
% 11.09/11.31 (![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)))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(46,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')).
% 11.09/11.31 tff(47,plain,
% 11.09/11.31 (![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)))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[46, 45])).
% 11.09/11.31 tff(48,plain,(
% 11.09/11.31 ![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)))),
% 11.09/11.31 inference(skolemize,[status(sab)],[47])).
% 11.09/11.31 tff(49,plain,
% 11.09/11.31 (![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)))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[48, 44])).
% 11.09/11.31 tff(50,plain,
% 11.09/11.31 (((~![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)))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(51,plain,
% 11.09/11.31 ((~![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)))),
% 11.09/11.31 inference(quant_inst,[status(thm)],[])).
% 11.09/11.31 tff(52,plain,
% 11.09/11.31 ((~![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))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[51, 50])).
% 11.09/11.31 tff(53,plain,
% 11.09/11.31 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0)),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[52, 49, 42])).
% 11.09/11.31 tff(54,plain,
% 11.09/11.31 (^[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)))),
% 11.09/11.31 inference(bind,[status(th)],[])).
% 11.09/11.31 tff(55,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(quant_intro,[status(thm)],[54])).
% 11.09/11.31 tff(56,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(57,plain,
% 11.09/11.31 (^[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)))),
% 11.09/11.31 inference(bind,[status(th)],[])).
% 11.09/11.31 tff(58,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(quant_intro,[status(thm)],[57])).
% 11.09/11.31 tff(59,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')).
% 11.09/11.31 tff(60,plain,
% 11.09/11.31 (![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[59, 58])).
% 11.09/11.31 tff(61,plain,
% 11.09/11.31 (![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[60, 56])).
% 11.09/11.31 tff(62,plain,(
% 11.09/11.31 ![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 11.09/11.31 inference(skolemize,[status(sab)],[61])).
% 11.09/11.31 tff(63,plain,
% 11.09/11.31 (![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[62, 55])).
% 11.09/11.31 tff(64,plain,
% 11.09/11.31 (((~![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))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(65,plain,
% 11.09/11.31 ((~![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))),
% 11.09/11.31 inference(quant_inst,[status(thm)],[])).
% 11.09/11.31 tff(66,plain,
% 11.09/11.31 ((~![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)),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[65, 64])).
% 11.09/11.31 tff(67,plain,
% 11.09/11.31 (~node9(c_e_h_1, c_m, s0)),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[66, 63, 53])).
% 11.09/11.31 tff(68,plain,
% 11.09/11.31 (^[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))))),
% 11.09/11.31 inference(bind,[status(th)],[])).
% 11.09/11.31 tff(69,plain,
% 11.09/11.31 (![Y: $i, I0: $i, 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)))),
% 11.09/11.31 inference(quant_intro,[status(thm)],[68])).
% 11.09/11.31 tff(70,plain,
% 11.09/11.31 (![Y: $i, I0: $i, 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)))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(71,plain,
% 11.09/11.31 (^[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))))),
% 11.09/11.31 inference(bind,[status(th)],[])).
% 11.09/11.31 tff(72,plain,
% 11.09/11.31 (![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)))),
% 11.09/11.31 inference(quant_intro,[status(thm)],[71])).
% 11.09/11.31 tff(73,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')).
% 11.09/11.31 tff(74,plain,
% 11.09/11.31 (![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[73, 72])).
% 11.09/11.31 tff(75,plain,
% 11.09/11.31 (![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[74, 70])).
% 11.09/11.31 tff(76,plain,(
% 11.09/11.31 ![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 11.09/11.31 inference(skolemize,[status(sab)],[75])).
% 11.09/11.31 tff(77,plain,
% 11.09/11.31 (![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[76, 69])).
% 11.09/11.31 tff(78,plain,
% 11.09/11.31 (((~![Y: $i, I0: $i, 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, s1)) | node9(c_e_h_1, c_m, s0) | (~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)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | node9(c_e_h_1, c_m, s0) | (~node10(c_e_h_1, c_m, s0, s1)))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(79,plain,
% 11.09/11.31 ((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))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | node9(c_e_h_1, c_m, s0) | (~node10(c_e_h_1, c_m, s0, s1)))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(80,plain,
% 11.09/11.31 (((~![Y: $i, I0: $i, 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)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | node9(c_e_h_1, c_m, s0) | (~node10(c_e_h_1, c_m, s0, s1))))),
% 11.09/11.31 inference(monotonicity,[status(thm)],[79])).
% 11.09/11.31 tff(81,plain,
% 11.09/11.31 (((~![Y: $i, I0: $i, 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)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | node9(c_e_h_1, c_m, s0) | (~node10(c_e_h_1, c_m, s0, s1)))),
% 11.09/11.31 inference(transitivity,[status(thm)],[80, 78])).
% 11.09/11.31 tff(82,plain,
% 11.09/11.31 ((~![Y: $i, I0: $i, 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)))),
% 11.09/11.31 inference(quant_inst,[status(thm)],[])).
% 11.09/11.31 tff(83,plain,
% 11.09/11.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | node9(c_e_h_1, c_m, s0) | (~node10(c_e_h_1, c_m, s0, s1))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[82, 81])).
% 11.09/11.31 tff(84,plain,
% 11.09/11.31 ($false),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[83, 77, 2, 67, 3])).
% 11.09/11.31 tff(85,plain,((~node10(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,[]))).
% 11.09/11.31 tff(86,plain,
% 11.09/11.31 (~node10(c_e_h_1, c_m, s0, s1)),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[85, 2])).
% 11.09/11.31 tff(87,plain,
% 11.09/11.31 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | trans(X, Y)) <=> ((~succ(X, Y)) | trans(X, Y)))),
% 11.09/11.31 inference(bind,[status(th)],[])).
% 11.09/11.31 tff(88,plain,
% 11.09/11.31 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 11.09/11.31 inference(quant_intro,[status(thm)],[87])).
% 11.09/11.31 tff(89,plain,
% 11.09/11.31 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(90,axiom,(![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound11')).
% 11.09/11.31 tff(91,plain,
% 11.09/11.31 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[90, 89])).
% 11.09/11.31 tff(92,plain,(
% 11.09/11.31 ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 11.09/11.31 inference(skolemize,[status(sab)],[91])).
% 11.09/11.31 tff(93,plain,
% 11.09/11.31 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[92, 88])).
% 11.09/11.31 tff(94,plain,
% 11.09/11.31 (succ(s0, s1) <=> succ(s0, s1)),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(95,axiom,(succ(s0, s1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound1')).
% 11.09/11.31 tff(96,plain,
% 11.09/11.31 (succ(s0, s1)),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[95, 94])).
% 11.09/11.31 tff(97,plain,
% 11.09/11.31 (((~![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))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(98,plain,
% 11.09/11.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s0, s1)) | trans(s0, s1))),
% 11.09/11.31 inference(quant_inst,[status(thm)],[])).
% 11.09/11.31 tff(99,plain,
% 11.09/11.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s0, s1)) | trans(s0, s1)),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[98, 97])).
% 11.09/11.31 tff(100,plain,
% 11.09/11.31 (trans(s0, s1)),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[99, 96, 93])).
% 11.09/11.31 tff(101,plain,
% 11.09/11.31 (^[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)))),
% 11.09/11.31 inference(bind,[status(th)],[])).
% 11.09/11.31 tff(102,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(quant_intro,[status(thm)],[101])).
% 11.09/11.31 tff(103,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(104,plain,
% 11.09/11.31 (^[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)))),
% 11.09/11.31 inference(bind,[status(th)],[])).
% 11.09/11.31 tff(105,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(quant_intro,[status(thm)],[104])).
% 11.09/11.31 tff(106,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')).
% 11.09/11.31 tff(107,plain,
% 11.09/11.31 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[106, 105])).
% 11.09/11.31 tff(108,plain,
% 11.09/11.31 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[107, 103])).
% 11.09/11.31 tff(109,plain,(
% 11.09/11.31 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 11.09/11.31 inference(skolemize,[status(sab)],[108])).
% 11.09/11.31 tff(110,plain,
% 11.09/11.31 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[109, 102])).
% 11.09/11.31 tff(111,plain,
% 11.09/11.31 (((~![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))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(112,plain,
% 11.09/11.31 ((~![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))),
% 11.09/11.31 inference(quant_inst,[status(thm)],[])).
% 11.09/11.31 tff(113,plain,
% 11.09/11.31 ((~![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)),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[112, 111])).
% 11.09/11.31 tff(114,plain,
% 11.09/11.31 (node10(c_e_h_1, c_m, s0, s1) | node11(c_e_h_1, c_m, s0, s1)),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[113, 110, 100])).
% 11.09/11.31 tff(115,plain,
% 11.09/11.31 (node11(c_e_h_1, c_m, s0, s1)),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[114, 86])).
% 11.09/11.31 tff(116,plain,
% 11.09/11.31 (^[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)))),
% 11.09/11.31 inference(bind,[status(th)],[])).
% 11.09/11.31 tff(117,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(quant_intro,[status(thm)],[116])).
% 11.09/11.31 tff(118,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(119,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')).
% 11.09/11.31 tff(120,plain,
% 11.09/11.31 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[119, 118])).
% 11.09/11.31 tff(121,plain,(
% 11.09/11.31 ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))),
% 11.09/11.31 inference(skolemize,[status(sab)],[120])).
% 11.09/11.31 tff(122,plain,
% 11.09/11.31 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[121, 117])).
% 11.09/11.31 tff(123,plain,
% 11.09/11.31 (((~![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))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(124,plain,
% 11.09/11.31 ((~![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))),
% 11.09/11.31 inference(quant_inst,[status(thm)],[])).
% 11.09/11.31 tff(125,plain,
% 11.09/11.31 ((~![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)),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[124, 123])).
% 11.09/11.31 tff(126,plain,
% 11.09/11.31 (~m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_m, s0)),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[125, 122, 14])).
% 11.09/11.31 tff(127,plain,
% 11.09/11.31 (^[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)))),
% 11.09/11.31 inference(bind,[status(th)],[])).
% 11.09/11.31 tff(128,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(quant_intro,[status(thm)],[127])).
% 11.09/11.31 tff(129,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(130,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')).
% 11.09/11.31 tff(131,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[130, 129])).
% 11.09/11.31 tff(132,plain,(
% 11.09/11.31 ![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))),
% 11.09/11.31 inference(skolemize,[status(sab)],[131])).
% 11.09/11.31 tff(133,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[132, 128])).
% 11.09/11.31 tff(134,plain,
% 11.09/11.31 (((~![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))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(135,plain,
% 11.09/11.31 ((~![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))),
% 11.09/11.31 inference(quant_inst,[status(thm)],[])).
% 11.09/11.31 tff(136,plain,
% 11.09/11.31 ((~![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)),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[135, 134])).
% 11.09/11.31 tff(137,plain,
% 11.09/11.31 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[136, 133, 126])).
% 11.09/11.31 tff(138,plain,
% 11.09/11.31 (^[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)))),
% 11.09/11.31 inference(bind,[status(th)],[])).
% 11.09/11.31 tff(139,plain,
% 11.09/11.31 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_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))),
% 11.09/11.31 inference(quant_intro,[status(thm)],[138])).
% 11.09/11.31 tff(140,plain,
% 11.09/11.31 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_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))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(141,plain,
% 11.09/11.31 (^[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)))),
% 11.09/11.31 inference(bind,[status(th)],[])).
% 11.09/11.31 tff(142,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(quant_intro,[status(thm)],[141])).
% 11.09/11.31 tff(143,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')).
% 11.09/11.31 tff(144,plain,
% 11.09/11.31 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[143, 142])).
% 11.09/11.31 tff(145,plain,
% 11.09/11.31 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[144, 140])).
% 11.09/11.31 tff(146,plain,(
% 11.09/11.31 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 11.09/11.31 inference(skolemize,[status(sab)],[145])).
% 11.09/11.31 tff(147,plain,
% 11.09/11.31 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[146, 139])).
% 11.09/11.31 tff(148,plain,
% 11.09/11.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, 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))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(149,plain,
% 11.09/11.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, 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))),
% 11.09/11.31 inference(quant_inst,[status(thm)],[])).
% 11.09/11.31 tff(150,plain,
% 11.09/11.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | (~node11(c_e_h_1, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[149, 148])).
% 11.09/11.31 tff(151,plain,
% 11.09/11.31 ($false),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[150, 147, 2, 137, 115])).
% 11.09/11.31 tff(152,plain,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.31 tff(153,plain,
% 11.09/11.31 (^[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)))),
% 11.09/11.31 inference(bind,[status(th)],[])).
% 11.09/11.31 tff(154,plain,
% 11.09/11.31 (![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_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 11.09/11.31 inference(quant_intro,[status(thm)],[153])).
% 11.09/11.31 tff(155,plain,
% 11.09/11.31 (![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_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(156,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')).
% 11.09/11.31 tff(157,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[156, 155])).
% 11.09/11.31 tff(158,plain,(
% 11.09/11.31 ![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))),
% 11.09/11.31 inference(skolemize,[status(sab)],[157])).
% 11.09/11.31 tff(159,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[158, 154])).
% 11.09/11.31 tff(160,plain,
% 11.09/11.31 (((~![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))) | ((~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))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(161,plain,
% 11.09/11.31 ((~![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))) | ((~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))),
% 11.09/11.31 inference(quant_inst,[status(thm)],[])).
% 11.09/11.31 tff(162,plain,
% 11.09/11.31 ((~![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))) | (~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)),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[161, 160])).
% 11.09/11.31 tff(163,plain,
% 11.09/11.31 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s1)),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[162, 159, 152])).
% 11.09/11.31 tff(164,plain,
% 11.09/11.31 (^[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)))),
% 11.09/11.31 inference(bind,[status(th)],[])).
% 11.09/11.31 tff(165,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(quant_intro,[status(thm)],[164])).
% 11.09/11.31 tff(166,plain,
% 11.09/11.31 (![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))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(167,plain,
% 11.09/11.31 (^[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)))),
% 11.09/11.31 inference(bind,[status(th)],[])).
% 11.09/11.31 tff(168,plain,
% 11.09/11.31 (![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))),
% 11.09/11.32 inference(quant_intro,[status(thm)],[167])).
% 11.09/11.32 tff(169,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')).
% 11.09/11.32 tff(170,plain,
% 11.09/11.32 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[169, 168])).
% 11.09/11.32 tff(171,plain,
% 11.09/11.32 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[170, 166])).
% 11.09/11.32 tff(172,plain,(
% 11.09/11.32 ![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 11.09/11.32 inference(skolemize,[status(sab)],[171])).
% 11.09/11.32 tff(173,plain,
% 11.09/11.32 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[172, 165])).
% 11.09/11.32 tff(174,plain,
% 11.09/11.32 (((~![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))),
% 11.09/11.32 inference(rewrite,[status(thm)],[])).
% 11.09/11.32 tff(175,plain,
% 11.09/11.32 ((~![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))),
% 11.09/11.32 inference(quant_inst,[status(thm)],[])).
% 11.09/11.32 tff(176,plain,
% 11.09/11.32 ((~![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)),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[175, 174])).
% 11.09/11.32 tff(177,plain,
% 11.09/11.32 (~node20(c_e_h_1, c_l, s1)),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[176, 173, 163])).
% 11.09/11.32 tff(178,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s3)), introduced(assumption)).
% 11.09/11.32 tff(179,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s2)), introduced(assumption)).
% 11.09/11.32 tff(180,assumption,(node22(c_e_h_2, c_q, s1, s2)), introduced(assumption)).
% 11.09/11.32 tff(181,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s1)), introduced(assumption)).
% 11.09/11.32 tff(182,assumption,(m_c_h_element_v_out(c_e_h_2, c_f, s0)), introduced(assumption)).
% 11.09/11.32 tff(183,plain,
% 11.09/11.32 (^[I0: $i, I1: $i] : refl((~m_c_h_element_v_out(I0, I1, s0)) <=> (~m_c_h_element_v_out(I0, I1, s0)))),
% 11.09/11.32 inference(bind,[status(th)],[])).
% 11.09/11.32 tff(184,plain,
% 11.09/11.32 (![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))),
% 11.09/11.32 inference(quant_intro,[status(thm)],[183])).
% 11.09/11.32 tff(185,plain,
% 11.09/11.32 (![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))),
% 11.09/11.32 inference(rewrite,[status(thm)],[])).
% 11.09/11.32 tff(186,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')).
% 11.09/11.32 tff(187,plain,
% 11.09/11.32 (![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[186, 185])).
% 11.09/11.32 tff(188,plain,(
% 11.09/11.32 ![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))),
% 11.09/11.32 inference(skolemize,[status(sab)],[187])).
% 11.09/11.32 tff(189,plain,
% 11.09/11.32 (![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[188, 184])).
% 11.09/11.32 tff(190,plain,
% 11.09/11.32 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s0))),
% 11.09/11.32 inference(quant_inst,[status(thm)],[])).
% 11.09/11.32 tff(191,plain,
% 11.09/11.32 ($false),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[190, 189, 182])).
% 11.09/11.32 tff(192,plain,(~m_c_h_element_v_out(c_e_h_2, c_f, s0)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.32 tff(193,plain,
% 11.09/11.32 (^[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)))),
% 11.09/11.32 inference(bind,[status(th)],[])).
% 11.09/11.32 tff(194,plain,
% 11.09/11.32 (![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))),
% 11.09/11.32 inference(quant_intro,[status(thm)],[193])).
% 11.09/11.32 tff(195,plain,
% 11.09/11.32 (![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))),
% 11.09/11.32 inference(rewrite,[status(thm)],[])).
% 11.09/11.32 tff(196,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')).
% 11.09/11.32 tff(197,plain,
% 11.09/11.32 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[196, 195])).
% 11.09/11.32 tff(198,plain,(
% 11.09/11.32 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))),
% 11.09/11.32 inference(skolemize,[status(sab)],[197])).
% 11.09/11.32 tff(199,plain,
% 11.09/11.32 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[198, 194])).
% 11.09/11.32 tff(200,plain,
% 11.09/11.32 (((~![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))),
% 11.09/11.32 inference(rewrite,[status(thm)],[])).
% 11.09/11.32 tff(201,plain,
% 11.09/11.32 ((~![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))),
% 11.09/11.32 inference(quant_inst,[status(thm)],[])).
% 11.09/11.32 tff(202,plain,
% 11.09/11.32 ((~![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)),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[201, 200])).
% 11.09/11.32 tff(203,plain,
% 11.09/11.32 (~m_and_h_gate_v_in1(c_e_h_2, c_q, s0)),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[202, 199, 192])).
% 11.09/11.32 tff(204,plain,
% 11.09/11.32 (^[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)))),
% 11.09/11.32 inference(bind,[status(th)],[])).
% 11.09/11.32 tff(205,plain,
% 11.09/11.32 (![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))),
% 11.09/11.32 inference(quant_intro,[status(thm)],[204])).
% 11.09/11.32 tff(206,plain,
% 11.09/11.32 (![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))),
% 11.09/11.32 inference(rewrite,[status(thm)],[])).
% 11.09/11.32 tff(207,plain,
% 11.09/11.32 (^[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)))),
% 11.09/11.32 inference(bind,[status(th)],[])).
% 11.09/11.32 tff(208,plain,
% 11.09/11.32 (![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))),
% 11.09/11.32 inference(quant_intro,[status(thm)],[207])).
% 11.09/11.32 tff(209,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')).
% 11.09/11.32 tff(210,plain,
% 11.09/11.32 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[209, 208])).
% 11.09/11.32 tff(211,plain,
% 11.09/11.32 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[210, 206])).
% 11.09/11.32 tff(212,plain,(
% 11.09/11.32 ![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 11.09/11.32 inference(skolemize,[status(sab)],[211])).
% 11.09/11.32 tff(213,plain,
% 11.09/11.32 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[212, 205])).
% 11.09/11.32 tff(214,plain,
% 11.09/11.32 (((~![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_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))),
% 11.09/11.32 inference(rewrite,[status(thm)],[])).
% 11.09/11.32 tff(215,plain,
% 11.09/11.32 ((~![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_q, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s0))),
% 11.09/11.32 inference(quant_inst,[status(thm)],[])).
% 11.09/11.32 tff(216,plain,
% 11.09/11.32 ((~![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_q, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s0)),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[215, 214])).
% 11.09/11.32 tff(217,plain,
% 11.09/11.32 (~node20(c_e_h_2, c_q, s0)),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[216, 213, 203])).
% 11.09/11.32 tff(218,assumption,(node21(c_e_h_2, c_q, s0, s1)), introduced(assumption)).
% 11.09/11.32 tff(219,plain,
% 11.09/11.32 (^[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))))),
% 11.09/11.32 inference(bind,[status(th)],[])).
% 11.09/11.32 tff(220,plain,
% 11.09/11.32 (![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))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 11.09/11.32 inference(quant_intro,[status(thm)],[219])).
% 11.09/11.32 tff(221,plain,
% 11.09/11.32 (![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))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 11.09/11.32 inference(rewrite,[status(thm)],[])).
% 11.09/11.32 tff(222,plain,
% 11.09/11.32 (^[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))))),
% 11.09/11.32 inference(bind,[status(th)],[])).
% 11.09/11.32 tff(223,plain,
% 11.09/11.32 (![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)))),
% 11.09/11.32 inference(quant_intro,[status(thm)],[222])).
% 11.09/11.32 tff(224,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')).
% 11.09/11.32 tff(225,plain,
% 11.09/11.32 (![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)))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[224, 223])).
% 11.09/11.32 tff(226,plain,
% 11.09/11.32 (![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)))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[225, 221])).
% 11.09/11.32 tff(227,plain,(
% 11.09/11.32 ![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)))),
% 11.09/11.32 inference(skolemize,[status(sab)],[226])).
% 11.09/11.32 tff(228,plain,
% 11.09/11.32 (![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)))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[227, 220])).
% 11.09/11.32 tff(229,plain,
% 11.09/11.32 (((~![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_q, s1)) | node20(c_e_h_2, c_q, s0) | (~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)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | node20(c_e_h_2, c_q, s0) | (~node21(c_e_h_2, c_q, s0, s1)))),
% 11.09/11.32 inference(rewrite,[status(thm)],[])).
% 11.09/11.32 tff(230,plain,
% 11.09/11.32 ((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))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | node20(c_e_h_2, c_q, s0) | (~node21(c_e_h_2, c_q, s0, s1)))),
% 11.09/11.32 inference(rewrite,[status(thm)],[])).
% 11.09/11.32 tff(231,plain,
% 11.09/11.32 (((~![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_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)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | node20(c_e_h_2, c_q, s0) | (~node21(c_e_h_2, c_q, s0, s1))))),
% 11.09/11.32 inference(monotonicity,[status(thm)],[230])).
% 11.09/11.32 tff(232,plain,
% 11.09/11.32 (((~![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_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)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | node20(c_e_h_2, c_q, s0) | (~node21(c_e_h_2, c_q, s0, s1)))),
% 11.09/11.32 inference(transitivity,[status(thm)],[231, 229])).
% 11.09/11.32 tff(233,plain,
% 11.09/11.32 ((~![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_q, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | (~node21(c_e_h_2, c_q, s0, s1)))),
% 11.09/11.32 inference(quant_inst,[status(thm)],[])).
% 11.09/11.32 tff(234,plain,
% 11.09/11.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | node20(c_e_h_2, c_q, s0) | (~node21(c_e_h_2, c_q, s0, s1))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[233, 232])).
% 11.09/11.32 tff(235,plain,
% 11.09/11.32 ($false),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[234, 228, 181, 218, 217])).
% 11.09/11.32 tff(236,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,[]))).
% 11.09/11.32 tff(237,plain,
% 11.09/11.32 (~node21(c_e_h_2, c_q, s0, s1)),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[236, 181])).
% 11.09/11.32 tff(238,plain,
% 11.09/11.32 (^[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)))),
% 11.09/11.32 inference(bind,[status(th)],[])).
% 11.09/11.32 tff(239,plain,
% 11.09/11.32 (![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))),
% 11.09/11.32 inference(quant_intro,[status(thm)],[238])).
% 11.09/11.32 tff(240,plain,
% 11.09/11.32 (![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))),
% 11.09/11.32 inference(rewrite,[status(thm)],[])).
% 11.09/11.32 tff(241,plain,
% 11.09/11.32 (^[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)))),
% 11.09/11.32 inference(bind,[status(th)],[])).
% 11.09/11.32 tff(242,plain,
% 11.09/11.32 (![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))),
% 11.09/11.32 inference(quant_intro,[status(thm)],[241])).
% 11.09/11.32 tff(243,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')).
% 11.09/11.32 tff(244,plain,
% 11.09/11.32 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[243, 242])).
% 11.09/11.32 tff(245,plain,
% 11.09/11.32 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[244, 240])).
% 11.09/11.32 tff(246,plain,(
% 11.09/11.32 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 11.09/11.32 inference(skolemize,[status(sab)],[245])).
% 11.09/11.32 tff(247,plain,
% 11.09/11.32 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[246, 239])).
% 11.09/11.32 tff(248,plain,
% 11.09/11.32 (((~![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))),
% 11.09/11.32 inference(rewrite,[status(thm)],[])).
% 11.09/11.32 tff(249,plain,
% 11.09/11.32 ((~![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))),
% 11.09/11.32 inference(quant_inst,[status(thm)],[])).
% 11.09/11.32 tff(250,plain,
% 11.09/11.32 ((~![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)),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[249, 248])).
% 11.09/11.32 tff(251,plain,
% 11.09/11.32 (node21(c_e_h_2, c_q, s0, s1) | node22(c_e_h_2, c_q, s0, s1)),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[250, 247, 100])).
% 11.09/11.32 tff(252,plain,
% 11.09/11.32 (node22(c_e_h_2, c_q, s0, s1)),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[251, 237])).
% 11.09/11.32 tff(253,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s0)), introduced(assumption)).
% 11.09/11.32 tff(254,plain,
% 11.09/11.32 (^[I0: $i, I1: $i] : refl((~m_and_h_gate_v_out(I0, I1, s0)) <=> (~m_and_h_gate_v_out(I0, I1, s0)))),
% 11.09/11.32 inference(bind,[status(th)],[])).
% 11.09/11.32 tff(255,plain,
% 11.09/11.32 (![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))),
% 11.09/11.32 inference(quant_intro,[status(thm)],[254])).
% 11.09/11.32 tff(256,plain,
% 11.09/11.32 (![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))),
% 11.09/11.32 inference(rewrite,[status(thm)],[])).
% 11.09/11.32 tff(257,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')).
% 11.09/11.32 tff(258,plain,
% 11.09/11.32 (![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[257, 256])).
% 11.09/11.32 tff(259,plain,(
% 11.09/11.32 ![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))),
% 11.09/11.32 inference(skolemize,[status(sab)],[258])).
% 11.09/11.32 tff(260,plain,
% 11.09/11.32 (![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[259, 255])).
% 11.09/11.32 tff(261,plain,
% 11.09/11.32 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s0))),
% 11.09/11.32 inference(quant_inst,[status(thm)],[])).
% 11.09/11.32 tff(262,plain,
% 11.09/11.32 ($false),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[261, 260, 253])).
% 11.09/11.32 tff(263,plain,(~m_and_h_gate_v_out(c_e_h_2, c_q, s0)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.32 tff(264,plain,
% 11.09/11.32 (^[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)))),
% 11.09/11.32 inference(bind,[status(th)],[])).
% 11.09/11.32 tff(265,plain,
% 11.09/11.32 (![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)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 11.09/11.32 inference(quant_intro,[status(thm)],[264])).
% 11.09/11.32 tff(266,plain,
% 11.09/11.32 (![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)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 11.09/11.32 inference(rewrite,[status(thm)],[])).
% 11.09/11.32 tff(267,plain,
% 11.09/11.32 (^[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)))),
% 11.09/11.32 inference(bind,[status(th)],[])).
% 11.09/11.32 tff(268,plain,
% 11.09/11.32 (![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))),
% 11.09/11.32 inference(quant_intro,[status(thm)],[267])).
% 11.09/11.32 tff(269,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')).
% 11.09/11.32 tff(270,plain,
% 11.09/11.32 (![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))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[269, 268])).
% 11.09/11.32 tff(271,plain,
% 11.09/11.32 (![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))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[270, 266])).
% 11.09/11.32 tff(272,plain,(
% 11.09/11.32 ![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))),
% 11.09/11.32 inference(skolemize,[status(sab)],[271])).
% 11.09/11.32 tff(273,plain,
% 11.09/11.32 (![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))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[272, 265])).
% 11.09/11.32 tff(274,plain,
% 11.09/11.32 (((~![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_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))),
% 11.09/11.32 inference(rewrite,[status(thm)],[])).
% 11.09/11.32 tff(275,plain,
% 11.09/11.32 ((~![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_q, s1)) | (~node22(c_e_h_2, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_q, s0))),
% 11.09/11.32 inference(quant_inst,[status(thm)],[])).
% 11.09/11.32 tff(276,plain,
% 11.09/11.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | (~node22(c_e_h_2, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_q, s0)),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[275, 274])).
% 11.09/11.32 tff(277,plain,
% 11.09/11.32 ($false),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[276, 273, 181, 263, 252])).
% 11.09/11.32 tff(278,plain,(~m_and_h_gate_v_out(c_e_h_2, c_q, s1)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.32 tff(279,plain,
% 11.09/11.32 (((~![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_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))),
% 11.09/11.32 inference(rewrite,[status(thm)],[])).
% 11.09/11.32 tff(280,plain,
% 11.09/11.32 ((~![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_q, s2)) | (~node22(c_e_h_2, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_q, s1))),
% 11.09/11.32 inference(quant_inst,[status(thm)],[])).
% 11.09/11.32 tff(281,plain,
% 11.09/11.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | (~node22(c_e_h_2, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_q, s1)),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[280, 279])).
% 11.09/11.32 tff(282,plain,
% 11.09/11.32 ($false),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[281, 273, 278, 179, 180])).
% 11.09/11.32 tff(283,plain,((~node22(c_e_h_2, c_q, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s2))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.32 tff(284,plain,
% 11.09/11.32 (~node22(c_e_h_2, c_q, s1, s2)),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[283, 179])).
% 11.09/11.32 tff(285,assumption,(m_c_h_element_v_out(c_e_h_2, c_f, s1)), introduced(assumption)).
% 11.09/11.32 tff(286,assumption,(node18(c_e_h_2, c_f, s0, s1)), introduced(assumption)).
% 11.09/11.32 tff(287,plain,
% 11.09/11.32 (^[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))))),
% 11.09/11.32 inference(bind,[status(th)],[])).
% 11.09/11.32 tff(288,plain,
% 11.09/11.32 (![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))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 11.09/11.32 inference(quant_intro,[status(thm)],[287])).
% 11.09/11.32 tff(289,plain,
% 11.09/11.32 (![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))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 11.09/11.32 inference(rewrite,[status(thm)],[])).
% 11.09/11.32 tff(290,plain,
% 11.09/11.32 (^[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))))),
% 11.09/11.32 inference(bind,[status(th)],[])).
% 11.09/11.32 tff(291,plain,
% 11.09/11.32 (![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))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 11.09/11.32 inference(quant_intro,[status(thm)],[290])).
% 11.09/11.32 tff(292,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')).
% 11.09/11.32 tff(293,plain,
% 11.09/11.32 (![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)))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[292, 291])).
% 11.09/11.32 tff(294,plain,
% 11.09/11.32 (![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)))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[293, 289])).
% 11.09/11.32 tff(295,plain,(
% 11.09/11.32 ![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)))),
% 11.09/11.32 inference(skolemize,[status(sab)],[294])).
% 11.09/11.32 tff(296,plain,
% 11.09/11.32 (![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)))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[295, 288])).
% 11.09/11.32 tff(297,plain,
% 11.09/11.32 (((~![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_f, s0) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | (~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) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | (~node18(c_e_h_2, c_f, s0, s1)))),
% 11.09/11.32 inference(rewrite,[status(thm)],[])).
% 11.09/11.32 tff(298,plain,
% 11.09/11.32 (((~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) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | (~node18(c_e_h_2, c_f, s0, s1)))),
% 11.09/11.32 inference(rewrite,[status(thm)],[])).
% 11.09/11.32 tff(299,plain,
% 11.09/11.32 (((~![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_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) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | (~node18(c_e_h_2, c_f, s0, s1))))),
% 11.09/11.32 inference(monotonicity,[status(thm)],[298])).
% 11.09/11.32 tff(300,plain,
% 11.09/11.32 (((~![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_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) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | (~node18(c_e_h_2, c_f, s0, s1)))),
% 11.09/11.32 inference(transitivity,[status(thm)],[299, 297])).
% 11.09/11.32 tff(301,plain,
% 11.09/11.32 ((~![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_f, s1)) | m_c_h_element_v_out(c_e_h_2, c_f, s0) | (~node18(c_e_h_2, c_f, s0, s1)))),
% 11.09/11.32 inference(quant_inst,[status(thm)],[])).
% 11.09/11.32 tff(302,plain,
% 11.09/11.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s0) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | (~node18(c_e_h_2, c_f, s0, s1))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[301, 300])).
% 11.09/11.32 tff(303,plain,
% 11.09/11.32 ($false),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[302, 296, 192, 285, 286])).
% 11.09/11.32 tff(304,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,[]))).
% 11.09/11.32 tff(305,plain,
% 11.09/11.32 (~node18(c_e_h_2, c_f, s0, s1)),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[304, 285])).
% 11.09/11.32 tff(306,plain,
% 11.09/11.32 (^[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)))),
% 11.09/11.32 inference(bind,[status(th)],[])).
% 11.09/11.32 tff(307,plain,
% 11.09/11.32 (![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))),
% 11.09/11.32 inference(quant_intro,[status(thm)],[306])).
% 11.09/11.32 tff(308,plain,
% 11.09/11.32 (![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))),
% 11.09/11.32 inference(rewrite,[status(thm)],[])).
% 11.09/11.32 tff(309,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')).
% 11.09/11.32 tff(310,plain,
% 11.09/11.32 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[309, 308])).
% 11.09/11.32 tff(311,plain,(
% 11.09/11.32 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))),
% 11.09/11.32 inference(skolemize,[status(sab)],[310])).
% 11.09/11.32 tff(312,plain,
% 11.09/11.32 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[311, 307])).
% 11.09/11.32 tff(313,plain,
% 11.09/11.32 (((~![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))),
% 11.09/11.32 inference(rewrite,[status(thm)],[])).
% 11.09/11.32 tff(314,plain,
% 11.09/11.32 ((~![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))),
% 11.09/11.32 inference(quant_inst,[status(thm)],[])).
% 11.09/11.32 tff(315,plain,
% 11.09/11.32 ((~![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)),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[314, 313])).
% 11.09/11.32 tff(316,plain,
% 11.09/11.32 (node19(c_e_h_2, c_f, s0, s1)),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[315, 312, 100])).
% 11.09/11.32 tff(317,plain,
% 11.09/11.32 (^[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))))),
% 11.09/11.32 inference(bind,[status(th)],[])).
% 11.09/11.32 tff(318,plain,
% 11.09/11.32 (![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)))),
% 11.09/11.33 inference(quant_intro,[status(thm)],[317])).
% 11.09/11.33 tff(319,plain,
% 11.09/11.33 (![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)))),
% 11.09/11.33 inference(rewrite,[status(thm)],[])).
% 11.09/11.33 tff(320,plain,
% 11.09/11.33 (^[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))))),
% 11.09/11.33 inference(bind,[status(th)],[])).
% 11.09/11.33 tff(321,plain,
% 11.09/11.33 (![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)))),
% 11.09/11.33 inference(quant_intro,[status(thm)],[320])).
% 11.09/11.33 tff(322,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')).
% 11.09/11.33 tff(323,plain,
% 11.09/11.33 (![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 11.09/11.33 inference(modus_ponens,[status(thm)],[322, 321])).
% 11.09/11.33 tff(324,plain,
% 11.09/11.33 (![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 11.09/11.33 inference(modus_ponens,[status(thm)],[323, 319])).
% 11.09/11.33 tff(325,plain,(
% 11.09/11.33 ![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 11.09/11.33 inference(skolemize,[status(sab)],[324])).
% 11.09/11.33 tff(326,plain,
% 11.09/11.33 (![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 11.09/11.33 inference(modus_ponens,[status(thm)],[325, 318])).
% 11.09/11.33 tff(327,plain,
% 11.09/11.33 (((~![Y: $i, 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) | (~node19(c_e_h_2, c_f, s0, s1)) | node18(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)))) | node17(c_e_h_2, c_f, s0) | (~node19(c_e_h_2, c_f, s0, s1)) | node18(c_e_h_2, c_f, s0, s1))),
% 11.09/11.33 inference(rewrite,[status(thm)],[])).
% 11.09/11.33 tff(328,plain,
% 11.09/11.33 ((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))) <=> (node17(c_e_h_2, c_f, s0) | (~node19(c_e_h_2, c_f, s0, s1)) | node18(c_e_h_2, c_f, s0, s1))),
% 11.09/11.33 inference(rewrite,[status(thm)],[])).
% 11.09/11.33 tff(329,plain,
% 11.09/11.33 (((~![Y: $i, 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)))) | (node17(c_e_h_2, c_f, s0) | (~node19(c_e_h_2, c_f, s0, s1)) | node18(c_e_h_2, c_f, s0, s1)))),
% 11.09/11.33 inference(monotonicity,[status(thm)],[328])).
% 11.09/11.33 tff(330,plain,
% 11.09/11.33 (((~![Y: $i, 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)))) | node17(c_e_h_2, c_f, s0) | (~node19(c_e_h_2, c_f, s0, s1)) | node18(c_e_h_2, c_f, s0, s1))),
% 11.09/11.33 inference(transitivity,[status(thm)],[329, 327])).
% 11.09/11.33 tff(331,plain,
% 11.09/11.33 ((~![Y: $i, 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)))),
% 11.09/11.33 inference(quant_inst,[status(thm)],[])).
% 11.09/11.33 tff(332,plain,
% 11.09/11.33 ((~![Y: $i, 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) | (~node19(c_e_h_2, c_f, s0, s1)) | node18(c_e_h_2, c_f, s0, s1)),
% 11.09/11.33 inference(modus_ponens,[status(thm)],[331, 330])).
% 11.09/11.33 tff(333,plain,
% 11.09/11.33 (node17(c_e_h_2, c_f, s0) | node18(c_e_h_2, c_f, s0, s1)),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[332, 326, 316])).
% 11.09/11.33 tff(334,plain,
% 11.09/11.33 (node17(c_e_h_2, c_f, s0)),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[333, 305])).
% 11.09/11.33 tff(335,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s0)), introduced(assumption)).
% 11.09/11.33 tff(336,plain,
% 11.09/11.33 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s0))),
% 11.09/11.33 inference(quant_inst,[status(thm)],[])).
% 11.09/11.33 tff(337,plain,
% 11.09/11.33 ($false),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[336, 260, 335])).
% 11.09/11.33 tff(338,plain,(~m_and_h_gate_v_out(c_e_h_2, c_i, s0)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.33 tff(339,plain,
% 11.09/11.33 (^[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)))),
% 11.09/11.33 inference(bind,[status(th)],[])).
% 11.09/11.33 tff(340,plain,
% 11.09/11.33 (![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))),
% 11.09/11.33 inference(quant_intro,[status(thm)],[339])).
% 11.09/11.33 tff(341,plain,
% 11.09/11.33 (![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))),
% 11.09/11.33 inference(rewrite,[status(thm)],[])).
% 11.09/11.33 tff(342,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')).
% 11.09/11.33 tff(343,plain,
% 11.09/11.33 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 11.09/11.33 inference(modus_ponens,[status(thm)],[342, 341])).
% 11.09/11.33 tff(344,plain,(
% 11.09/11.33 ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 11.09/11.33 inference(skolemize,[status(sab)],[343])).
% 11.09/11.33 tff(345,plain,
% 11.09/11.33 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 11.09/11.33 inference(modus_ponens,[status(thm)],[344, 340])).
% 11.09/11.33 tff(346,plain,
% 11.09/11.33 (((~![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))),
% 11.09/11.33 inference(rewrite,[status(thm)],[])).
% 11.09/11.33 tff(347,plain,
% 11.09/11.33 ((~![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))),
% 11.09/11.33 inference(quant_inst,[status(thm)],[])).
% 11.09/11.33 tff(348,plain,
% 11.09/11.33 ((~![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)),
% 11.09/11.33 inference(modus_ponens,[status(thm)],[347, 346])).
% 11.09/11.33 tff(349,plain,
% 11.09/11.33 (~m_c_h_element_v_in2(c_e_h_2, c_f, s0)),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[348, 345, 338])).
% 11.09/11.33 tff(350,plain,
% 11.09/11.33 (^[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))))),
% 11.09/11.33 inference(bind,[status(th)],[])).
% 11.09/11.33 tff(351,plain,
% 11.09/11.33 (![I0: $i, X: $i, 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)))),
% 11.09/11.33 inference(quant_intro,[status(thm)],[350])).
% 11.09/11.33 tff(352,plain,
% 11.09/11.33 (![I0: $i, X: $i, 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)))),
% 11.09/11.33 inference(rewrite,[status(thm)],[])).
% 11.09/11.33 tff(353,plain,
% 11.09/11.33 (^[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))))),
% 11.09/11.33 inference(bind,[status(th)],[])).
% 11.09/11.33 tff(354,plain,
% 11.09/11.33 (![I0: $i, X: $i, 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)))),
% 11.09/11.33 inference(quant_intro,[status(thm)],[353])).
% 11.09/11.33 tff(355,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')).
% 11.09/11.33 tff(356,plain,
% 11.09/11.33 (![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 11.09/11.33 inference(modus_ponens,[status(thm)],[355, 354])).
% 11.09/11.33 tff(357,plain,
% 11.09/11.33 (![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 11.09/11.33 inference(modus_ponens,[status(thm)],[356, 352])).
% 11.09/11.33 tff(358,plain,(
% 11.09/11.33 ![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 11.09/11.33 inference(skolemize,[status(sab)],[357])).
% 11.09/11.33 tff(359,plain,
% 11.09/11.33 (![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 11.09/11.33 inference(modus_ponens,[status(thm)],[358, 351])).
% 11.09/11.33 tff(360,plain,
% 11.09/11.33 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, 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, s0) | (~m_c_h_element_v_in1(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_in2(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)))),
% 11.09/11.33 inference(rewrite,[status(thm)],[])).
% 11.09/11.33 tff(361,plain,
% 11.09/11.33 (((~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_in2(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)))),
% 11.09/11.33 inference(rewrite,[status(thm)],[])).
% 11.09/11.33 tff(362,plain,
% 11.09/11.33 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | 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_in2(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))))),
% 11.09/11.33 inference(monotonicity,[status(thm)],[361])).
% 11.09/11.33 tff(363,plain,
% 11.09/11.33 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | 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_in2(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)))),
% 11.09/11.33 inference(transitivity,[status(thm)],[362, 360])).
% 11.09/11.33 tff(364,plain,
% 11.09/11.33 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | 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)))),
% 11.09/11.33 inference(quant_inst,[status(thm)],[])).
% 11.09/11.33 tff(365,plain,
% 11.09/11.33 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, 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, s0) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s0)) | (~node17(c_e_h_2, c_f, s0))),
% 11.09/11.33 inference(modus_ponens,[status(thm)],[364, 363])).
% 11.09/11.33 tff(366,plain,
% 11.09/11.33 ((~m_c_h_element_v_in1(c_e_h_2, c_f, s0)) | (~node17(c_e_h_2, c_f, s0))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[365, 359, 349])).
% 11.09/11.33 tff(367,plain,
% 11.09/11.33 (~m_c_h_element_v_in1(c_e_h_2, c_f, s0)),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[366, 334])).
% 11.09/11.33 tff(368,plain,
% 11.09/11.33 (^[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)))),
% 11.09/11.33 inference(bind,[status(th)],[])).
% 11.09/11.33 tff(369,plain,
% 11.09/11.33 (![I0: $i, X: $i, 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))),
% 11.09/11.33 inference(quant_intro,[status(thm)],[368])).
% 11.09/11.33 tff(370,plain,
% 11.09/11.33 (![I0: $i, X: $i, 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))),
% 11.09/11.33 inference(rewrite,[status(thm)],[])).
% 11.09/11.33 tff(371,plain,
% 11.09/11.33 (^[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)))),
% 11.09/11.33 inference(bind,[status(th)],[])).
% 11.09/11.33 tff(372,plain,
% 11.09/11.33 (![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))),
% 11.09/11.33 inference(quant_intro,[status(thm)],[371])).
% 11.09/11.33 tff(373,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')).
% 11.09/11.33 tff(374,plain,
% 11.09/11.33 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 11.09/11.33 inference(modus_ponens,[status(thm)],[373, 372])).
% 11.09/11.33 tff(375,plain,
% 11.09/11.33 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 11.09/11.33 inference(modus_ponens,[status(thm)],[374, 370])).
% 11.09/11.33 tff(376,plain,(
% 11.09/11.33 ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 11.09/11.33 inference(skolemize,[status(sab)],[375])).
% 11.09/11.33 tff(377,plain,
% 11.09/11.33 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 11.09/11.33 inference(modus_ponens,[status(thm)],[376, 369])).
% 11.09/11.33 tff(378,plain,
% 11.09/11.33 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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))),
% 11.09/11.33 inference(rewrite,[status(thm)],[])).
% 11.09/11.33 tff(379,plain,
% 11.09/11.33 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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))),
% 11.09/11.33 inference(quant_inst,[status(thm)],[])).
% 11.09/11.33 tff(380,plain,
% 11.09/11.33 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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)),
% 11.09/11.33 inference(modus_ponens,[status(thm)],[379, 378])).
% 11.09/11.33 tff(381,plain,
% 11.09/11.33 ((~node16(c_e_h_2, c_f, s0)) | m_c_h_element_v_in1(c_e_h_2, c_f, s0)),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[380, 377, 349])).
% 11.09/11.33 tff(382,plain,
% 11.09/11.33 (~node16(c_e_h_2, c_f, s0)),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[381, 367])).
% 11.09/11.33 tff(383,assumption,(node15(c_e_h_2, c_f, s0, s1)), introduced(assumption)).
% 11.09/11.33 tff(384,plain,
% 11.09/11.33 (^[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)))),
% 11.09/11.33 inference(bind,[status(th)],[])).
% 11.09/11.33 tff(385,plain,
% 11.09/11.33 (![Y: $i, I0: $i, X: $i, I1: $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))),
% 11.09/11.33 inference(quant_intro,[status(thm)],[384])).
% 11.09/11.33 tff(386,plain,
% 11.09/11.33 (![Y: $i, I0: $i, X: $i, I1: $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))),
% 11.09/11.33 inference(rewrite,[status(thm)],[])).
% 11.09/11.33 tff(387,plain,
% 11.09/11.33 (^[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)))),
% 11.09/11.33 inference(bind,[status(th)],[])).
% 11.09/11.33 tff(388,plain,
% 11.09/11.33 (![Y: $i, 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))),
% 11.09/11.33 inference(quant_intro,[status(thm)],[387])).
% 11.09/11.33 tff(389,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')).
% 11.09/11.33 tff(390,plain,
% 11.09/11.33 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 11.09/11.33 inference(modus_ponens,[status(thm)],[389, 388])).
% 11.09/11.33 tff(391,plain,
% 11.09/11.33 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 11.09/11.33 inference(modus_ponens,[status(thm)],[390, 386])).
% 11.09/11.33 tff(392,plain,(
% 11.09/11.33 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 11.09/11.33 inference(skolemize,[status(sab)],[391])).
% 11.09/11.33 tff(393,plain,
% 11.09/11.33 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 11.09/11.33 inference(modus_ponens,[status(thm)],[392, 385])).
% 11.09/11.33 tff(394,plain,
% 11.09/11.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 11.19/11.33 inference(rewrite,[status(thm)],[])).
% 11.19/11.33 tff(395,plain,
% 11.19/11.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 11.19/11.33 inference(quant_inst,[status(thm)],[])).
% 11.19/11.33 tff(396,plain,
% 11.19/11.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | (~node15(c_e_h_2, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_f, s0)),
% 11.19/11.33 inference(modus_ponens,[status(thm)],[395, 394])).
% 11.19/11.33 tff(397,plain,
% 11.19/11.33 ($false),
% 11.19/11.33 inference(unit_resolution,[status(thm)],[396, 393, 192, 285, 383])).
% 11.19/11.33 tff(398,plain,((~node15(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,[]))).
% 11.19/11.33 tff(399,plain,
% 11.19/11.33 (~node15(c_e_h_2, c_f, s0, s1)),
% 11.19/11.33 inference(unit_resolution,[status(thm)],[398, 285])).
% 11.19/11.33 tff(400,plain,
% 11.19/11.33 (^[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))))),
% 11.19/11.33 inference(bind,[status(th)],[])).
% 11.19/11.33 tff(401,plain,
% 11.19/11.33 (![Y: $i, I0: $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)))),
% 11.19/11.33 inference(quant_intro,[status(thm)],[400])).
% 11.19/11.33 tff(402,plain,
% 11.19/11.33 (![Y: $i, I0: $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)))),
% 11.19/11.33 inference(rewrite,[status(thm)],[])).
% 11.19/11.33 tff(403,plain,
% 11.19/11.33 (^[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)))))),
% 11.19/11.33 inference(bind,[status(th)],[])).
% 11.19/11.33 tff(404,plain,
% 11.19/11.33 (![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)))),
% 11.19/11.33 inference(quant_intro,[status(thm)],[403])).
% 11.19/11.33 tff(405,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')).
% 11.19/11.33 tff(406,plain,
% 11.19/11.33 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 11.19/11.33 inference(modus_ponens,[status(thm)],[405, 404])).
% 11.19/11.33 tff(407,plain,
% 11.19/11.33 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 11.19/11.33 inference(modus_ponens,[status(thm)],[406, 402])).
% 11.19/11.33 tff(408,plain,(
% 11.19/11.33 ![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 11.19/11.33 inference(skolemize,[status(sab)],[407])).
% 11.19/11.33 tff(409,plain,
% 11.19/11.33 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 11.19/11.33 inference(modus_ponens,[status(thm)],[408, 401])).
% 11.19/11.33 tff(410,plain,
% 11.19/11.33 (((~![Y: $i, I0: $i, X: $i, I1: $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) | (~node19(c_e_h_2, c_f, s0, s1)) | 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)))) | node16(c_e_h_2, c_f, s0) | (~node19(c_e_h_2, c_f, s0, s1)) | node15(c_e_h_2, c_f, s0, s1) | node14(c_e_h_2, c_f, s0, s1))),
% 11.19/11.33 inference(rewrite,[status(thm)],[])).
% 11.19/11.33 tff(411,plain,
% 11.19/11.33 ((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))) <=> (node16(c_e_h_2, c_f, s0) | (~node19(c_e_h_2, c_f, s0, s1)) | node15(c_e_h_2, c_f, s0, s1) | node14(c_e_h_2, c_f, s0, s1))),
% 11.19/11.33 inference(rewrite,[status(thm)],[])).
% 11.19/11.33 tff(412,plain,
% 11.19/11.33 (((~![Y: $i, I0: $i, X: $i, I1: $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)))) | (node16(c_e_h_2, c_f, s0) | (~node19(c_e_h_2, c_f, s0, s1)) | node15(c_e_h_2, c_f, s0, s1) | node14(c_e_h_2, c_f, s0, s1)))),
% 11.19/11.33 inference(monotonicity,[status(thm)],[411])).
% 11.19/11.33 tff(413,plain,
% 11.19/11.33 (((~![Y: $i, I0: $i, X: $i, I1: $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)))) | node16(c_e_h_2, c_f, s0) | (~node19(c_e_h_2, c_f, s0, s1)) | node15(c_e_h_2, c_f, s0, s1) | node14(c_e_h_2, c_f, s0, s1))),
% 11.19/11.33 inference(transitivity,[status(thm)],[412, 410])).
% 11.19/11.33 tff(414,plain,
% 11.19/11.33 ((~![Y: $i, I0: $i, X: $i, I1: $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)))),
% 11.19/11.33 inference(quant_inst,[status(thm)],[])).
% 11.19/11.33 tff(415,plain,
% 11.19/11.33 ((~![Y: $i, I0: $i, X: $i, I1: $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) | (~node19(c_e_h_2, c_f, s0, s1)) | node15(c_e_h_2, c_f, s0, s1) | node14(c_e_h_2, c_f, s0, s1)),
% 11.19/11.33 inference(modus_ponens,[status(thm)],[414, 413])).
% 11.19/11.33 tff(416,plain,
% 11.19/11.33 (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)),
% 11.19/11.33 inference(unit_resolution,[status(thm)],[415, 409, 316])).
% 11.19/11.33 tff(417,plain,
% 11.19/11.33 (node14(c_e_h_2, c_f, s0, s1)),
% 11.19/11.33 inference(unit_resolution,[status(thm)],[416, 399, 382])).
% 11.19/11.33 tff(418,plain,
% 11.19/11.33 (^[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))))),
% 11.19/11.33 inference(bind,[status(th)],[])).
% 11.19/11.33 tff(419,plain,
% 11.19/11.33 (![Y: $i, I0: $i, X: $i, I1: $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)))),
% 11.19/11.33 inference(quant_intro,[status(thm)],[418])).
% 11.19/11.33 tff(420,plain,
% 11.19/11.33 (![Y: $i, I0: $i, X: $i, I1: $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)))),
% 11.19/11.33 inference(rewrite,[status(thm)],[])).
% 11.19/11.33 tff(421,plain,
% 11.19/11.33 (^[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))))),
% 11.19/11.33 inference(bind,[status(th)],[])).
% 11.19/11.33 tff(422,plain,
% 11.19/11.33 (![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)))),
% 11.19/11.33 inference(quant_intro,[status(thm)],[421])).
% 11.19/11.33 tff(423,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')).
% 11.19/11.33 tff(424,plain,
% 11.19/11.33 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 11.19/11.33 inference(modus_ponens,[status(thm)],[423, 422])).
% 11.19/11.33 tff(425,plain,
% 11.19/11.33 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 11.19/11.33 inference(modus_ponens,[status(thm)],[424, 420])).
% 11.19/11.33 tff(426,plain,(
% 11.19/11.33 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 11.19/11.33 inference(skolemize,[status(sab)],[425])).
% 11.19/11.33 tff(427,plain,
% 11.19/11.33 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 11.19/11.33 inference(modus_ponens,[status(thm)],[426, 419])).
% 11.19/11.33 tff(428,plain,
% 11.19/11.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_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) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | (~node14(c_e_h_2, 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_2, c_f, s0) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | (~node14(c_e_h_2, c_f, s0, s1)))),
% 11.19/11.33 inference(rewrite,[status(thm)],[])).
% 11.19/11.33 tff(429,plain,
% 11.19/11.33 (((~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) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | (~node14(c_e_h_2, c_f, s0, s1)))),
% 11.19/11.33 inference(rewrite,[status(thm)],[])).
% 11.19/11.33 tff(430,plain,
% 11.19/11.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | (~node14(c_e_h_2, c_f, s0, s1))))),
% 11.19/11.33 inference(monotonicity,[status(thm)],[429])).
% 11.19/11.33 tff(431,plain,
% 11.19/11.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | (~node14(c_e_h_2, c_f, s0, s1)))),
% 11.19/11.33 inference(transitivity,[status(thm)],[430, 428])).
% 11.19/11.33 tff(432,plain,
% 11.19/11.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))),
% 11.19/11.34 inference(quant_inst,[status(thm)],[])).
% 11.19/11.34 tff(433,plain,
% 11.19/11.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | (~node14(c_e_h_2, c_f, s0, s1))),
% 11.19/11.34 inference(modus_ponens,[status(thm)],[432, 431])).
% 11.19/11.34 tff(434,plain,
% 11.19/11.34 ($false),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[433, 427, 367, 285, 417])).
% 11.19/11.34 tff(435,plain,(~m_c_h_element_v_out(c_e_h_2, c_f, s1)), inference(lemma,lemma(discharge,[]))).
% 11.19/11.34 tff(436,assumption,(m_and_h_gate_v_in1(c_e_h_2, c_q, s1)), introduced(assumption)).
% 11.19/11.34 tff(437,assumption,(~m_c_h_element_v_out(c_e_h_2, c_f, s1)), introduced(assumption)).
% 11.19/11.34 tff(438,plain,
% 11.19/11.34 (((~![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))),
% 11.19/11.34 inference(rewrite,[status(thm)],[])).
% 11.19/11.34 tff(439,plain,
% 11.19/11.34 ((~![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))),
% 11.19/11.34 inference(quant_inst,[status(thm)],[])).
% 11.19/11.34 tff(440,plain,
% 11.19/11.34 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s1)) | m_c_h_element_v_out(c_e_h_2, c_f, s1)),
% 11.19/11.34 inference(modus_ponens,[status(thm)],[439, 438])).
% 11.19/11.34 tff(441,plain,
% 11.19/11.34 ($false),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[440, 199, 437, 436])).
% 11.19/11.34 tff(442,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,[]))).
% 11.19/11.34 tff(443,plain,
% 11.19/11.34 (~m_and_h_gate_v_in1(c_e_h_2, c_q, s1)),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[442, 435])).
% 11.19/11.34 tff(444,assumption,(node20(c_e_h_2, c_q, s1)), introduced(assumption)).
% 11.19/11.34 tff(445,assumption,(~m_and_h_gate_v_in1(c_e_h_2, c_q, s1)), introduced(assumption)).
% 11.19/11.34 tff(446,plain,
% 11.19/11.34 (((~![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))),
% 11.19/11.34 inference(rewrite,[status(thm)],[])).
% 11.19/11.34 tff(447,plain,
% 11.19/11.34 ((~![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))),
% 11.19/11.34 inference(quant_inst,[status(thm)],[])).
% 11.19/11.34 tff(448,plain,
% 11.19/11.34 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s1)),
% 11.19/11.34 inference(modus_ponens,[status(thm)],[447, 446])).
% 11.19/11.34 tff(449,plain,
% 11.19/11.34 ($false),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[448, 213, 445, 444])).
% 11.19/11.34 tff(450,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,[]))).
% 11.19/11.34 tff(451,plain,
% 11.19/11.34 (~node20(c_e_h_2, c_q, s1)),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[450, 443])).
% 11.19/11.34 tff(452,assumption,(~node20(c_e_h_2, c_q, s1)), introduced(assumption)).
% 11.19/11.34 tff(453,assumption,(node21(c_e_h_2, c_q, s1, s2)), introduced(assumption)).
% 11.19/11.34 tff(454,plain,
% 11.19/11.34 (((~![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)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | (~node21(c_e_h_2, c_q, s1, s2)) | node20(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)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | (~node21(c_e_h_2, c_q, s1, s2)) | node20(c_e_h_2, c_q, s1))),
% 11.19/11.34 inference(rewrite,[status(thm)],[])).
% 11.19/11.34 tff(455,plain,
% 11.19/11.34 ((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))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | (~node21(c_e_h_2, c_q, s1, s2)) | node20(c_e_h_2, c_q, s1))),
% 11.19/11.34 inference(rewrite,[status(thm)],[])).
% 11.19/11.34 tff(456,plain,
% 11.19/11.34 (((~![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_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)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | (~node21(c_e_h_2, c_q, s1, s2)) | node20(c_e_h_2, c_q, s1)))),
% 11.19/11.34 inference(monotonicity,[status(thm)],[455])).
% 11.19/11.34 tff(457,plain,
% 11.19/11.34 (((~![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_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)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | (~node21(c_e_h_2, c_q, s1, s2)) | node20(c_e_h_2, c_q, s1))),
% 11.19/11.34 inference(transitivity,[status(thm)],[456, 454])).
% 11.19/11.34 tff(458,plain,
% 11.19/11.34 ((~![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_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)))),
% 11.19/11.34 inference(quant_inst,[status(thm)],[])).
% 11.19/11.34 tff(459,plain,
% 11.19/11.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | (~node21(c_e_h_2, c_q, s1, s2)) | node20(c_e_h_2, c_q, s1)),
% 11.19/11.34 inference(modus_ponens,[status(thm)],[458, 457])).
% 11.19/11.34 tff(460,plain,
% 11.19/11.34 ($false),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[459, 228, 179, 453, 452])).
% 11.19/11.34 tff(461,plain,((~node21(c_e_h_2, c_q, s1, s2)) | (~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,[]))).
% 11.19/11.34 tff(462,plain,
% 11.19/11.34 ((~node21(c_e_h_2, c_q, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s2))),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[461, 451])).
% 11.19/11.34 tff(463,plain,
% 11.19/11.34 (~node21(c_e_h_2, c_q, s1, s2)),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[462, 179])).
% 11.19/11.34 tff(464,plain,
% 11.19/11.34 (succ(s1, s2) <=> succ(s1, s2)),
% 11.19/11.34 inference(rewrite,[status(thm)],[])).
% 11.19/11.34 tff(465,axiom,(succ(s1, s2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound2')).
% 11.19/11.34 tff(466,plain,
% 11.19/11.34 (succ(s1, s2)),
% 11.19/11.34 inference(modus_ponens,[status(thm)],[465, 464])).
% 11.19/11.34 tff(467,plain,
% 11.19/11.34 (((~![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))),
% 11.19/11.34 inference(rewrite,[status(thm)],[])).
% 11.19/11.34 tff(468,plain,
% 11.19/11.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s1, s2)) | trans(s1, s2))),
% 11.19/11.34 inference(quant_inst,[status(thm)],[])).
% 11.19/11.34 tff(469,plain,
% 11.19/11.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s1, s2)) | trans(s1, s2)),
% 11.19/11.34 inference(modus_ponens,[status(thm)],[468, 467])).
% 11.19/11.34 tff(470,plain,
% 11.19/11.34 (trans(s1, s2)),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[469, 466, 93])).
% 11.19/11.34 tff(471,plain,
% 11.19/11.34 (((~![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))),
% 11.19/11.34 inference(rewrite,[status(thm)],[])).
% 11.19/11.34 tff(472,plain,
% 11.19/11.34 ((~![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))),
% 11.19/11.34 inference(quant_inst,[status(thm)],[])).
% 11.19/11.34 tff(473,plain,
% 11.19/11.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_2, c_q, s1, s2) | node22(c_e_h_2, c_q, s1, s2)),
% 11.19/11.34 inference(modus_ponens,[status(thm)],[472, 471])).
% 11.19/11.34 tff(474,plain,
% 11.19/11.34 (node21(c_e_h_2, c_q, s1, s2) | node22(c_e_h_2, c_q, s1, s2)),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[473, 247, 470])).
% 11.19/11.34 tff(475,plain,
% 11.19/11.34 ($false),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[474, 463, 284])).
% 11.19/11.34 tff(476,plain,(~m_and_h_gate_v_out(c_e_h_2, c_q, s2)), inference(lemma,lemma(discharge,[]))).
% 11.19/11.34 tff(477,plain,
% 11.19/11.34 (((~![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_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))),
% 11.19/11.34 inference(rewrite,[status(thm)],[])).
% 11.19/11.34 tff(478,plain,
% 11.19/11.34 ((~![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_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))),
% 11.19/11.34 inference(quant_inst,[status(thm)],[])).
% 11.19/11.34 tff(479,plain,
% 11.19/11.34 ((~![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_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)),
% 11.19/11.34 inference(modus_ponens,[status(thm)],[478, 477])).
% 11.19/11.34 tff(480,plain,
% 11.19/11.34 ((~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | (~node22(c_e_h_2, c_q, s2, s3))),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[479, 273, 476])).
% 11.19/11.34 tff(481,plain,
% 11.19/11.34 (~node22(c_e_h_2, c_q, s2, s3)),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[480, 178])).
% 11.19/11.34 tff(482,assumption,(m_c_h_element_v_out(c_e_h_2, c_f, s2)), introduced(assumption)).
% 11.19/11.34 tff(483,assumption,(node15(c_e_h_2, c_f, s1, s2)), introduced(assumption)).
% 11.19/11.34 tff(484,plain,
% 11.19/11.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 11.19/11.34 inference(rewrite,[status(thm)],[])).
% 11.19/11.34 tff(485,plain,
% 11.19/11.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 11.19/11.34 inference(quant_inst,[status(thm)],[])).
% 11.19/11.34 tff(486,plain,
% 11.19/11.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | (~node15(c_e_h_2, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s1)),
% 11.19/11.34 inference(modus_ponens,[status(thm)],[485, 484])).
% 11.19/11.34 tff(487,plain,
% 11.19/11.34 ($false),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[486, 393, 482, 435, 483])).
% 11.19/11.34 tff(488,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,[]))).
% 11.19/11.34 tff(489,plain,
% 11.19/11.34 (~node15(c_e_h_2, c_f, s1, s2)),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[488, 482])).
% 11.19/11.34 tff(490,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_f, s1)), introduced(assumption)).
% 11.19/11.34 tff(491,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s1)), introduced(assumption)).
% 11.19/11.34 tff(492,assumption,(node21(c_e_h_2, c_i, s0, s1)), introduced(assumption)).
% 11.19/11.34 tff(493,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s0)), introduced(assumption)).
% 11.19/11.34 tff(494,plain,
% 11.19/11.34 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s0))),
% 11.19/11.34 inference(quant_inst,[status(thm)],[])).
% 11.19/11.34 tff(495,plain,
% 11.19/11.34 ($false),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[494, 189, 493])).
% 11.19/11.34 tff(496,plain,(~m_c_h_element_v_out(c_e_h_2, c_h, s0)), inference(lemma,lemma(discharge,[]))).
% 11.19/11.34 tff(497,plain,
% 11.19/11.34 (^[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)))),
% 11.19/11.34 inference(bind,[status(th)],[])).
% 11.19/11.34 tff(498,plain,
% 11.19/11.34 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))),
% 11.19/11.34 inference(quant_intro,[status(thm)],[497])).
% 11.19/11.34 tff(499,plain,
% 11.19/11.34 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))),
% 11.19/11.34 inference(rewrite,[status(thm)],[])).
% 11.19/11.34 tff(500,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')).
% 11.19/11.34 tff(501,plain,
% 11.19/11.34 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))),
% 11.19/11.34 inference(modus_ponens,[status(thm)],[500, 499])).
% 11.19/11.34 tff(502,plain,(
% 11.19/11.34 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))),
% 11.19/11.34 inference(skolemize,[status(sab)],[501])).
% 11.19/11.34 tff(503,plain,
% 11.19/11.34 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))),
% 11.19/11.34 inference(modus_ponens,[status(thm)],[502, 498])).
% 11.19/11.34 tff(504,plain,
% 11.19/11.34 (((~![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_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))),
% 11.19/11.34 inference(rewrite,[status(thm)],[])).
% 11.19/11.34 tff(505,plain,
% 11.19/11.34 ((~![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_2, c_i, s0)) | m_c_h_element_v_out(c_e_h_2, c_h, s0))),
% 11.19/11.34 inference(quant_inst,[status(thm)],[])).
% 11.19/11.34 tff(506,plain,
% 11.19/11.34 ((~![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_2, c_i, s0)) | m_c_h_element_v_out(c_e_h_2, c_h, s0)),
% 11.19/11.34 inference(modus_ponens,[status(thm)],[505, 504])).
% 11.19/11.34 tff(507,plain,
% 11.19/11.34 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s0)),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[506, 503, 496])).
% 11.19/11.34 tff(508,plain,
% 11.19/11.34 (((~![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))),
% 11.19/11.34 inference(rewrite,[status(thm)],[])).
% 11.19/11.34 tff(509,plain,
% 11.19/11.34 ((~![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))),
% 11.19/11.34 inference(quant_inst,[status(thm)],[])).
% 11.19/11.34 tff(510,plain,
% 11.19/11.34 ((~![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)),
% 11.19/11.34 inference(modus_ponens,[status(thm)],[509, 508])).
% 11.19/11.34 tff(511,plain,
% 11.19/11.34 (~node20(c_e_h_2, c_i, s0)),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[510, 213, 507])).
% 11.19/11.34 tff(512,plain,
% 11.19/11.34 (((~![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_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)))),
% 11.19/11.34 inference(rewrite,[status(thm)],[])).
% 11.19/11.34 tff(513,plain,
% 11.19/11.34 ((~![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_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)))),
% 11.19/11.34 inference(quant_inst,[status(thm)],[])).
% 11.19/11.34 tff(514,plain,
% 11.19/11.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | (~node21(c_e_h_2, c_i, s0, s1))),
% 11.19/11.34 inference(modus_ponens,[status(thm)],[513, 512])).
% 11.19/11.34 tff(515,plain,
% 11.19/11.34 ($false),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[514, 228, 511, 492, 491])).
% 11.19/11.34 tff(516,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,[]))).
% 11.19/11.34 tff(517,plain,
% 11.19/11.34 (~node21(c_e_h_2, c_i, s0, s1)),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[516, 491])).
% 11.19/11.34 tff(518,plain,
% 11.19/11.34 (((~![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))),
% 11.19/11.34 inference(rewrite,[status(thm)],[])).
% 11.19/11.34 tff(519,plain,
% 11.19/11.34 ((~![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))),
% 11.19/11.34 inference(quant_inst,[status(thm)],[])).
% 11.19/11.34 tff(520,plain,
% 11.19/11.34 ((~![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)),
% 11.19/11.34 inference(modus_ponens,[status(thm)],[519, 518])).
% 11.19/11.34 tff(521,plain,
% 11.19/11.34 (node21(c_e_h_2, c_i, s0, s1) | node22(c_e_h_2, c_i, s0, s1)),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[520, 247, 100])).
% 11.19/11.34 tff(522,plain,
% 11.19/11.34 (node22(c_e_h_2, c_i, s0, s1)),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[521, 517])).
% 11.19/11.34 tff(523,plain,
% 11.19/11.34 (((~![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_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))),
% 11.19/11.34 inference(rewrite,[status(thm)],[])).
% 11.19/11.34 tff(524,plain,
% 11.19/11.34 ((~![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_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))),
% 11.19/11.34 inference(quant_inst,[status(thm)],[])).
% 11.19/11.34 tff(525,plain,
% 11.19/11.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | (~node22(c_e_h_2, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_i, s0)),
% 11.19/11.34 inference(modus_ponens,[status(thm)],[524, 523])).
% 11.19/11.34 tff(526,plain,
% 11.19/11.34 ($false),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[525, 273, 338, 522, 491])).
% 11.19/11.34 tff(527,plain,(~m_and_h_gate_v_out(c_e_h_2, c_i, s1)), inference(lemma,lemma(discharge,[]))).
% 11.19/11.34 tff(528,plain,
% 11.19/11.34 (((~![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))),
% 11.19/11.34 inference(rewrite,[status(thm)],[])).
% 11.19/11.34 tff(529,plain,
% 11.19/11.34 ((~![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))),
% 11.19/11.34 inference(quant_inst,[status(thm)],[])).
% 11.19/11.34 tff(530,plain,
% 11.19/11.34 ((~![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)),
% 11.19/11.34 inference(modus_ponens,[status(thm)],[529, 528])).
% 11.19/11.34 tff(531,plain,
% 11.19/11.34 (~m_c_h_element_v_in2(c_e_h_2, c_f, s1)),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[530, 345, 527])).
% 11.19/11.34 tff(532,plain,
% 11.19/11.34 (((~![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_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))),
% 11.19/11.34 inference(rewrite,[status(thm)],[])).
% 11.19/11.34 tff(533,plain,
% 11.19/11.34 ((~![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_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))),
% 11.19/11.34 inference(quant_inst,[status(thm)],[])).
% 11.19/11.34 tff(534,plain,
% 11.19/11.34 ((~![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_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)),
% 11.19/11.34 inference(modus_ponens,[status(thm)],[533, 532])).
% 11.19/11.34 tff(535,plain,
% 11.19/11.34 ((~node16(c_e_h_2, c_f, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1)),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[534, 377, 531])).
% 11.19/11.34 tff(536,plain,
% 11.19/11.34 (~node16(c_e_h_2, c_f, s1)),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[535, 490])).
% 11.19/11.34 tff(537,plain,
% 11.19/11.34 (((~![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))),
% 11.19/11.34 inference(rewrite,[status(thm)],[])).
% 11.19/11.34 tff(538,plain,
% 11.19/11.34 ((~![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))),
% 11.19/11.34 inference(quant_inst,[status(thm)],[])).
% 11.19/11.34 tff(539,plain,
% 11.19/11.34 ((~![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)),
% 11.19/11.34 inference(modus_ponens,[status(thm)],[538, 537])).
% 11.19/11.34 tff(540,plain,
% 11.19/11.34 (node19(c_e_h_2, c_f, s1, s2)),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[539, 312, 470])).
% 11.19/11.34 tff(541,plain,
% 11.19/11.34 (((~![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)))) | (node14(c_e_h_2, c_f, s1, s2) | node16(c_e_h_2, c_f, s1) | (~node19(c_e_h_2, c_f, s1, s2)) | node15(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)))) | node14(c_e_h_2, c_f, s1, s2) | node16(c_e_h_2, c_f, s1) | (~node19(c_e_h_2, c_f, s1, s2)) | node15(c_e_h_2, c_f, s1, s2))),
% 11.19/11.34 inference(rewrite,[status(thm)],[])).
% 11.19/11.34 tff(542,plain,
% 11.19/11.34 ((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))) <=> (node14(c_e_h_2, c_f, s1, s2) | node16(c_e_h_2, c_f, s1) | (~node19(c_e_h_2, c_f, s1, s2)) | node15(c_e_h_2, c_f, s1, s2))),
% 11.19/11.34 inference(rewrite,[status(thm)],[])).
% 11.19/11.34 tff(543,plain,
% 11.19/11.34 (((~![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_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)))) | (node14(c_e_h_2, c_f, s1, s2) | node16(c_e_h_2, c_f, s1) | (~node19(c_e_h_2, c_f, s1, s2)) | node15(c_e_h_2, c_f, s1, s2)))),
% 11.19/11.34 inference(monotonicity,[status(thm)],[542])).
% 11.19/11.34 tff(544,plain,
% 11.19/11.34 (((~![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_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)))) | node14(c_e_h_2, c_f, s1, s2) | node16(c_e_h_2, c_f, s1) | (~node19(c_e_h_2, c_f, s1, s2)) | node15(c_e_h_2, c_f, s1, s2))),
% 11.19/11.34 inference(transitivity,[status(thm)],[543, 541])).
% 11.19/11.34 tff(545,plain,
% 11.19/11.34 ((~![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_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)))),
% 11.19/11.34 inference(quant_inst,[status(thm)],[])).
% 11.19/11.34 tff(546,plain,
% 11.19/11.34 ((~![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)))) | node14(c_e_h_2, c_f, s1, s2) | node16(c_e_h_2, c_f, s1) | (~node19(c_e_h_2, c_f, s1, s2)) | node15(c_e_h_2, c_f, s1, s2)),
% 11.19/11.34 inference(modus_ponens,[status(thm)],[545, 544])).
% 11.19/11.34 tff(547,plain,
% 11.19/11.34 (node14(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)),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[546, 409, 540])).
% 11.19/11.34 tff(548,plain,
% 11.19/11.34 (node14(c_e_h_2, c_f, s1, s2)),
% 11.19/11.34 inference(unit_resolution,[status(thm)],[547, 536, 489])).
% 11.19/11.34 tff(549,plain,
% 11.19/11.34 (((~![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_2, c_f, s1) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | (~node14(c_e_h_2, 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_in1(c_e_h_2, c_f, s1) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | (~node14(c_e_h_2, c_f, s1, s2)))),
% 11.19/11.34 inference(rewrite,[status(thm)],[])).
% 11.19/11.34 tff(550,plain,
% 11.19/11.34 (((~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) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | (~node14(c_e_h_2, c_f, s1, s2)))),
% 11.19/11.34 inference(rewrite,[status(thm)],[])).
% 11.19/11.34 tff(551,plain,
% 11.19/11.34 (((~![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_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) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | (~node14(c_e_h_2, c_f, s1, s2))))),
% 11.19/11.34 inference(monotonicity,[status(thm)],[550])).
% 11.19/11.34 tff(552,plain,
% 11.19/11.34 (((~![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_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) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | (~node14(c_e_h_2, c_f, s1, s2)))),
% 11.19/11.34 inference(transitivity,[status(thm)],[551, 549])).
% 11.19/11.34 tff(553,plain,
% 11.19/11.34 ((~![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_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)))),
% 11.19/11.34 inference(quant_inst,[status(thm)],[])).
% 11.19/11.35 tff(554,plain,
% 11.19/11.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | (~node14(c_e_h_2, c_f, s1, s2))),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[553, 552])).
% 11.19/11.35 tff(555,plain,
% 11.19/11.35 ($false),
% 11.19/11.35 inference(unit_resolution,[status(thm)],[554, 427, 482, 490, 548])).
% 11.19/11.35 tff(556,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,[]))).
% 11.19/11.35 tff(557,plain,
% 11.19/11.35 (m_c_h_element_v_in1(c_e_h_2, c_f, s1)),
% 11.19/11.35 inference(unit_resolution,[status(thm)],[556, 482])).
% 11.19/11.35 tff(558,plain,
% 11.19/11.35 (((~![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)))) | ((~node17(c_e_h_2, c_f, s1)) | m_c_h_element_v_in2(c_e_h_2, c_f, s1) | (~m_c_h_element_v_in1(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_in2(c_e_h_2, c_f, s1) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)))),
% 11.19/11.35 inference(rewrite,[status(thm)],[])).
% 11.19/11.35 tff(559,plain,
% 11.19/11.35 (((~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_in2(c_e_h_2, c_f, s1) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)))),
% 11.19/11.35 inference(rewrite,[status(thm)],[])).
% 11.19/11.35 tff(560,plain,
% 11.19/11.35 (((~![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_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_in2(c_e_h_2, c_f, s1) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1))))),
% 11.19/11.35 inference(monotonicity,[status(thm)],[559])).
% 11.19/11.35 tff(561,plain,
% 11.19/11.35 (((~![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_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_in2(c_e_h_2, c_f, s1) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)))),
% 11.19/11.35 inference(transitivity,[status(thm)],[560, 558])).
% 11.19/11.35 tff(562,plain,
% 11.19/11.35 ((~![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_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)))),
% 11.19/11.35 inference(quant_inst,[status(thm)],[])).
% 11.19/11.35 tff(563,plain,
% 11.19/11.35 ((~![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)))) | (~node17(c_e_h_2, c_f, s1)) | m_c_h_element_v_in2(c_e_h_2, c_f, s1) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1))),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[562, 561])).
% 11.19/11.35 tff(564,plain,
% 11.19/11.35 ((~node17(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1))),
% 11.19/11.35 inference(unit_resolution,[status(thm)],[563, 359, 531])).
% 11.19/11.35 tff(565,plain,
% 11.19/11.35 (~node17(c_e_h_2, c_f, s1)),
% 11.19/11.35 inference(unit_resolution,[status(thm)],[564, 557])).
% 11.19/11.35 tff(566,plain,
% 11.19/11.35 (((~![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, s1, s2) | node17(c_e_h_2, c_f, s1) | (~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)))) | node18(c_e_h_2, c_f, s1, s2) | node17(c_e_h_2, c_f, s1) | (~node19(c_e_h_2, c_f, s1, s2)))),
% 11.19/11.35 inference(rewrite,[status(thm)],[])).
% 11.19/11.35 tff(567,plain,
% 11.19/11.35 ((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))) <=> (node18(c_e_h_2, c_f, s1, s2) | node17(c_e_h_2, c_f, s1) | (~node19(c_e_h_2, c_f, s1, s2)))),
% 11.19/11.35 inference(rewrite,[status(thm)],[])).
% 11.19/11.35 tff(568,plain,
% 11.19/11.35 (((~![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_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)))) | (node18(c_e_h_2, c_f, s1, s2) | node17(c_e_h_2, c_f, s1) | (~node19(c_e_h_2, c_f, s1, s2))))),
% 11.19/11.35 inference(monotonicity,[status(thm)],[567])).
% 11.19/11.35 tff(569,plain,
% 11.19/11.35 (((~![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_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)))) | node18(c_e_h_2, c_f, s1, s2) | node17(c_e_h_2, c_f, s1) | (~node19(c_e_h_2, c_f, s1, s2)))),
% 11.19/11.35 inference(transitivity,[status(thm)],[568, 566])).
% 11.19/11.35 tff(570,plain,
% 11.19/11.35 ((~![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_2, c_f, s1) | node18(c_e_h_2, c_f, s1, s2) | (~node19(c_e_h_2, c_f, s1, s2)))),
% 11.19/11.35 inference(quant_inst,[status(thm)],[])).
% 11.19/11.35 tff(571,plain,
% 11.19/11.35 ((~![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, s1, s2) | node17(c_e_h_2, c_f, s1) | (~node19(c_e_h_2, c_f, s1, s2))),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[570, 569])).
% 11.19/11.35 tff(572,plain,
% 11.19/11.35 (node18(c_e_h_2, c_f, s1, s2) | node17(c_e_h_2, c_f, s1)),
% 11.19/11.35 inference(unit_resolution,[status(thm)],[571, 326, 540])).
% 11.19/11.35 tff(573,plain,
% 11.19/11.35 (node18(c_e_h_2, c_f, s1, s2)),
% 11.19/11.35 inference(unit_resolution,[status(thm)],[572, 565])).
% 11.19/11.35 tff(574,plain,
% 11.19/11.35 (((~![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_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, 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) | (~node18(c_e_h_2, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)))),
% 11.19/11.35 inference(rewrite,[status(thm)],[])).
% 11.19/11.35 tff(575,plain,
% 11.19/11.35 (((~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) | (~node18(c_e_h_2, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)))),
% 11.19/11.35 inference(rewrite,[status(thm)],[])).
% 11.19/11.35 tff(576,plain,
% 11.19/11.35 (((~![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_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) | (~node18(c_e_h_2, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2))))),
% 11.19/11.35 inference(monotonicity,[status(thm)],[575])).
% 11.19/11.35 tff(577,plain,
% 11.19/11.35 (((~![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_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) | (~node18(c_e_h_2, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)))),
% 11.19/11.35 inference(transitivity,[status(thm)],[576, 574])).
% 11.19/11.35 tff(578,plain,
% 11.19/11.35 ((~![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_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)))),
% 11.19/11.35 inference(quant_inst,[status(thm)],[])).
% 11.19/11.35 tff(579,plain,
% 11.19/11.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s1) | (~node18(c_e_h_2, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2))),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[578, 577])).
% 11.19/11.35 tff(580,plain,
% 11.19/11.35 ($false),
% 11.19/11.35 inference(unit_resolution,[status(thm)],[579, 296, 482, 435, 573])).
% 11.19/11.35 tff(581,plain,(~m_c_h_element_v_out(c_e_h_2, c_f, s2)), inference(lemma,lemma(discharge,[]))).
% 11.19/11.35 tff(582,plain,
% 11.19/11.35 (((~![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_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))),
% 11.19/11.35 inference(rewrite,[status(thm)],[])).
% 11.19/11.35 tff(583,plain,
% 11.19/11.35 ((~![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_2, c_q, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s2))),
% 11.19/11.35 inference(quant_inst,[status(thm)],[])).
% 11.19/11.35 tff(584,plain,
% 11.19/11.35 ((~![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_2, c_q, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s2)),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[583, 582])).
% 11.19/11.35 tff(585,plain,
% 11.19/11.35 (~m_and_h_gate_v_in1(c_e_h_2, c_q, s2)),
% 11.19/11.35 inference(unit_resolution,[status(thm)],[584, 199, 581])).
% 11.19/11.35 tff(586,plain,
% 11.19/11.35 (((~![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))),
% 11.19/11.35 inference(rewrite,[status(thm)],[])).
% 11.19/11.35 tff(587,plain,
% 11.19/11.35 ((~![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))),
% 11.19/11.35 inference(quant_inst,[status(thm)],[])).
% 11.19/11.35 tff(588,plain,
% 11.19/11.35 ((~![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)),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[587, 586])).
% 11.19/11.35 tff(589,plain,
% 11.19/11.35 (~node20(c_e_h_2, c_q, s2)),
% 11.19/11.35 inference(unit_resolution,[status(thm)],[588, 213, 585])).
% 11.19/11.35 tff(590,plain,
% 11.19/11.35 (((~![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)))) | ((~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)))),
% 11.19/11.35 inference(rewrite,[status(thm)],[])).
% 11.19/11.35 tff(591,plain,
% 11.19/11.35 ((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)))),
% 11.19/11.35 inference(rewrite,[status(thm)],[])).
% 11.19/11.35 tff(592,plain,
% 11.19/11.35 (((~![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_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))))),
% 11.19/11.35 inference(monotonicity,[status(thm)],[591])).
% 11.19/11.35 tff(593,plain,
% 11.19/11.35 (((~![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_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)))),
% 11.19/11.35 inference(transitivity,[status(thm)],[592, 590])).
% 11.19/11.35 tff(594,plain,
% 11.19/11.35 ((~![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_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)))),
% 11.19/11.35 inference(quant_inst,[status(thm)],[])).
% 11.19/11.35 tff(595,plain,
% 11.19/11.35 ((~![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)))) | (~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))),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[594, 593])).
% 11.19/11.35 tff(596,plain,
% 11.19/11.35 ((~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | (~node21(c_e_h_2, c_q, s2, s3))),
% 11.19/11.35 inference(unit_resolution,[status(thm)],[595, 228, 589])).
% 11.19/11.35 tff(597,plain,
% 11.19/11.35 (~node21(c_e_h_2, c_q, s2, s3)),
% 11.19/11.35 inference(unit_resolution,[status(thm)],[596, 178])).
% 11.19/11.35 tff(598,plain,
% 11.19/11.35 (succ(s2, s3) <=> succ(s2, s3)),
% 11.19/11.35 inference(rewrite,[status(thm)],[])).
% 11.19/11.35 tff(599,axiom,(succ(s2, s3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound3')).
% 11.19/11.35 tff(600,plain,
% 11.19/11.35 (succ(s2, s3)),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[599, 598])).
% 11.19/11.35 tff(601,plain,
% 11.19/11.35 (((~![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))),
% 11.19/11.35 inference(rewrite,[status(thm)],[])).
% 11.19/11.35 tff(602,plain,
% 11.19/11.35 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s2, s3)) | trans(s2, s3))),
% 11.19/11.35 inference(quant_inst,[status(thm)],[])).
% 11.19/11.35 tff(603,plain,
% 11.19/11.35 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s2, s3)) | trans(s2, s3)),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[602, 601])).
% 11.19/11.35 tff(604,plain,
% 11.19/11.35 (trans(s2, s3)),
% 11.19/11.35 inference(unit_resolution,[status(thm)],[603, 600, 93])).
% 11.19/11.35 tff(605,plain,
% 11.19/11.35 (((~![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))),
% 11.19/11.35 inference(rewrite,[status(thm)],[])).
% 11.19/11.35 tff(606,plain,
% 11.19/11.35 ((~![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))),
% 11.19/11.35 inference(quant_inst,[status(thm)],[])).
% 11.19/11.35 tff(607,plain,
% 11.19/11.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_2, c_q, s2, s3) | node22(c_e_h_2, c_q, s2, s3)),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[606, 605])).
% 11.19/11.35 tff(608,plain,
% 11.19/11.35 ($false),
% 11.19/11.35 inference(unit_resolution,[status(thm)],[607, 247, 604, 597, 481])).
% 11.19/11.35 tff(609,plain,(~m_and_h_gate_v_out(c_e_h_2, c_q, s3)), inference(lemma,lemma(discharge,[]))).
% 11.19/11.35 tff(610,plain,
% 11.19/11.35 (^[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)))),
% 11.19/11.35 inference(bind,[status(th)],[])).
% 11.19/11.35 tff(611,plain,
% 11.19/11.35 (![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))),
% 11.19/11.35 inference(quant_intro,[status(thm)],[610])).
% 11.19/11.35 tff(612,plain,
% 11.19/11.35 (![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))),
% 11.19/11.35 inference(rewrite,[status(thm)],[])).
% 11.19/11.35 tff(613,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')).
% 11.19/11.35 tff(614,plain,
% 11.19/11.35 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[613, 612])).
% 11.19/11.35 tff(615,plain,(
% 11.19/11.35 ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))),
% 11.19/11.35 inference(skolemize,[status(sab)],[614])).
% 11.19/11.35 tff(616,plain,
% 11.19/11.35 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[615, 611])).
% 11.19/11.35 tff(617,plain,
% 11.19/11.35 (m_cell_v_left(c_e_h_2, c_e_h_3) <=> m_cell_v_left(c_e_h_2, c_e_h_3)),
% 11.19/11.35 inference(rewrite,[status(thm)],[])).
% 11.19/11.35 tff(618,axiom,(m_cell_v_left(c_e_h_2, c_e_h_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_4')).
% 11.19/11.35 tff(619,plain,
% 11.19/11.35 (m_cell_v_left(c_e_h_2, c_e_h_3)),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[618, 617])).
% 11.19/11.35 tff(620,plain,
% 11.19/11.35 (((~![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))),
% 11.19/11.35 inference(rewrite,[status(thm)],[])).
% 11.19/11.35 tff(621,plain,
% 11.19/11.35 ((~![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))),
% 11.19/11.35 inference(quant_inst,[status(thm)],[])).
% 11.19/11.35 tff(622,plain,
% 11.19/11.35 ((~![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)),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[621, 620])).
% 11.19/11.35 tff(623,plain,
% 11.19/11.35 (node3(c_e_h_2, c_e_h_3, s3)),
% 11.19/11.35 inference(unit_resolution,[status(thm)],[622, 619, 616])).
% 11.19/11.35 tff(624,plain,
% 11.19/11.35 (^[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)))),
% 11.19/11.35 inference(bind,[status(th)],[])).
% 11.19/11.35 tff(625,plain,
% 11.19/11.35 (![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))),
% 11.19/11.35 inference(quant_intro,[status(thm)],[624])).
% 11.19/11.35 tff(626,plain,
% 11.19/11.35 (![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))),
% 11.19/11.35 inference(rewrite,[status(thm)],[])).
% 11.19/11.35 tff(627,plain,
% 11.19/11.35 (^[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)))),
% 11.19/11.35 inference(bind,[status(th)],[])).
% 11.19/11.35 tff(628,plain,
% 11.19/11.35 (![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))),
% 11.19/11.35 inference(quant_intro,[status(thm)],[627])).
% 11.19/11.35 tff(629,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')).
% 11.19/11.35 tff(630,plain,
% 11.19/11.35 (![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))),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[629, 628])).
% 11.19/11.35 tff(631,plain,
% 11.19/11.35 (![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))),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[630, 626])).
% 11.19/11.35 tff(632,plain,(
% 11.19/11.35 ![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))),
% 11.19/11.35 inference(skolemize,[status(sab)],[631])).
% 11.19/11.35 tff(633,plain,
% 11.19/11.35 (![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))),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[632, 625])).
% 11.19/11.35 tff(634,plain,
% 11.19/11.35 (((~![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))),
% 11.19/11.35 inference(rewrite,[status(thm)],[])).
% 11.19/11.35 tff(635,plain,
% 11.19/11.35 ((~![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))),
% 11.19/11.35 inference(quant_inst,[status(thm)],[])).
% 11.19/11.35 tff(636,plain,
% 11.19/11.35 ((~![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)),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[635, 634])).
% 11.19/11.35 tff(637,plain,
% 11.19/11.35 ((~m_cell_v_ack(c_e_h_3, s3)) | m_and_h_gate_v_out(c_e_h_2, c_q, s3)),
% 11.19/11.35 inference(unit_resolution,[status(thm)],[636, 633, 623])).
% 11.19/11.35 tff(638,plain,
% 11.19/11.35 (~m_cell_v_ack(c_e_h_3, s3)),
% 11.19/11.35 inference(unit_resolution,[status(thm)],[637, 609])).
% 11.19/11.35 tff(639,plain,
% 11.19/11.35 (^[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)))),
% 11.19/11.35 inference(bind,[status(th)],[])).
% 11.19/11.35 tff(640,plain,
% 11.19/11.35 (![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))),
% 11.19/11.35 inference(quant_intro,[status(thm)],[639])).
% 11.19/11.35 tff(641,plain,
% 11.19/11.35 (![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))),
% 11.19/11.35 inference(rewrite,[status(thm)],[])).
% 11.19/11.35 tff(642,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')).
% 11.19/11.35 tff(643,plain,
% 11.19/11.35 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[642, 641])).
% 11.19/11.35 tff(644,plain,(
% 11.19/11.35 ![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))),
% 11.19/11.35 inference(skolemize,[status(sab)],[643])).
% 11.19/11.35 tff(645,plain,
% 11.19/11.35 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[644, 640])).
% 11.19/11.35 tff(646,plain,
% 11.19/11.35 (((~![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))),
% 11.19/11.35 inference(rewrite,[status(thm)],[])).
% 11.19/11.35 tff(647,plain,
% 11.19/11.35 ((~![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))),
% 11.19/11.35 inference(quant_inst,[status(thm)],[])).
% 11.19/11.35 tff(648,plain,
% 11.19/11.35 ((~![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)),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[647, 646])).
% 11.19/11.35 tff(649,plain,
% 11.19/11.35 (~m_or_h_gate_v_in2(c_e_h_3, c_j, s3)),
% 11.19/11.35 inference(unit_resolution,[status(thm)],[648, 645, 638])).
% 11.19/11.35 tff(650,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s3)), introduced(assumption)).
% 11.19/11.35 tff(651,assumption,(node21(c_e_h_3, c_l, s2, s3)), introduced(assumption)).
% 11.19/11.35 tff(652,assumption,(m_and_h_gate_v_out(c_e_h_3, c_k, s2)), introduced(assumption)).
% 11.19/11.35 tff(653,assumption,(m_or_h_gate_v_out(c_e_h_3, c_g, s0)), introduced(assumption)).
% 11.19/11.35 tff(654,plain,
% 11.19/11.35 (^[I0: $i, I1: $i] : refl((~m_or_h_gate_v_out(I0, I1, s0)) <=> (~m_or_h_gate_v_out(I0, I1, s0)))),
% 11.19/11.35 inference(bind,[status(th)],[])).
% 11.19/11.35 tff(655,plain,
% 11.19/11.35 (![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))),
% 11.19/11.35 inference(quant_intro,[status(thm)],[654])).
% 11.19/11.35 tff(656,plain,
% 11.19/11.35 (![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))),
% 11.19/11.35 inference(rewrite,[status(thm)],[])).
% 11.19/11.35 tff(657,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')).
% 11.19/11.35 tff(658,plain,
% 11.19/11.35 (![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[657, 656])).
% 11.19/11.35 tff(659,plain,(
% 11.19/11.35 ![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))),
% 11.19/11.35 inference(skolemize,[status(sab)],[658])).
% 11.19/11.35 tff(660,plain,
% 11.19/11.35 (![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[659, 655])).
% 11.19/11.35 tff(661,plain,
% 11.19/11.35 ((~![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s0))),
% 11.19/11.35 inference(quant_inst,[status(thm)],[])).
% 11.19/11.35 tff(662,plain,
% 11.19/11.35 ($false),
% 11.19/11.35 inference(unit_resolution,[status(thm)],[661, 660, 653])).
% 11.19/11.35 tff(663,plain,(~m_or_h_gate_v_out(c_e_h_3, c_g, s0)), inference(lemma,lemma(discharge,[]))).
% 11.19/11.35 tff(664,assumption,(m_or_h_gate_v_out(c_e_h_3, c_g, s1)), introduced(assumption)).
% 11.19/11.35 tff(665,assumption,(m_and_h_gate_v_out(c_e_h_3, c_d, s0)), introduced(assumption)).
% 11.19/11.35 tff(666,plain,
% 11.19/11.35 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s0))),
% 11.19/11.35 inference(quant_inst,[status(thm)],[])).
% 11.19/11.35 tff(667,plain,
% 11.19/11.35 ($false),
% 11.19/11.35 inference(unit_resolution,[status(thm)],[666, 260, 665])).
% 11.19/11.35 tff(668,plain,(~m_and_h_gate_v_out(c_e_h_3, c_d, s0)), inference(lemma,lemma(discharge,[]))).
% 11.19/11.35 tff(669,plain,
% 11.19/11.35 (^[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)))),
% 11.19/11.35 inference(bind,[status(th)],[])).
% 11.19/11.35 tff(670,plain,
% 11.19/11.35 (![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))),
% 11.19/11.35 inference(quant_intro,[status(thm)],[669])).
% 11.19/11.35 tff(671,plain,
% 11.19/11.35 (![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))),
% 11.19/11.35 inference(rewrite,[status(thm)],[])).
% 11.19/11.35 tff(672,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')).
% 11.19/11.35 tff(673,plain,
% 11.19/11.35 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[672, 671])).
% 11.19/11.35 tff(674,plain,(
% 11.19/11.35 ![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 11.19/11.35 inference(skolemize,[status(sab)],[673])).
% 11.19/11.35 tff(675,plain,
% 11.19/11.35 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[674, 670])).
% 11.19/11.35 tff(676,plain,
% 11.19/11.35 (((~![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))),
% 11.19/11.35 inference(rewrite,[status(thm)],[])).
% 11.19/11.35 tff(677,plain,
% 11.19/11.35 ((~![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))),
% 11.19/11.35 inference(quant_inst,[status(thm)],[])).
% 11.19/11.35 tff(678,plain,
% 11.19/11.35 ((~![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)),
% 11.19/11.35 inference(modus_ponens,[status(thm)],[677, 676])).
% 11.19/11.35 tff(679,plain,
% 11.19/11.35 (~m_or_h_gate_v_in2(c_e_h_3, c_g, s0)),
% 11.19/11.35 inference(unit_resolution,[status(thm)],[678, 675, 668])).
% 11.19/11.35 tff(680,assumption,(node5(c_e_h_3, c_g, s0, s1)), introduced(assumption)).
% 11.19/11.36 tff(681,assumption,(m_and_h_gate_v_out(c_e_h_3, c_c, s0)), introduced(assumption)).
% 11.19/11.36 tff(682,plain,
% 11.19/11.36 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s0))),
% 11.19/11.36 inference(quant_inst,[status(thm)],[])).
% 11.19/11.36 tff(683,plain,
% 11.19/11.36 ($false),
% 11.19/11.36 inference(unit_resolution,[status(thm)],[682, 260, 681])).
% 11.19/11.36 tff(684,plain,(~m_and_h_gate_v_out(c_e_h_3, c_c, s0)), inference(lemma,lemma(discharge,[]))).
% 11.19/11.36 tff(685,plain,
% 11.19/11.36 (^[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)))),
% 11.19/11.36 inference(bind,[status(th)],[])).
% 11.19/11.36 tff(686,plain,
% 11.19/11.36 (![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))),
% 11.19/11.36 inference(quant_intro,[status(thm)],[685])).
% 11.19/11.36 tff(687,plain,
% 11.19/11.36 (![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))),
% 11.19/11.36 inference(rewrite,[status(thm)],[])).
% 11.19/11.36 tff(688,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')).
% 11.19/11.36 tff(689,plain,
% 11.19/11.36 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 11.19/11.36 inference(modus_ponens,[status(thm)],[688, 687])).
% 11.19/11.36 tff(690,plain,(
% 11.19/11.36 ![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 11.19/11.36 inference(skolemize,[status(sab)],[689])).
% 11.19/11.36 tff(691,plain,
% 11.19/11.36 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 11.19/11.36 inference(modus_ponens,[status(thm)],[690, 686])).
% 11.19/11.36 tff(692,plain,
% 11.19/11.36 (((~![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))),
% 11.19/11.36 inference(rewrite,[status(thm)],[])).
% 11.19/11.36 tff(693,plain,
% 11.19/11.36 ((~![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))),
% 11.19/11.36 inference(quant_inst,[status(thm)],[])).
% 11.19/11.36 tff(694,plain,
% 11.19/11.36 ((~![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)),
% 11.19/11.36 inference(modus_ponens,[status(thm)],[693, 692])).
% 11.19/11.36 tff(695,plain,
% 11.19/11.36 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s0)),
% 11.19/11.36 inference(unit_resolution,[status(thm)],[694, 691, 684])).
% 11.19/11.36 tff(696,plain,
% 11.19/11.36 (^[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))))),
% 11.19/11.36 inference(bind,[status(th)],[])).
% 11.19/11.36 tff(697,plain,
% 11.19/11.36 (![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))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))),
% 11.19/11.36 inference(quant_intro,[status(thm)],[696])).
% 11.19/11.36 tff(698,plain,
% 11.19/11.36 (![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))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))),
% 11.19/11.36 inference(rewrite,[status(thm)],[])).
% 11.19/11.36 tff(699,plain,
% 11.19/11.36 (^[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)))))),
% 11.19/11.36 inference(bind,[status(th)],[])).
% 11.19/11.36 tff(700,plain,
% 11.19/11.36 (![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)))),
% 11.19/11.36 inference(quant_intro,[status(thm)],[699])).
% 11.19/11.36 tff(701,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')).
% 11.19/11.36 tff(702,plain,
% 11.19/11.36 (![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)))),
% 11.19/11.36 inference(modus_ponens,[status(thm)],[701, 700])).
% 11.19/11.36 tff(703,plain,
% 11.19/11.36 (![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)))),
% 11.19/11.36 inference(modus_ponens,[status(thm)],[702, 698])).
% 11.19/11.36 tff(704,plain,(
% 11.19/11.36 ![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)))),
% 11.19/11.36 inference(skolemize,[status(sab)],[703])).
% 11.19/11.36 tff(705,plain,
% 11.19/11.36 (![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)))),
% 11.19/11.36 inference(modus_ponens,[status(thm)],[704, 697])).
% 11.19/11.36 tff(706,plain,
% 11.19/11.36 (((~![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_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) | (~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_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) | (~node5(c_e_h_3, c_g, s0, s1)))),
% 11.19/11.36 inference(rewrite,[status(thm)],[])).
% 11.19/11.36 tff(707,plain,
% 11.19/11.36 ((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_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) | (~node5(c_e_h_3, c_g, s0, s1)))),
% 11.19/11.36 inference(rewrite,[status(thm)],[])).
% 11.19/11.36 tff(708,plain,
% 11.19/11.36 (((~![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_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_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) | (~node5(c_e_h_3, c_g, s0, s1))))),
% 11.19/11.36 inference(monotonicity,[status(thm)],[707])).
% 11.19/11.36 tff(709,plain,
% 11.19/11.36 (((~![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_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_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) | (~node5(c_e_h_3, c_g, s0, s1)))),
% 11.19/11.36 inference(transitivity,[status(thm)],[708, 706])).
% 11.19/11.36 tff(710,plain,
% 11.19/11.36 ((~![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_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)))),
% 11.19/11.36 inference(quant_inst,[status(thm)],[])).
% 11.19/11.36 tff(711,plain,
% 11.19/11.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s0) | m_or_h_gate_v_in2(c_e_h_3, c_g, s0) | (~node5(c_e_h_3, c_g, s0, s1))),
% 11.19/11.36 inference(modus_ponens,[status(thm)],[710, 709])).
% 11.19/11.36 tff(712,plain,
% 11.19/11.36 ($false),
% 11.19/11.36 inference(unit_resolution,[status(thm)],[711, 705, 664, 695, 680, 679])).
% 11.19/11.36 tff(713,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,[]))).
% 11.19/11.36 tff(714,plain,
% 11.19/11.36 (~node5(c_e_h_3, c_g, s0, s1)),
% 11.19/11.36 inference(unit_resolution,[status(thm)],[713, 664])).
% 11.19/11.36 tff(715,plain,
% 11.19/11.36 (^[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))))),
% 11.19/11.36 inference(bind,[status(th)],[])).
% 11.19/11.36 tff(716,plain,
% 11.19/11.36 (![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)))),
% 11.19/11.36 inference(quant_intro,[status(thm)],[715])).
% 11.19/11.36 tff(717,plain,
% 11.19/11.36 (![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)))),
% 11.19/11.36 inference(rewrite,[status(thm)],[])).
% 11.19/11.36 tff(718,plain,
% 11.19/11.36 (^[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))))),
% 11.19/11.36 inference(bind,[status(th)],[])).
% 11.19/11.36 tff(719,plain,
% 11.19/11.36 (![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)))),
% 11.19/11.36 inference(quant_intro,[status(thm)],[718])).
% 11.19/11.36 tff(720,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')).
% 11.19/11.36 tff(721,plain,
% 11.19/11.36 (![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))),
% 11.19/11.36 inference(modus_ponens,[status(thm)],[720, 719])).
% 11.19/11.36 tff(722,plain,
% 11.19/11.36 (![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))),
% 11.19/11.36 inference(modus_ponens,[status(thm)],[721, 717])).
% 11.19/11.36 tff(723,plain,(
% 11.19/11.36 ![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))),
% 11.19/11.36 inference(skolemize,[status(sab)],[722])).
% 11.19/11.36 tff(724,plain,
% 11.19/11.36 (![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))),
% 11.19/11.36 inference(modus_ponens,[status(thm)],[723, 716])).
% 11.19/11.36 tff(725,plain,
% 11.19/11.36 (((~![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_3, c_g, s0, s1) | node5(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)) | node6(c_e_h_3, c_g, s0, s1) | node5(c_e_h_3, c_g, s0, s1))),
% 11.19/11.36 inference(rewrite,[status(thm)],[])).
% 11.19/11.36 tff(726,plain,
% 11.19/11.36 ((node6(c_e_h_3, c_g, s0, s1) | node5(c_e_h_3, c_g, s0, s1) | (~trans(s0, s1))) <=> ((~trans(s0, s1)) | node6(c_e_h_3, c_g, s0, s1) | node5(c_e_h_3, c_g, s0, s1))),
% 11.19/11.36 inference(rewrite,[status(thm)],[])).
% 11.19/11.36 tff(727,plain,
% 11.19/11.36 (((~![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_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)) | node6(c_e_h_3, c_g, s0, s1) | node5(c_e_h_3, c_g, s0, s1)))),
% 11.19/11.36 inference(monotonicity,[status(thm)],[726])).
% 11.19/11.36 tff(728,plain,
% 11.19/11.36 (((~![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_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)) | node6(c_e_h_3, c_g, s0, s1) | node5(c_e_h_3, c_g, s0, s1))),
% 11.19/11.36 inference(transitivity,[status(thm)],[727, 725])).
% 11.19/11.36 tff(729,plain,
% 11.19/11.36 ((~![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_3, c_g, s0, s1) | node5(c_e_h_3, c_g, s0, s1) | (~trans(s0, s1)))),
% 11.19/11.36 inference(quant_inst,[status(thm)],[])).
% 11.19/11.36 tff(730,plain,
% 11.19/11.36 ((~![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_3, c_g, s0, s1) | node5(c_e_h_3, c_g, s0, s1)),
% 11.19/11.36 inference(modus_ponens,[status(thm)],[729, 728])).
% 11.19/11.36 tff(731,plain,
% 11.19/11.36 (node6(c_e_h_3, c_g, s0, s1) | node5(c_e_h_3, c_g, s0, s1)),
% 11.19/11.36 inference(unit_resolution,[status(thm)],[730, 724, 100])).
% 11.19/11.36 tff(732,plain,
% 11.19/11.36 (node6(c_e_h_3, c_g, s0, s1)),
% 11.19/11.36 inference(unit_resolution,[status(thm)],[731, 714])).
% 11.19/11.36 tff(733,plain,
% 11.19/11.36 (^[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)))),
% 11.19/11.36 inference(bind,[status(th)],[])).
% 11.19/11.36 tff(734,plain,
% 11.19/11.36 (![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)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))),
% 11.19/11.36 inference(quant_intro,[status(thm)],[733])).
% 11.19/11.36 tff(735,plain,
% 11.19/11.36 (![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)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))),
% 11.19/11.36 inference(rewrite,[status(thm)],[])).
% 11.19/11.36 tff(736,plain,
% 11.19/11.36 (^[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)))),
% 11.19/11.36 inference(bind,[status(th)],[])).
% 11.19/11.36 tff(737,plain,
% 11.19/11.36 (![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))),
% 11.19/11.36 inference(quant_intro,[status(thm)],[736])).
% 11.19/11.36 tff(738,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')).
% 11.19/11.36 tff(739,plain,
% 11.19/11.36 (![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))),
% 11.19/11.36 inference(modus_ponens,[status(thm)],[738, 737])).
% 11.19/11.36 tff(740,plain,
% 11.19/11.36 (![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))),
% 11.19/11.36 inference(modus_ponens,[status(thm)],[739, 735])).
% 11.19/11.36 tff(741,plain,(
% 11.19/11.36 ![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))),
% 11.19/11.36 inference(skolemize,[status(sab)],[740])).
% 11.19/11.36 tff(742,plain,
% 11.19/11.36 (![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))),
% 11.19/11.36 inference(modus_ponens,[status(thm)],[741, 734])).
% 11.19/11.36 tff(743,plain,
% 11.19/11.36 (((~![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_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)))),
% 11.19/11.36 inference(rewrite,[status(thm)],[])).
% 11.19/11.36 tff(744,plain,
% 11.19/11.36 (((~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)))),
% 11.19/11.36 inference(rewrite,[status(thm)],[])).
% 11.19/11.36 tff(745,plain,
% 11.19/11.36 (((~![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_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))))),
% 11.19/11.36 inference(monotonicity,[status(thm)],[744])).
% 11.19/11.36 tff(746,plain,
% 11.19/11.36 (((~![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_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)))),
% 11.19/11.36 inference(transitivity,[status(thm)],[745, 743])).
% 11.19/11.36 tff(747,plain,
% 11.19/11.36 ((~![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_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))),
% 11.19/11.36 inference(quant_inst,[status(thm)],[])).
% 11.19/11.36 tff(748,plain,
% 11.19/11.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0) | (~node6(c_e_h_3, c_g, s0, s1))),
% 11.19/11.36 inference(modus_ponens,[status(thm)],[747, 746])).
% 11.19/11.36 tff(749,plain,
% 11.19/11.36 ($false),
% 11.19/11.36 inference(unit_resolution,[status(thm)],[748, 742, 664, 732, 663])).
% 11.19/11.36 tff(750,plain,(~m_or_h_gate_v_out(c_e_h_3, c_g, s1)), inference(lemma,lemma(discharge,[]))).
% 11.19/11.36 tff(751,plain,
% 11.19/11.36 (^[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)))),
% 11.19/11.36 inference(bind,[status(th)],[])).
% 11.19/11.36 tff(752,plain,
% 11.19/11.36 (![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))),
% 11.19/11.36 inference(quant_intro,[status(thm)],[751])).
% 11.19/11.36 tff(753,plain,
% 11.19/11.36 (![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))),
% 11.19/11.36 inference(rewrite,[status(thm)],[])).
% 11.19/11.36 tff(754,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')).
% 11.19/11.36 tff(755,plain,
% 11.19/11.36 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 11.19/11.36 inference(modus_ponens,[status(thm)],[754, 753])).
% 11.19/11.36 tff(756,plain,(
% 11.19/11.36 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 11.19/11.36 inference(skolemize,[status(sab)],[755])).
% 11.19/11.36 tff(757,plain,
% 11.19/11.36 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 11.19/11.36 inference(modus_ponens,[status(thm)],[756, 752])).
% 11.19/11.36 tff(758,plain,
% 11.19/11.36 (((~![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))),
% 11.19/11.36 inference(rewrite,[status(thm)],[])).
% 11.19/11.36 tff(759,plain,
% 11.19/11.36 ((~![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))),
% 11.19/11.36 inference(quant_inst,[status(thm)],[])).
% 11.19/11.36 tff(760,plain,
% 11.19/11.36 ((~![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)),
% 11.19/11.36 inference(modus_ponens,[status(thm)],[759, 758])).
% 11.19/11.36 tff(761,plain,
% 11.19/11.36 ((~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)),
% 11.19/11.36 inference(unit_resolution,[status(thm)],[760, 757])).
% 11.19/11.36 tff(762,plain,
% 11.19/11.36 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s1)),
% 11.19/11.36 inference(unit_resolution,[status(thm)],[761, 750])).
% 11.19/11.36 tff(763,plain,
% 11.19/11.36 (((~![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))),
% 11.19/11.36 inference(rewrite,[status(thm)],[])).
% 11.19/11.36 tff(764,plain,
% 11.19/11.36 ((~![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))),
% 11.19/11.36 inference(quant_inst,[status(thm)],[])).
% 11.19/11.36 tff(765,plain,
% 11.19/11.36 ((~![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)),
% 11.19/11.36 inference(modus_ponens,[status(thm)],[764, 763])).
% 11.19/11.36 tff(766,plain,
% 11.19/11.36 (~node20(c_e_h_3, c_k, s1)),
% 11.19/11.36 inference(unit_resolution,[status(thm)],[765, 213, 762])).
% 11.19/11.36 tff(767,assumption,(m_and_h_gate_v_out(c_e_h_3, c_k, s0)), introduced(assumption)).
% 11.19/11.36 tff(768,plain,
% 11.19/11.36 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s0))),
% 11.19/11.36 inference(quant_inst,[status(thm)],[])).
% 11.19/11.36 tff(769,plain,
% 11.19/11.36 ($false),
% 11.19/11.36 inference(unit_resolution,[status(thm)],[768, 260, 767])).
% 11.19/11.36 tff(770,plain,(~m_and_h_gate_v_out(c_e_h_3, c_k, s0)), inference(lemma,lemma(discharge,[]))).
% 11.19/11.36 tff(771,assumption,(m_and_h_gate_v_out(c_e_h_3, c_k, s1)), introduced(assumption)).
% 11.19/11.36 tff(772,plain,
% 11.19/11.36 (((~![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))),
% 11.19/11.36 inference(rewrite,[status(thm)],[])).
% 11.19/11.36 tff(773,plain,
% 11.19/11.36 ((~![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))),
% 11.19/11.36 inference(quant_inst,[status(thm)],[])).
% 11.19/11.36 tff(774,plain,
% 11.19/11.36 ((~![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)),
% 11.19/11.36 inference(modus_ponens,[status(thm)],[773, 772])).
% 11.19/11.36 tff(775,plain,
% 11.19/11.36 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s0)),
% 11.19/11.36 inference(unit_resolution,[status(thm)],[774, 757, 663])).
% 11.19/11.36 tff(776,plain,
% 11.19/11.36 (((~![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))),
% 11.19/11.36 inference(rewrite,[status(thm)],[])).
% 11.19/11.36 tff(777,plain,
% 11.19/11.36 ((~![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))),
% 11.19/11.36 inference(quant_inst,[status(thm)],[])).
% 11.19/11.36 tff(778,plain,
% 11.19/11.36 ((~![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)),
% 11.19/11.36 inference(modus_ponens,[status(thm)],[777, 776])).
% 11.19/11.36 tff(779,plain,
% 11.19/11.36 (~node20(c_e_h_3, c_k, s0)),
% 11.19/11.36 inference(unit_resolution,[status(thm)],[778, 213, 775])).
% 11.19/11.36 tff(780,assumption,(node21(c_e_h_3, c_k, s0, s1)), introduced(assumption)).
% 11.19/11.36 tff(781,plain,
% 11.19/11.36 (((~![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_k, s0) | (~node21(c_e_h_3, c_k, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, 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) | (~node21(c_e_h_3, c_k, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s1)))),
% 11.19/11.36 inference(rewrite,[status(thm)],[])).
% 11.19/11.36 tff(782,plain,
% 11.19/11.36 ((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))) <=> (node20(c_e_h_3, c_k, s0) | (~node21(c_e_h_3, c_k, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s1)))),
% 11.19/11.36 inference(rewrite,[status(thm)],[])).
% 11.19/11.36 tff(783,plain,
% 11.19/11.36 (((~![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_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) | (~node21(c_e_h_3, c_k, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s1))))),
% 11.19/11.36 inference(monotonicity,[status(thm)],[782])).
% 11.19/11.36 tff(784,plain,
% 11.19/11.36 (((~![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_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) | (~node21(c_e_h_3, c_k, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s1)))),
% 11.19/11.36 inference(transitivity,[status(thm)],[783, 781])).
% 11.19/11.36 tff(785,plain,
% 11.19/11.36 ((~![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_k, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s1)) | (~node21(c_e_h_3, c_k, s0, s1)))),
% 11.19/11.36 inference(quant_inst,[status(thm)],[])).
% 11.19/11.36 tff(786,plain,
% 11.19/11.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s0) | (~node21(c_e_h_3, c_k, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s1))),
% 11.19/11.36 inference(modus_ponens,[status(thm)],[785, 784])).
% 11.19/11.36 tff(787,plain,
% 11.19/11.36 ($false),
% 11.19/11.36 inference(unit_resolution,[status(thm)],[786, 228, 780, 779, 771])).
% 11.19/11.36 tff(788,plain,((~node21(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,[]))).
% 11.19/11.36 tff(789,plain,
% 11.19/11.36 (~node21(c_e_h_3, c_k, s0, s1)),
% 11.19/11.36 inference(unit_resolution,[status(thm)],[788, 771])).
% 11.19/11.36 tff(790,plain,
% 11.19/11.36 (((~![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))),
% 11.19/11.36 inference(rewrite,[status(thm)],[])).
% 11.19/11.36 tff(791,plain,
% 11.19/11.36 ((~![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))),
% 11.19/11.36 inference(quant_inst,[status(thm)],[])).
% 11.19/11.36 tff(792,plain,
% 11.19/11.36 ((~![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)),
% 11.19/11.36 inference(modus_ponens,[status(thm)],[791, 790])).
% 11.19/11.37 tff(793,plain,
% 11.19/11.37 (node21(c_e_h_3, c_k, s0, s1) | node22(c_e_h_3, c_k, s0, s1)),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[792, 247, 100])).
% 11.19/11.37 tff(794,plain,
% 11.19/11.37 (node22(c_e_h_3, c_k, s0, s1)),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[793, 789])).
% 11.19/11.37 tff(795,plain,
% 11.19/11.37 (((~![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_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))),
% 11.19/11.37 inference(rewrite,[status(thm)],[])).
% 11.19/11.37 tff(796,plain,
% 11.19/11.37 ((~![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_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))),
% 11.19/11.37 inference(quant_inst,[status(thm)],[])).
% 11.19/11.37 tff(797,plain,
% 11.19/11.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s1)) | (~node22(c_e_h_3, c_k, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_k, s0)),
% 11.19/11.37 inference(modus_ponens,[status(thm)],[796, 795])).
% 11.19/11.37 tff(798,plain,
% 11.19/11.37 ($false),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[797, 273, 794, 771, 770])).
% 11.19/11.37 tff(799,plain,(~m_and_h_gate_v_out(c_e_h_3, c_k, s1)), inference(lemma,lemma(discharge,[]))).
% 11.19/11.37 tff(800,assumption,(node22(c_e_h_3, c_k, s1, s2)), introduced(assumption)).
% 11.19/11.37 tff(801,plain,
% 11.19/11.37 (((~![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_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))),
% 11.19/11.37 inference(rewrite,[status(thm)],[])).
% 11.19/11.37 tff(802,plain,
% 11.19/11.37 ((~![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_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))),
% 11.19/11.37 inference(quant_inst,[status(thm)],[])).
% 11.19/11.37 tff(803,plain,
% 11.19/11.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s2)) | (~node22(c_e_h_3, c_k, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_k, s1)),
% 11.19/11.37 inference(modus_ponens,[status(thm)],[802, 801])).
% 11.19/11.37 tff(804,plain,
% 11.19/11.37 ($false),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[803, 273, 800, 799, 652])).
% 11.19/11.37 tff(805,plain,((~node22(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,[]))).
% 11.19/11.37 tff(806,plain,
% 11.19/11.37 (~node22(c_e_h_3, c_k, s1, s2)),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[805, 652])).
% 11.19/11.37 tff(807,plain,
% 11.19/11.37 (((~![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))),
% 11.19/11.37 inference(rewrite,[status(thm)],[])).
% 11.19/11.37 tff(808,plain,
% 11.19/11.37 ((~![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))),
% 11.19/11.37 inference(quant_inst,[status(thm)],[])).
% 11.19/11.37 tff(809,plain,
% 11.19/11.37 ((~![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)),
% 11.19/11.37 inference(modus_ponens,[status(thm)],[808, 807])).
% 11.19/11.37 tff(810,plain,
% 11.19/11.37 (node21(c_e_h_3, c_k, s1, s2) | node22(c_e_h_3, c_k, s1, s2)),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[809, 247, 470])).
% 11.19/11.37 tff(811,plain,
% 11.19/11.37 (node21(c_e_h_3, c_k, s1, s2)),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[810, 806])).
% 11.19/11.37 tff(812,plain,
% 11.19/11.37 (((~![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_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) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s2)) | (~node21(c_e_h_3, c_k, s1, s2)))),
% 11.19/11.37 inference(rewrite,[status(thm)],[])).
% 11.19/11.37 tff(813,plain,
% 11.19/11.37 ((~![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_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)))),
% 11.19/11.37 inference(quant_inst,[status(thm)],[])).
% 11.19/11.37 tff(814,plain,
% 11.19/11.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s2)) | (~node21(c_e_h_3, c_k, s1, s2))),
% 11.19/11.37 inference(modus_ponens,[status(thm)],[813, 812])).
% 11.19/11.37 tff(815,plain,
% 11.19/11.37 ($false),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[814, 228, 811, 766, 652])).
% 11.19/11.37 tff(816,plain,(~m_and_h_gate_v_out(c_e_h_3, c_k, s2)), inference(lemma,lemma(discharge,[]))).
% 11.19/11.37 tff(817,plain,
% 11.19/11.37 (^[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)))),
% 11.19/11.37 inference(bind,[status(th)],[])).
% 11.19/11.37 tff(818,plain,
% 11.19/11.37 (![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))),
% 11.19/11.37 inference(quant_intro,[status(thm)],[817])).
% 11.19/11.37 tff(819,plain,
% 11.19/11.37 (![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))),
% 11.19/11.37 inference(rewrite,[status(thm)],[])).
% 11.19/11.37 tff(820,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')).
% 11.19/11.37 tff(821,plain,
% 11.19/11.37 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))),
% 11.19/11.37 inference(modus_ponens,[status(thm)],[820, 819])).
% 11.19/11.37 tff(822,plain,(
% 11.19/11.37 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))),
% 11.19/11.37 inference(skolemize,[status(sab)],[821])).
% 11.19/11.37 tff(823,plain,
% 11.19/11.37 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))),
% 11.19/11.37 inference(modus_ponens,[status(thm)],[822, 818])).
% 11.19/11.37 tff(824,plain,
% 11.19/11.37 (((~![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))),
% 11.19/11.37 inference(rewrite,[status(thm)],[])).
% 11.19/11.37 tff(825,plain,
% 11.19/11.37 ((~![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))),
% 11.19/11.37 inference(quant_inst,[status(thm)],[])).
% 11.19/11.37 tff(826,plain,
% 11.19/11.37 ((~![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)),
% 11.19/11.37 inference(modus_ponens,[status(thm)],[825, 824])).
% 11.19/11.37 tff(827,plain,
% 11.19/11.37 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s2)),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[826, 823, 816])).
% 11.19/11.37 tff(828,plain,
% 11.19/11.37 (((~![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))),
% 11.19/11.37 inference(rewrite,[status(thm)],[])).
% 11.19/11.37 tff(829,plain,
% 11.19/11.37 ((~![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))),
% 11.19/11.37 inference(quant_inst,[status(thm)],[])).
% 11.19/11.37 tff(830,plain,
% 11.19/11.37 ((~![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)),
% 11.19/11.37 inference(modus_ponens,[status(thm)],[829, 828])).
% 11.19/11.37 tff(831,plain,
% 11.19/11.37 (~node20(c_e_h_3, c_l, s2)),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[830, 213, 827])).
% 11.19/11.37 tff(832,plain,
% 11.19/11.37 (((~![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_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)))),
% 11.19/11.37 inference(rewrite,[status(thm)],[])).
% 11.19/11.37 tff(833,plain,
% 11.19/11.37 ((~![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_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)))),
% 11.19/11.37 inference(quant_inst,[status(thm)],[])).
% 11.19/11.37 tff(834,plain,
% 11.19/11.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | (~node21(c_e_h_3, c_l, s2, s3))),
% 11.19/11.37 inference(modus_ponens,[status(thm)],[833, 832])).
% 11.19/11.37 tff(835,plain,
% 11.19/11.37 ($false),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[834, 228, 831, 651, 650])).
% 11.19/11.37 tff(836,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,[]))).
% 11.19/11.37 tff(837,plain,
% 11.19/11.37 (~node21(c_e_h_3, c_l, s2, s3)),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[836, 650])).
% 11.19/11.37 tff(838,plain,
% 11.19/11.37 (((~![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))),
% 11.19/11.37 inference(rewrite,[status(thm)],[])).
% 11.19/11.37 tff(839,plain,
% 11.19/11.37 ((~![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))),
% 11.19/11.37 inference(quant_inst,[status(thm)],[])).
% 11.19/11.37 tff(840,plain,
% 11.19/11.37 ((~![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)),
% 11.19/11.37 inference(modus_ponens,[status(thm)],[839, 838])).
% 11.19/11.37 tff(841,plain,
% 11.19/11.37 (node21(c_e_h_3, c_l, s2, s3) | node22(c_e_h_3, c_l, s2, s3)),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[840, 247, 604])).
% 11.19/11.37 tff(842,plain,
% 11.19/11.37 (node22(c_e_h_3, c_l, s2, s3)),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[841, 837])).
% 11.19/11.37 tff(843,plain,
% 11.19/11.37 (((~![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))),
% 11.19/11.37 inference(rewrite,[status(thm)],[])).
% 11.19/11.37 tff(844,plain,
% 11.19/11.37 ((~![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))),
% 11.19/11.37 inference(quant_inst,[status(thm)],[])).
% 11.19/11.37 tff(845,plain,
% 11.19/11.37 ((~![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)),
% 11.19/11.37 inference(modus_ponens,[status(thm)],[844, 843])).
% 11.19/11.37 tff(846,plain,
% 11.19/11.37 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s1)),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[845, 823, 799])).
% 11.19/11.37 tff(847,plain,
% 11.19/11.37 (((~![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))),
% 11.19/11.37 inference(rewrite,[status(thm)],[])).
% 11.19/11.37 tff(848,plain,
% 11.19/11.37 ((~![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))),
% 11.19/11.37 inference(quant_inst,[status(thm)],[])).
% 11.19/11.37 tff(849,plain,
% 11.19/11.37 ((~![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)),
% 11.19/11.37 inference(modus_ponens,[status(thm)],[848, 847])).
% 11.19/11.37 tff(850,plain,
% 11.19/11.37 (~node20(c_e_h_3, c_l, s1)),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[849, 213, 846])).
% 11.19/11.37 tff(851,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s2)), introduced(assumption)).
% 11.19/11.37 tff(852,assumption,(node21(c_e_h_3, c_l, s1, s2)), introduced(assumption)).
% 11.19/11.37 tff(853,assumption,(~node20(c_e_h_3, c_l, s1)), introduced(assumption)).
% 11.19/11.37 tff(854,plain,
% 11.19/11.37 (((~![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_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)))) | 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)))),
% 11.19/11.37 inference(rewrite,[status(thm)],[])).
% 11.19/11.37 tff(855,plain,
% 11.19/11.37 ((~![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_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)))),
% 11.19/11.37 inference(quant_inst,[status(thm)],[])).
% 11.19/11.37 tff(856,plain,
% 11.19/11.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | (~node21(c_e_h_3, c_l, s1, s2))),
% 11.19/11.37 inference(modus_ponens,[status(thm)],[855, 854])).
% 11.19/11.37 tff(857,plain,
% 11.19/11.37 ($false),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[856, 228, 851, 853, 852])).
% 11.19/11.37 tff(858,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 11.19/11.37 tff(859,plain,
% 11.19/11.37 (~node21(c_e_h_3, c_l, s1, s2)),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[858, 851, 850])).
% 11.19/11.37 tff(860,plain,
% 11.19/11.37 (((~![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))),
% 11.19/11.37 inference(rewrite,[status(thm)],[])).
% 11.19/11.37 tff(861,plain,
% 11.19/11.37 ((~![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))),
% 11.19/11.37 inference(quant_inst,[status(thm)],[])).
% 11.19/11.37 tff(862,plain,
% 11.19/11.37 ((~![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)),
% 11.19/11.37 inference(modus_ponens,[status(thm)],[861, 860])).
% 11.19/11.37 tff(863,plain,
% 11.19/11.37 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s0)),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[862, 823, 770])).
% 11.19/11.37 tff(864,plain,
% 11.19/11.37 (((~![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))),
% 11.19/11.37 inference(rewrite,[status(thm)],[])).
% 11.19/11.37 tff(865,plain,
% 11.19/11.37 ((~![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))),
% 11.19/11.37 inference(quant_inst,[status(thm)],[])).
% 11.19/11.37 tff(866,plain,
% 11.19/11.37 ((~![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)),
% 11.19/11.37 inference(modus_ponens,[status(thm)],[865, 864])).
% 11.19/11.37 tff(867,plain,
% 11.19/11.37 (~node20(c_e_h_3, c_l, s0)),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[866, 213, 863])).
% 11.19/11.37 tff(868,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s1)), introduced(assumption)).
% 11.19/11.37 tff(869,assumption,(node22(c_e_h_3, c_l, s0, s1)), introduced(assumption)).
% 11.19/11.37 tff(870,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s0)), introduced(assumption)).
% 11.19/11.37 tff(871,plain,
% 11.19/11.37 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s0))),
% 11.19/11.37 inference(quant_inst,[status(thm)],[])).
% 11.19/11.37 tff(872,plain,
% 11.19/11.37 ($false),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[871, 260, 870])).
% 11.19/11.37 tff(873,plain,(~m_and_h_gate_v_out(c_e_h_3, c_l, s0)), inference(lemma,lemma(discharge,[]))).
% 11.19/11.37 tff(874,plain,
% 11.19/11.37 (((~![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_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))),
% 11.19/11.37 inference(rewrite,[status(thm)],[])).
% 11.19/11.37 tff(875,plain,
% 11.19/11.37 ((~![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_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))),
% 11.19/11.37 inference(quant_inst,[status(thm)],[])).
% 11.19/11.37 tff(876,plain,
% 11.19/11.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | (~node22(c_e_h_3, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_l, s0)),
% 11.19/11.37 inference(modus_ponens,[status(thm)],[875, 874])).
% 11.19/11.37 tff(877,plain,
% 11.19/11.37 ($false),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[876, 273, 873, 868, 869])).
% 11.19/11.37 tff(878,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,[]))).
% 11.19/11.37 tff(879,plain,
% 11.19/11.37 (~node22(c_e_h_3, c_l, s0, s1)),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[878, 868])).
% 11.19/11.37 tff(880,plain,
% 11.19/11.37 (((~![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))),
% 11.19/11.37 inference(rewrite,[status(thm)],[])).
% 11.19/11.37 tff(881,plain,
% 11.19/11.37 ((~![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))),
% 11.19/11.37 inference(quant_inst,[status(thm)],[])).
% 11.19/11.37 tff(882,plain,
% 11.19/11.37 ((~![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)),
% 11.19/11.37 inference(modus_ponens,[status(thm)],[881, 880])).
% 11.19/11.37 tff(883,plain,
% 11.19/11.37 (node21(c_e_h_3, c_l, s0, s1) | node22(c_e_h_3, c_l, s0, s1)),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[882, 247, 100])).
% 11.19/11.37 tff(884,plain,
% 11.19/11.37 (node21(c_e_h_3, c_l, s0, s1)),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[883, 879])).
% 11.19/11.37 tff(885,plain,
% 11.19/11.37 (((~![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)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | node20(c_e_h_3, c_l, s0) | (~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)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | node20(c_e_h_3, c_l, s0) | (~node21(c_e_h_3, c_l, s0, s1)))),
% 11.19/11.37 inference(rewrite,[status(thm)],[])).
% 11.19/11.37 tff(886,plain,
% 11.19/11.37 ((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))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | node20(c_e_h_3, c_l, s0) | (~node21(c_e_h_3, c_l, s0, s1)))),
% 11.19/11.37 inference(rewrite,[status(thm)],[])).
% 11.19/11.37 tff(887,plain,
% 11.19/11.37 (((~![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_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)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | node20(c_e_h_3, c_l, s0) | (~node21(c_e_h_3, c_l, s0, s1))))),
% 11.19/11.37 inference(monotonicity,[status(thm)],[886])).
% 11.19/11.37 tff(888,plain,
% 11.19/11.37 (((~![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_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)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | node20(c_e_h_3, c_l, s0) | (~node21(c_e_h_3, c_l, s0, s1)))),
% 11.19/11.37 inference(transitivity,[status(thm)],[887, 885])).
% 11.19/11.37 tff(889,plain,
% 11.19/11.37 ((~![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_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)))),
% 11.19/11.37 inference(quant_inst,[status(thm)],[])).
% 11.19/11.37 tff(890,plain,
% 11.19/11.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | node20(c_e_h_3, c_l, s0) | (~node21(c_e_h_3, c_l, s0, s1))),
% 11.19/11.37 inference(modus_ponens,[status(thm)],[889, 888])).
% 11.19/11.37 tff(891,plain,
% 11.19/11.37 ($false),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[890, 228, 868, 884, 867])).
% 11.19/11.37 tff(892,plain,(~m_and_h_gate_v_out(c_e_h_3, c_l, s1)), inference(lemma,lemma(discharge,[]))).
% 11.19/11.37 tff(893,assumption,(node22(c_e_h_3, c_l, s1, s2)), introduced(assumption)).
% 11.19/11.37 tff(894,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_l, s1)), introduced(assumption)).
% 11.19/11.37 tff(895,plain,
% 11.19/11.37 (((~![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_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))),
% 11.19/11.37 inference(rewrite,[status(thm)],[])).
% 11.19/11.37 tff(896,plain,
% 11.19/11.37 ((~![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_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))),
% 11.19/11.37 inference(quant_inst,[status(thm)],[])).
% 11.19/11.37 tff(897,plain,
% 11.19/11.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | (~node22(c_e_h_3, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_l, s1)),
% 11.19/11.37 inference(modus_ponens,[status(thm)],[896, 895])).
% 11.19/11.37 tff(898,plain,
% 11.19/11.37 ($false),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[897, 273, 894, 851, 893])).
% 11.19/11.37 tff(899,plain,((~node22(c_e_h_3, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2))), inference(lemma,lemma(discharge,[]))).
% 11.19/11.37 tff(900,plain,
% 11.19/11.37 (~node22(c_e_h_3, c_l, s1, s2)),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[899, 851, 892])).
% 11.19/11.37 tff(901,plain,
% 11.19/11.37 (((~![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))),
% 11.19/11.37 inference(rewrite,[status(thm)],[])).
% 11.19/11.37 tff(902,plain,
% 11.19/11.37 ((~![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))),
% 11.19/11.37 inference(quant_inst,[status(thm)],[])).
% 11.19/11.37 tff(903,plain,
% 11.19/11.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_l, s1, s2) | node22(c_e_h_3, c_l, s1, s2)),
% 11.19/11.37 inference(modus_ponens,[status(thm)],[902, 901])).
% 11.19/11.37 tff(904,plain,
% 11.19/11.37 (node21(c_e_h_3, c_l, s1, s2) | node22(c_e_h_3, c_l, s1, s2)),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[903, 247, 470])).
% 11.19/11.37 tff(905,plain,
% 11.19/11.37 ($false),
% 11.19/11.37 inference(unit_resolution,[status(thm)],[904, 900, 859])).
% 11.19/11.37 tff(906,plain,(~m_and_h_gate_v_out(c_e_h_3, c_l, s2)), inference(lemma,lemma(discharge,[]))).
% 11.19/11.37 tff(907,plain,
% 11.19/11.37 (((~![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_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))),
% 11.19/11.37 inference(rewrite,[status(thm)],[])).
% 11.19/11.37 tff(908,plain,
% 11.19/11.37 ((~![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_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))),
% 11.19/11.37 inference(quant_inst,[status(thm)],[])).
% 11.19/11.37 tff(909,plain,
% 11.19/11.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | (~node22(c_e_h_3, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_l, s2)),
% 11.19/11.37 inference(modus_ponens,[status(thm)],[908, 907])).
% 11.19/11.38 tff(910,plain,
% 11.19/11.38 ($false),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[909, 273, 906, 842, 650])).
% 11.19/11.38 tff(911,plain,(~m_and_h_gate_v_out(c_e_h_3, c_l, s3)), inference(lemma,lemma(discharge,[]))).
% 11.19/11.38 tff(912,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_l, s3)), introduced(assumption)).
% 11.19/11.38 tff(913,assumption,(m_or_h_gate_v_in1(c_e_h_3, c_j, s3)), introduced(assumption)).
% 11.19/11.38 tff(914,plain,
% 11.19/11.38 (^[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)))),
% 11.19/11.38 inference(bind,[status(th)],[])).
% 11.19/11.38 tff(915,plain,
% 11.19/11.38 (![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))),
% 11.19/11.38 inference(quant_intro,[status(thm)],[914])).
% 11.19/11.38 tff(916,plain,
% 11.19/11.38 (![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))),
% 11.19/11.38 inference(rewrite,[status(thm)],[])).
% 11.19/11.38 tff(917,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')).
% 11.19/11.38 tff(918,plain,
% 11.19/11.38 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))),
% 11.19/11.38 inference(modus_ponens,[status(thm)],[917, 916])).
% 11.19/11.38 tff(919,plain,(
% 11.19/11.38 ![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))),
% 11.19/11.38 inference(skolemize,[status(sab)],[918])).
% 11.19/11.38 tff(920,plain,
% 11.19/11.38 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))),
% 11.19/11.38 inference(modus_ponens,[status(thm)],[919, 915])).
% 11.19/11.38 tff(921,plain,
% 11.19/11.38 (((~![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))),
% 11.19/11.38 inference(rewrite,[status(thm)],[])).
% 11.19/11.38 tff(922,plain,
% 11.19/11.38 ((~![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))),
% 11.19/11.38 inference(quant_inst,[status(thm)],[])).
% 11.19/11.38 tff(923,plain,
% 11.19/11.38 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s3)) | m_and_h_gate_v_out(c_e_h_3, c_l, s3)),
% 11.19/11.38 inference(modus_ponens,[status(thm)],[922, 921])).
% 11.19/11.38 tff(924,plain,
% 11.19/11.38 ($false),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[923, 920, 913, 912])).
% 11.19/11.38 tff(925,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 11.19/11.38 tff(926,plain,
% 11.19/11.38 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s3)),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[925, 911])).
% 11.19/11.38 tff(927,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s4)), introduced(assumption)).
% 11.19/11.38 tff(928,assumption,(node6(c_e_h_3, c_j, s3, s4)), introduced(assumption)).
% 11.19/11.38 tff(929,plain,
% 11.19/11.38 (((~![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))),
% 11.19/11.38 inference(rewrite,[status(thm)],[])).
% 11.19/11.38 tff(930,plain,
% 11.19/11.38 ((~![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))),
% 11.19/11.38 inference(quant_inst,[status(thm)],[])).
% 11.19/11.38 tff(931,plain,
% 11.19/11.38 ((~![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)),
% 11.19/11.38 inference(modus_ponens,[status(thm)],[930, 929])).
% 11.19/11.38 tff(932,plain,
% 11.19/11.38 (node3(c_e_h_2, c_e_h_3, s2)),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[931, 619, 616])).
% 11.19/11.38 tff(933,plain,
% 11.19/11.38 (((~![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))),
% 11.19/11.38 inference(rewrite,[status(thm)],[])).
% 11.19/11.38 tff(934,plain,
% 11.19/11.38 ((~![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))),
% 11.19/11.38 inference(quant_inst,[status(thm)],[])).
% 11.19/11.38 tff(935,plain,
% 11.19/11.38 ((~![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)),
% 11.19/11.38 inference(modus_ponens,[status(thm)],[934, 933])).
% 11.19/11.38 tff(936,plain,
% 11.19/11.38 ((~m_cell_v_ack(c_e_h_3, s2)) | m_and_h_gate_v_out(c_e_h_2, c_q, s2)),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[935, 633, 932])).
% 11.19/11.38 tff(937,plain,
% 11.19/11.38 (~m_cell_v_ack(c_e_h_3, s2)),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[936, 476])).
% 11.19/11.38 tff(938,plain,
% 11.19/11.38 (((~![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))),
% 11.19/11.38 inference(rewrite,[status(thm)],[])).
% 11.19/11.38 tff(939,plain,
% 11.19/11.38 ((~![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))),
% 11.19/11.38 inference(quant_inst,[status(thm)],[])).
% 11.19/11.38 tff(940,plain,
% 11.19/11.38 ((~![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)),
% 11.19/11.38 inference(modus_ponens,[status(thm)],[939, 938])).
% 11.19/11.38 tff(941,plain,
% 11.19/11.38 (~m_or_h_gate_v_in2(c_e_h_3, c_j, s2)),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[940, 645, 937])).
% 11.19/11.38 tff(942,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s2)), introduced(assumption)).
% 11.19/11.38 tff(943,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s1)), introduced(assumption)).
% 11.19/11.38 tff(944,assumption,(node5(c_e_h_3, c_j, s0, s1)), introduced(assumption)).
% 11.19/11.38 tff(945,plain,
% 11.19/11.38 (((~![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))),
% 11.19/11.38 inference(rewrite,[status(thm)],[])).
% 11.19/11.38 tff(946,plain,
% 11.19/11.38 ((~![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))),
% 11.19/11.38 inference(quant_inst,[status(thm)],[])).
% 11.19/11.38 tff(947,plain,
% 11.19/11.38 ((~![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)),
% 11.19/11.38 inference(modus_ponens,[status(thm)],[946, 945])).
% 11.19/11.38 tff(948,plain,
% 11.19/11.38 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s0)),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[947, 920, 873])).
% 11.19/11.38 tff(949,plain,
% 11.19/11.38 (((~![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))),
% 11.19/11.38 inference(rewrite,[status(thm)],[])).
% 11.19/11.38 tff(950,plain,
% 11.19/11.38 ((~![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))),
% 11.19/11.38 inference(quant_inst,[status(thm)],[])).
% 11.19/11.38 tff(951,plain,
% 11.19/11.38 ((~![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)),
% 11.19/11.38 inference(modus_ponens,[status(thm)],[950, 949])).
% 11.19/11.38 tff(952,plain,
% 11.19/11.38 (node3(c_e_h_2, c_e_h_3, s0)),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[951, 619, 616])).
% 11.19/11.38 tff(953,plain,
% 11.19/11.38 (((~![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))),
% 11.19/11.38 inference(rewrite,[status(thm)],[])).
% 11.19/11.38 tff(954,plain,
% 11.19/11.38 ((~![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))),
% 11.19/11.38 inference(quant_inst,[status(thm)],[])).
% 11.19/11.38 tff(955,plain,
% 11.19/11.38 ((~![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)),
% 11.19/11.38 inference(modus_ponens,[status(thm)],[954, 953])).
% 11.19/11.38 tff(956,plain,
% 11.19/11.38 ((~m_cell_v_ack(c_e_h_3, s0)) | m_and_h_gate_v_out(c_e_h_2, c_q, s0)),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[955, 633, 952])).
% 11.19/11.38 tff(957,plain,
% 11.19/11.38 (~m_cell_v_ack(c_e_h_3, s0)),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[956, 263])).
% 11.19/11.38 tff(958,plain,
% 11.19/11.38 (((~![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))),
% 11.19/11.38 inference(rewrite,[status(thm)],[])).
% 11.19/11.38 tff(959,plain,
% 11.19/11.38 ((~![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))),
% 11.19/11.38 inference(quant_inst,[status(thm)],[])).
% 11.19/11.38 tff(960,plain,
% 11.19/11.38 ((~![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)),
% 11.19/11.38 inference(modus_ponens,[status(thm)],[959, 958])).
% 11.19/11.38 tff(961,plain,
% 11.19/11.38 (~m_or_h_gate_v_in2(c_e_h_3, c_j, s0)),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[960, 645, 957])).
% 11.19/11.38 tff(962,plain,
% 11.19/11.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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, s1)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s0) | m_or_h_gate_v_in1(c_e_h_3, c_j, s0) | (~node5(c_e_h_3, 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_3, c_j, s1)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s0) | m_or_h_gate_v_in1(c_e_h_3, c_j, s0) | (~node5(c_e_h_3, c_j, s0, s1)))),
% 11.19/11.38 inference(rewrite,[status(thm)],[])).
% 11.19/11.38 tff(963,plain,
% 11.19/11.38 ((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_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_in1(c_e_h_3, c_j, s0) | (~node5(c_e_h_3, c_j, s0, s1)))),
% 11.19/11.38 inference(rewrite,[status(thm)],[])).
% 11.19/11.38 tff(964,plain,
% 11.19/11.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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_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_in1(c_e_h_3, c_j, s0) | (~node5(c_e_h_3, c_j, s0, s1))))),
% 11.19/11.38 inference(monotonicity,[status(thm)],[963])).
% 11.19/11.38 tff(965,plain,
% 11.19/11.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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_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_in1(c_e_h_3, c_j, s0) | (~node5(c_e_h_3, c_j, s0, s1)))),
% 11.19/11.38 inference(transitivity,[status(thm)],[964, 962])).
% 11.19/11.38 tff(966,plain,
% 11.19/11.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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)))),
% 11.19/11.38 inference(quant_inst,[status(thm)],[])).
% 11.19/11.38 tff(967,plain,
% 11.19/11.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s0) | m_or_h_gate_v_in1(c_e_h_3, c_j, s0) | (~node5(c_e_h_3, c_j, s0, s1))),
% 11.19/11.38 inference(modus_ponens,[status(thm)],[966, 965])).
% 11.19/11.38 tff(968,plain,
% 11.19/11.38 ($false),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[967, 705, 961, 948, 943, 944])).
% 11.19/11.38 tff(969,plain,((~node5(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,[]))).
% 11.19/11.38 tff(970,plain,
% 11.19/11.38 (~node5(c_e_h_3, c_j, s0, s1)),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[969, 943])).
% 11.19/11.38 tff(971,plain,
% 11.19/11.38 (((~![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))),
% 11.19/11.38 inference(rewrite,[status(thm)],[])).
% 11.19/11.38 tff(972,plain,
% 11.19/11.38 ((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))),
% 11.19/11.38 inference(rewrite,[status(thm)],[])).
% 11.19/11.38 tff(973,plain,
% 11.19/11.38 (((~![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)))),
% 11.19/11.38 inference(monotonicity,[status(thm)],[972])).
% 11.19/11.38 tff(974,plain,
% 11.19/11.38 (((~![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))),
% 11.19/11.38 inference(transitivity,[status(thm)],[973, 971])).
% 11.19/11.38 tff(975,plain,
% 11.19/11.38 ((~![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)))),
% 11.19/11.38 inference(quant_inst,[status(thm)],[])).
% 11.19/11.38 tff(976,plain,
% 11.19/11.38 ((~![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)),
% 11.19/11.38 inference(modus_ponens,[status(thm)],[975, 974])).
% 11.19/11.38 tff(977,plain,
% 11.19/11.38 (node5(c_e_h_3, c_j, s0, s1) | node6(c_e_h_3, c_j, s0, s1)),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[976, 724, 100])).
% 11.19/11.38 tff(978,plain,
% 11.19/11.38 (node6(c_e_h_3, c_j, s0, s1)),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[977, 970])).
% 11.19/11.38 tff(979,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s0)), introduced(assumption)).
% 11.19/11.38 tff(980,plain,
% 11.19/11.38 ((~![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s0))),
% 11.19/11.38 inference(quant_inst,[status(thm)],[])).
% 11.19/11.38 tff(981,plain,
% 11.19/11.38 ($false),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[980, 660, 979])).
% 11.19/11.38 tff(982,plain,(~m_or_h_gate_v_out(c_e_h_3, c_j, s0)), inference(lemma,lemma(discharge,[]))).
% 11.19/11.38 tff(983,plain,
% 11.19/11.38 (((~![Y: $i, I0: $i, X: $i, I1: $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)))),
% 11.19/11.38 inference(rewrite,[status(thm)],[])).
% 11.19/11.38 tff(984,plain,
% 11.19/11.38 (((~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)))),
% 11.19/11.38 inference(rewrite,[status(thm)],[])).
% 11.19/11.38 tff(985,plain,
% 11.19/11.38 (((~![Y: $i, I0: $i, X: $i, I1: $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))))),
% 11.19/11.38 inference(monotonicity,[status(thm)],[984])).
% 11.19/11.38 tff(986,plain,
% 11.19/11.38 (((~![Y: $i, I0: $i, X: $i, I1: $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)))),
% 11.19/11.38 inference(transitivity,[status(thm)],[985, 983])).
% 11.19/11.38 tff(987,plain,
% 11.19/11.38 ((~![Y: $i, I0: $i, X: $i, I1: $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))),
% 11.19/11.38 inference(quant_inst,[status(thm)],[])).
% 11.19/11.38 tff(988,plain,
% 11.19/11.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | m_or_h_gate_v_out(c_e_h_3, c_j, s0) | (~node6(c_e_h_3, c_j, s0, s1))),
% 11.19/11.38 inference(modus_ponens,[status(thm)],[987, 986])).
% 11.19/11.38 tff(989,plain,
% 11.19/11.38 ($false),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[988, 742, 982, 943, 978])).
% 11.19/11.38 tff(990,plain,(~m_or_h_gate_v_out(c_e_h_3, c_j, s1)), inference(lemma,lemma(discharge,[]))).
% 11.19/11.38 tff(991,assumption,(node6(c_e_h_3, c_j, s1, s2)), introduced(assumption)).
% 11.19/11.38 tff(992,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_j, s1)), introduced(assumption)).
% 11.19/11.38 tff(993,plain,
% 11.19/11.38 (((~![Y: $i, I0: $i, X: $i, I1: $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)))),
% 11.19/11.38 inference(rewrite,[status(thm)],[])).
% 11.19/11.38 tff(994,plain,
% 11.19/11.38 (((~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)))),
% 11.19/11.38 inference(rewrite,[status(thm)],[])).
% 11.19/11.38 tff(995,plain,
% 11.19/11.38 (((~![Y: $i, I0: $i, X: $i, I1: $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))))),
% 11.19/11.38 inference(monotonicity,[status(thm)],[994])).
% 11.19/11.38 tff(996,plain,
% 11.19/11.38 (((~![Y: $i, I0: $i, X: $i, I1: $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)))),
% 11.19/11.38 inference(transitivity,[status(thm)],[995, 993])).
% 11.19/11.38 tff(997,plain,
% 11.19/11.38 ((~![Y: $i, I0: $i, X: $i, I1: $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))),
% 11.19/11.38 inference(quant_inst,[status(thm)],[])).
% 11.19/11.38 tff(998,plain,
% 11.19/11.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~node6(c_e_h_3, c_j, s1, s2))),
% 11.19/11.38 inference(modus_ponens,[status(thm)],[997, 996])).
% 11.19/11.38 tff(999,plain,
% 11.19/11.38 ($false),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[998, 742, 942, 992, 991])).
% 11.19/11.38 tff(1000,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 11.19/11.38 tff(1001,plain,
% 11.19/11.38 ((~node6(c_e_h_3, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2))),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[1000, 990])).
% 11.19/11.38 tff(1002,plain,
% 11.19/11.38 (~node6(c_e_h_3, c_j, s1, s2)),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[1001, 942])).
% 11.19/11.38 tff(1003,plain,
% 11.19/11.38 (((~![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_3, c_j, s1, s2) | node6(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)) | node5(c_e_h_3, c_j, s1, s2) | node6(c_e_h_3, c_j, s1, s2))),
% 11.19/11.38 inference(rewrite,[status(thm)],[])).
% 11.19/11.38 tff(1004,plain,
% 11.19/11.38 ((node6(c_e_h_3, c_j, s1, s2) | node5(c_e_h_3, c_j, s1, s2) | (~trans(s1, s2))) <=> ((~trans(s1, s2)) | node5(c_e_h_3, c_j, s1, s2) | node6(c_e_h_3, c_j, s1, s2))),
% 11.19/11.38 inference(rewrite,[status(thm)],[])).
% 11.19/11.38 tff(1005,plain,
% 11.19/11.38 (((~![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)) | node5(c_e_h_3, c_j, s1, s2) | node6(c_e_h_3, c_j, s1, s2)))),
% 11.19/11.38 inference(monotonicity,[status(thm)],[1004])).
% 11.19/11.38 tff(1006,plain,
% 11.19/11.38 (((~![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)) | node5(c_e_h_3, c_j, s1, s2) | node6(c_e_h_3, c_j, s1, s2))),
% 11.19/11.38 inference(transitivity,[status(thm)],[1005, 1003])).
% 11.19/11.38 tff(1007,plain,
% 11.19/11.38 ((~![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)))),
% 11.19/11.38 inference(quant_inst,[status(thm)],[])).
% 11.19/11.38 tff(1008,plain,
% 11.19/11.38 ((~![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_3, c_j, s1, s2) | node6(c_e_h_3, c_j, s1, s2)),
% 11.19/11.38 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 11.19/11.38 tff(1009,plain,
% 11.19/11.38 (node5(c_e_h_3, c_j, s1, s2) | node6(c_e_h_3, c_j, s1, s2)),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[1008, 724, 470])).
% 11.19/11.38 tff(1010,plain,
% 11.19/11.38 (node5(c_e_h_3, c_j, s1, s2)),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[1009, 1002])).
% 11.19/11.38 tff(1011,assumption,(m_or_h_gate_v_in1(c_e_h_3, c_j, s1)), introduced(assumption)).
% 11.19/11.38 tff(1012,plain,
% 11.19/11.38 (((~![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))),
% 11.19/11.38 inference(rewrite,[status(thm)],[])).
% 11.19/11.38 tff(1013,plain,
% 11.19/11.38 ((~![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))),
% 11.19/11.38 inference(quant_inst,[status(thm)],[])).
% 11.19/11.38 tff(1014,plain,
% 11.19/11.38 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s1)) | m_and_h_gate_v_out(c_e_h_3, c_l, s1)),
% 11.19/11.38 inference(modus_ponens,[status(thm)],[1013, 1012])).
% 11.19/11.38 tff(1015,plain,
% 11.19/11.38 ($false),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[1014, 920, 1011, 894])).
% 11.19/11.38 tff(1016,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 11.19/11.38 tff(1017,plain,
% 11.19/11.38 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s1)),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[1016, 892])).
% 11.19/11.38 tff(1018,plain,
% 11.19/11.38 (((~![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))),
% 11.19/11.38 inference(rewrite,[status(thm)],[])).
% 11.19/11.38 tff(1019,plain,
% 11.19/11.38 ((~![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))),
% 11.19/11.38 inference(quant_inst,[status(thm)],[])).
% 11.19/11.38 tff(1020,plain,
% 11.19/11.38 ((~![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)),
% 11.19/11.38 inference(modus_ponens,[status(thm)],[1019, 1018])).
% 11.19/11.38 tff(1021,plain,
% 11.19/11.38 (node3(c_e_h_2, c_e_h_3, s1)),
% 11.19/11.38 inference(unit_resolution,[status(thm)],[1020, 619, 616])).
% 11.19/11.38 tff(1022,plain,
% 11.19/11.38 (((~![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))),
% 11.19/11.38 inference(rewrite,[status(thm)],[])).
% 11.19/11.38 tff(1023,plain,
% 11.19/11.38 ((~![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))),
% 11.19/11.38 inference(quant_inst,[status(thm)],[])).
% 11.19/11.38 tff(1024,plain,
% 11.19/11.38 ((~![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)),
% 11.19/11.39 inference(modus_ponens,[status(thm)],[1023, 1022])).
% 11.19/11.39 tff(1025,plain,
% 11.19/11.39 ((~m_cell_v_ack(c_e_h_3, s1)) | m_and_h_gate_v_out(c_e_h_2, c_q, s1)),
% 11.19/11.39 inference(unit_resolution,[status(thm)],[1024, 633, 1021])).
% 11.19/11.39 tff(1026,plain,
% 11.19/11.39 (~m_cell_v_ack(c_e_h_3, s1)),
% 11.19/11.39 inference(unit_resolution,[status(thm)],[1025, 278])).
% 11.19/11.39 tff(1027,plain,
% 11.19/11.39 (((~![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))),
% 11.19/11.39 inference(rewrite,[status(thm)],[])).
% 11.19/11.39 tff(1028,plain,
% 11.19/11.39 ((~![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))),
% 11.19/11.39 inference(quant_inst,[status(thm)],[])).
% 11.19/11.39 tff(1029,plain,
% 11.19/11.39 ((~![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)),
% 11.19/11.39 inference(modus_ponens,[status(thm)],[1028, 1027])).
% 11.19/11.39 tff(1030,plain,
% 11.19/11.39 (~m_or_h_gate_v_in2(c_e_h_3, c_j, s1)),
% 11.19/11.39 inference(unit_resolution,[status(thm)],[1029, 645, 1026])).
% 11.19/11.39 tff(1031,plain,
% 11.19/11.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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_in1(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~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_in1(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~node5(c_e_h_3, c_j, s1, s2)))),
% 11.19/11.39 inference(rewrite,[status(thm)],[])).
% 11.19/11.39 tff(1032,plain,
% 11.19/11.39 ((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_in1(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~node5(c_e_h_3, c_j, s1, s2)))),
% 11.19/11.39 inference(rewrite,[status(thm)],[])).
% 11.19/11.39 tff(1033,plain,
% 11.19/11.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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_in1(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~node5(c_e_h_3, c_j, s1, s2))))),
% 11.19/11.39 inference(monotonicity,[status(thm)],[1032])).
% 11.19/11.39 tff(1034,plain,
% 11.19/11.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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_in1(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~node5(c_e_h_3, c_j, s1, s2)))),
% 11.19/11.39 inference(transitivity,[status(thm)],[1033, 1031])).
% 11.19/11.39 tff(1035,plain,
% 11.19/11.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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)))),
% 11.19/11.39 inference(quant_inst,[status(thm)],[])).
% 11.19/11.39 tff(1036,plain,
% 11.19/11.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s1) | m_or_h_gate_v_in1(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~node5(c_e_h_3, c_j, s1, s2))),
% 11.19/11.39 inference(modus_ponens,[status(thm)],[1035, 1034])).
% 11.19/11.39 tff(1037,plain,
% 11.19/11.39 ($false),
% 11.19/11.39 inference(unit_resolution,[status(thm)],[1036, 705, 942, 1030, 1017, 1010])).
% 11.19/11.39 tff(1038,plain,(~m_or_h_gate_v_out(c_e_h_3, c_j, s2)), inference(lemma,lemma(discharge,[]))).
% 11.19/11.39 tff(1039,plain,
% 11.19/11.39 (((~![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))),
% 11.19/11.39 inference(rewrite,[status(thm)],[])).
% 11.19/11.39 tff(1040,plain,
% 11.19/11.39 ((~![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))),
% 11.19/11.39 inference(quant_inst,[status(thm)],[])).
% 11.19/11.39 tff(1041,plain,
% 11.19/11.39 ((~![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)),
% 11.19/11.39 inference(modus_ponens,[status(thm)],[1040, 1039])).
% 11.19/11.39 tff(1042,plain,
% 11.19/11.39 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s2)),
% 11.19/11.39 inference(unit_resolution,[status(thm)],[1041, 920, 906])).
% 11.19/11.39 tff(1043,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_j, s2)), introduced(assumption)).
% 11.19/11.39 tff(1044,assumption,(~m_or_h_gate_v_in2(c_e_h_3, c_j, s2)), introduced(assumption)).
% 11.19/11.39 tff(1045,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s3)), introduced(assumption)).
% 11.19/11.39 tff(1046,plain,
% 11.19/11.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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, s2) | (~node5(c_e_h_3, c_j, s2, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s2) | (~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_in2(c_e_h_3, c_j, s2) | (~node5(c_e_h_3, c_j, s2, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)))),
% 11.19/11.39 inference(rewrite,[status(thm)],[])).
% 11.19/11.39 tff(1047,plain,
% 11.19/11.39 ((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_in2(c_e_h_3, c_j, s2) | (~node5(c_e_h_3, c_j, s2, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)))),
% 11.19/11.39 inference(rewrite,[status(thm)],[])).
% 11.19/11.39 tff(1048,plain,
% 11.19/11.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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_in2(c_e_h_3, c_j, s2) | (~node5(c_e_h_3, c_j, s2, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3))))),
% 11.19/11.39 inference(monotonicity,[status(thm)],[1047])).
% 11.19/11.39 tff(1049,plain,
% 11.19/11.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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_in2(c_e_h_3, c_j, s2) | (~node5(c_e_h_3, c_j, s2, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)))),
% 11.25/11.39 inference(transitivity,[status(thm)],[1048, 1046])).
% 11.25/11.39 tff(1050,plain,
% 11.25/11.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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)))),
% 11.25/11.39 inference(quant_inst,[status(thm)],[])).
% 11.25/11.39 tff(1051,plain,
% 11.25/11.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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, s2) | (~node5(c_e_h_3, c_j, s2, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3))),
% 11.25/11.39 inference(modus_ponens,[status(thm)],[1050, 1049])).
% 11.25/11.39 tff(1052,plain,
% 11.25/11.39 (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_in1(c_e_h_3, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3))),
% 11.25/11.39 inference(unit_resolution,[status(thm)],[1051, 705])).
% 11.25/11.39 tff(1053,plain,
% 11.25/11.39 (~node5(c_e_h_3, c_j, s2, s3)),
% 11.25/11.39 inference(unit_resolution,[status(thm)],[1052, 1045, 1044, 1043])).
% 11.25/11.39 tff(1054,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_j, s2)), introduced(assumption)).
% 11.25/11.39 tff(1055,assumption,(node6(c_e_h_3, c_j, s2, s3)), introduced(assumption)).
% 11.25/11.39 tff(1056,plain,
% 11.25/11.39 (((~![Y: $i, I0: $i, X: $i, I1: $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, s2) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | (~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, s2) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | (~node6(c_e_h_3, c_j, s2, s3)))),
% 11.25/11.39 inference(rewrite,[status(thm)],[])).
% 11.25/11.39 tff(1057,plain,
% 11.25/11.39 (((~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, s2) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | (~node6(c_e_h_3, c_j, s2, s3)))),
% 11.25/11.39 inference(rewrite,[status(thm)],[])).
% 11.25/11.39 tff(1058,plain,
% 11.25/11.39 (((~![Y: $i, I0: $i, X: $i, I1: $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, s2) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | (~node6(c_e_h_3, c_j, s2, s3))))),
% 11.25/11.39 inference(monotonicity,[status(thm)],[1057])).
% 11.25/11.39 tff(1059,plain,
% 11.25/11.39 (((~![Y: $i, I0: $i, X: $i, I1: $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, s2) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | (~node6(c_e_h_3, c_j, s2, s3)))),
% 11.25/11.39 inference(transitivity,[status(thm)],[1058, 1056])).
% 11.25/11.39 tff(1060,plain,
% 11.25/11.39 ((~![Y: $i, I0: $i, X: $i, I1: $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))),
% 11.25/11.39 inference(quant_inst,[status(thm)],[])).
% 11.25/11.39 tff(1061,plain,
% 11.25/11.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | (~node6(c_e_h_3, c_j, s2, s3))),
% 11.25/11.39 inference(modus_ponens,[status(thm)],[1060, 1059])).
% 11.25/11.39 tff(1062,plain,
% 11.25/11.39 ($false),
% 11.25/11.39 inference(unit_resolution,[status(thm)],[1061, 742, 1054, 1045, 1055])).
% 11.25/11.39 tff(1063,plain,((~node6(c_e_h_3, c_j, s2, 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))), inference(lemma,lemma(discharge,[]))).
% 11.25/11.39 tff(1064,plain,
% 11.25/11.39 (~node6(c_e_h_3, c_j, s2, s3)),
% 11.25/11.39 inference(unit_resolution,[status(thm)],[1063, 1045, 1054])).
% 11.25/11.39 tff(1065,plain,
% 11.25/11.39 (((~![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))),
% 11.25/11.39 inference(rewrite,[status(thm)],[])).
% 11.25/11.39 tff(1066,plain,
% 11.25/11.39 ((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))),
% 11.25/11.39 inference(rewrite,[status(thm)],[])).
% 11.25/11.39 tff(1067,plain,
% 11.25/11.39 (((~![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)))),
% 11.25/11.39 inference(monotonicity,[status(thm)],[1066])).
% 11.25/11.39 tff(1068,plain,
% 11.25/11.39 (((~![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))),
% 11.25/11.39 inference(transitivity,[status(thm)],[1067, 1065])).
% 11.25/11.39 tff(1069,plain,
% 11.25/11.39 ((~![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)))),
% 11.25/11.39 inference(quant_inst,[status(thm)],[])).
% 11.25/11.39 tff(1070,plain,
% 11.25/11.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node5(c_e_h_3, c_j, s2, s3) | node6(c_e_h_3, c_j, s2, s3)),
% 11.25/11.39 inference(modus_ponens,[status(thm)],[1069, 1068])).
% 11.25/11.39 tff(1071,plain,
% 11.25/11.39 (node5(c_e_h_3, c_j, s2, s3) | node6(c_e_h_3, c_j, s2, s3)),
% 11.25/11.39 inference(unit_resolution,[status(thm)],[1070, 724, 604])).
% 11.25/11.39 tff(1072,plain,
% 11.25/11.39 ($false),
% 11.25/11.39 inference(unit_resolution,[status(thm)],[1071, 1064, 1053])).
% 11.25/11.39 tff(1073,plain,((~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_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,[]))).
% 11.25/11.39 tff(1074,plain,
% 11.25/11.39 ((~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_in2(c_e_h_3, c_j, s2)),
% 11.25/11.39 inference(unit_resolution,[status(thm)],[1073, 1042])).
% 11.25/11.39 tff(1075,plain,
% 11.25/11.39 ((~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)),
% 11.25/11.39 inference(unit_resolution,[status(thm)],[1074, 1038])).
% 11.25/11.39 tff(1076,plain,
% 11.25/11.39 (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)),
% 11.25/11.39 inference(unit_resolution,[status(thm)],[1075, 941])).
% 11.25/11.39 tff(1077,plain,
% 11.25/11.39 (((~![Y: $i, I0: $i, X: $i, I1: $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)))),
% 11.25/11.39 inference(rewrite,[status(thm)],[])).
% 11.25/11.39 tff(1078,plain,
% 11.25/11.39 (((~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)))),
% 11.25/11.39 inference(rewrite,[status(thm)],[])).
% 11.25/11.39 tff(1079,plain,
% 11.25/11.39 (((~![Y: $i, I0: $i, X: $i, I1: $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))))),
% 11.25/11.39 inference(monotonicity,[status(thm)],[1078])).
% 11.25/11.39 tff(1080,plain,
% 11.25/11.39 (((~![Y: $i, I0: $i, X: $i, I1: $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)))),
% 11.25/11.39 inference(transitivity,[status(thm)],[1079, 1077])).
% 11.25/11.39 tff(1081,plain,
% 11.25/11.39 ((~![Y: $i, I0: $i, X: $i, I1: $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))),
% 11.25/11.39 inference(quant_inst,[status(thm)],[])).
% 11.25/11.39 tff(1082,plain,
% 11.25/11.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | (~node6(c_e_h_3, c_j, s3, s4))),
% 11.25/11.39 inference(modus_ponens,[status(thm)],[1081, 1080])).
% 11.25/11.39 tff(1083,plain,
% 11.25/11.39 ($false),
% 11.25/11.39 inference(unit_resolution,[status(thm)],[1082, 742, 1076, 927, 928])).
% 11.25/11.39 tff(1084,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,[]))).
% 11.25/11.39 tff(1085,plain,
% 11.25/11.39 (~node6(c_e_h_3, c_j, s3, s4)),
% 11.25/11.39 inference(unit_resolution,[status(thm)],[1084, 927])).
% 11.25/11.39 tff(1086,plain,
% 11.25/11.39 (succ(s3, s4) <=> succ(s3, s4)),
% 11.25/11.39 inference(rewrite,[status(thm)],[])).
% 11.25/11.39 tff(1087,axiom,(succ(s3, s4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound4')).
% 11.25/11.39 tff(1088,plain,
% 11.25/11.39 (succ(s3, s4)),
% 11.25/11.39 inference(modus_ponens,[status(thm)],[1087, 1086])).
% 11.25/11.39 tff(1089,plain,
% 11.25/11.39 (((~![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))),
% 11.25/11.39 inference(rewrite,[status(thm)],[])).
% 11.25/11.39 tff(1090,plain,
% 11.25/11.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s3, s4)) | trans(s3, s4))),
% 11.25/11.39 inference(quant_inst,[status(thm)],[])).
% 11.25/11.39 tff(1091,plain,
% 11.25/11.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s3, s4)) | trans(s3, s4)),
% 11.25/11.39 inference(modus_ponens,[status(thm)],[1090, 1089])).
% 11.25/11.39 tff(1092,plain,
% 11.25/11.39 (trans(s3, s4)),
% 11.25/11.39 inference(unit_resolution,[status(thm)],[1091, 1088, 93])).
% 11.25/11.39 tff(1093,plain,
% 11.25/11.39 (((~![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_3, c_j, s3, s4) | node6(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)) | node5(c_e_h_3, c_j, s3, s4) | node6(c_e_h_3, c_j, s3, s4))),
% 11.25/11.39 inference(rewrite,[status(thm)],[])).
% 11.25/11.39 tff(1094,plain,
% 11.25/11.39 ((node6(c_e_h_3, c_j, s3, s4) | node5(c_e_h_3, c_j, s3, s4) | (~trans(s3, s4))) <=> ((~trans(s3, s4)) | node5(c_e_h_3, c_j, s3, s4) | node6(c_e_h_3, c_j, s3, s4))),
% 11.25/11.39 inference(rewrite,[status(thm)],[])).
% 11.25/11.39 tff(1095,plain,
% 11.25/11.39 (((~![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)) | node5(c_e_h_3, c_j, s3, s4) | node6(c_e_h_3, c_j, s3, s4)))),
% 11.25/11.39 inference(monotonicity,[status(thm)],[1094])).
% 11.25/11.39 tff(1096,plain,
% 11.25/11.39 (((~![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)) | node5(c_e_h_3, c_j, s3, s4) | node6(c_e_h_3, c_j, s3, s4))),
% 11.25/11.39 inference(transitivity,[status(thm)],[1095, 1093])).
% 11.25/11.39 tff(1097,plain,
% 11.25/11.39 ((~![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)))),
% 11.25/11.39 inference(quant_inst,[status(thm)],[])).
% 11.25/11.39 tff(1098,plain,
% 11.25/11.39 ((~![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_3, c_j, s3, s4) | node6(c_e_h_3, c_j, s3, s4)),
% 11.25/11.39 inference(modus_ponens,[status(thm)],[1097, 1096])).
% 11.25/11.39 tff(1099,plain,
% 11.25/11.39 (node5(c_e_h_3, c_j, s3, s4) | node6(c_e_h_3, c_j, s3, s4)),
% 11.25/11.39 inference(unit_resolution,[status(thm)],[1098, 724, 1092])).
% 11.25/11.39 tff(1100,plain,
% 11.25/11.39 (node5(c_e_h_3, c_j, s3, s4)),
% 11.25/11.39 inference(unit_resolution,[status(thm)],[1099, 1085])).
% 11.25/11.39 tff(1101,assumption,(~m_or_h_gate_v_in2(c_e_h_3, c_j, s3)), introduced(assumption)).
% 11.25/11.39 tff(1102,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_j, s3)), introduced(assumption)).
% 11.25/11.39 tff(1103,plain,
% 11.25/11.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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_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)))),
% 11.25/11.39 inference(rewrite,[status(thm)],[])).
% 11.25/11.39 tff(1104,plain,
% 11.25/11.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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)))),
% 11.25/11.39 inference(quant_inst,[status(thm)],[])).
% 11.25/11.39 tff(1105,plain,
% 11.25/11.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3) | m_or_h_gate_v_in2(c_e_h_3, c_j, s3) | (~node5(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4))),
% 11.25/11.39 inference(modus_ponens,[status(thm)],[1104, 1103])).
% 11.25/11.39 tff(1106,plain,
% 11.25/11.39 ($false),
% 11.25/11.39 inference(unit_resolution,[status(thm)],[1105, 705, 927, 1102, 1101, 1100])).
% 11.25/11.39 tff(1107,plain,((~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) | m_or_h_gate_v_in2(c_e_h_3, c_j, s3)), inference(lemma,lemma(discharge,[]))).
% 11.25/11.39 tff(1108,plain,
% 11.25/11.39 (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)),
% 11.25/11.39 inference(unit_resolution,[status(thm)],[1107, 926, 649])).
% 11.25/11.39 tff(1109,assumption,(m_c_h_element_v_in2(c_e_h_3, c_h, s4)), introduced(assumption)).
% 11.25/11.39 tff(1110,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_j, s4)), introduced(assumption)).
% 11.25/11.39 tff(1111,plain,
% 11.25/11.39 (^[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)))),
% 11.25/11.39 inference(bind,[status(th)],[])).
% 11.25/11.39 tff(1112,plain,
% 11.25/11.39 (![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))),
% 11.25/11.39 inference(quant_intro,[status(thm)],[1111])).
% 11.25/11.40 tff(1113,plain,
% 11.25/11.40 (![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))),
% 11.25/11.40 inference(rewrite,[status(thm)],[])).
% 11.25/11.40 tff(1114,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')).
% 11.25/11.40 tff(1115,plain,
% 11.25/11.40 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1114, 1113])).
% 11.25/11.40 tff(1116,plain,(
% 11.25/11.40 ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))),
% 11.25/11.40 inference(skolemize,[status(sab)],[1115])).
% 11.25/11.40 tff(1117,plain,
% 11.25/11.40 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1116, 1112])).
% 11.25/11.40 tff(1118,plain,
% 11.25/11.40 (((~![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_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))),
% 11.25/11.40 inference(rewrite,[status(thm)],[])).
% 11.25/11.40 tff(1119,plain,
% 11.25/11.40 ((~![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_3, c_h, s4)) | m_or_h_gate_v_out(c_e_h_3, c_j, s4))),
% 11.25/11.40 inference(quant_inst,[status(thm)],[])).
% 11.25/11.40 tff(1120,plain,
% 11.25/11.40 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | m_or_h_gate_v_out(c_e_h_3, c_j, s4)),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1119, 1118])).
% 11.25/11.40 tff(1121,plain,
% 11.25/11.40 ($false),
% 11.25/11.40 inference(unit_resolution,[status(thm)],[1120, 1117, 1110, 1109])).
% 11.25/11.40 tff(1122,plain,(m_or_h_gate_v_out(c_e_h_3, c_j, s4) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4))), inference(lemma,lemma(discharge,[]))).
% 11.25/11.40 tff(1123,plain,
% 11.25/11.40 (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)),
% 11.25/11.40 inference(unit_resolution,[status(thm)],[1122, 1108])).
% 11.25/11.40 tff(1124,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s5)), introduced(assumption)).
% 11.25/11.40 tff(1125,assumption,(node5(c_e_h_3, c_j, s4, s5)), introduced(assumption)).
% 11.25/11.40 tff(1126,plain,
% 11.25/11.40 (^[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)))),
% 11.25/11.40 inference(bind,[status(th)],[])).
% 11.25/11.40 tff(1127,plain,
% 11.25/11.40 (![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))),
% 11.25/11.40 inference(quant_intro,[status(thm)],[1126])).
% 11.25/11.40 tff(1128,plain,
% 11.25/11.40 (![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))),
% 11.25/11.40 inference(rewrite,[status(thm)],[])).
% 11.25/11.40 tff(1129,plain,
% 11.25/11.40 (^[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)))),
% 11.25/11.40 inference(bind,[status(th)],[])).
% 11.25/11.40 tff(1130,plain,
% 11.25/11.40 (![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))),
% 11.25/11.40 inference(quant_intro,[status(thm)],[1129])).
% 11.25/11.40 tff(1131,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')).
% 11.25/11.40 tff(1132,plain,
% 11.25/11.40 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 11.25/11.40 tff(1133,plain,
% 11.25/11.40 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1132, 1128])).
% 11.25/11.40 tff(1134,plain,(
% 11.25/11.40 ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))),
% 11.25/11.40 inference(skolemize,[status(sab)],[1133])).
% 11.25/11.40 tff(1135,plain,
% 11.25/11.40 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1134, 1127])).
% 11.25/11.40 tff(1136,plain,
% 11.25/11.40 (((~![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, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3))) <=> ((~![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, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3))),
% 11.25/11.40 inference(rewrite,[status(thm)],[])).
% 11.25/11.40 tff(1137,plain,
% 11.25/11.40 ((~![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, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3))),
% 11.25/11.40 inference(quant_inst,[status(thm)],[])).
% 11.25/11.40 tff(1138,plain,
% 11.25/11.40 ((~![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, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3)),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1137, 1136])).
% 11.25/11.40 tff(1139,plain,
% 11.25/11.40 (~m_and_h_gate_v_out(c_e_h_3, c_l, s3)),
% 11.25/11.40 inference(unit_resolution,[status(thm)],[1138, 1135, 1102])).
% 11.25/11.40 tff(1140,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s4)), introduced(assumption)).
% 11.25/11.40 tff(1141,assumption,(node22(c_e_h_3, c_l, s3, s4)), introduced(assumption)).
% 11.25/11.40 tff(1142,plain,
% 11.25/11.40 (((~![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_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))),
% 11.25/11.40 inference(rewrite,[status(thm)],[])).
% 11.25/11.40 tff(1143,plain,
% 11.25/11.40 ((~![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_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))),
% 11.25/11.40 inference(quant_inst,[status(thm)],[])).
% 11.25/11.40 tff(1144,plain,
% 11.25/11.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | (~node22(c_e_h_3, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_l, s3)),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1143, 1142])).
% 11.25/11.40 tff(1145,plain,
% 11.25/11.40 ($false),
% 11.25/11.40 inference(unit_resolution,[status(thm)],[1144, 273, 1141, 912, 1140])).
% 11.25/11.40 tff(1146,plain,((~node22(c_e_h_3, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4))), inference(lemma,lemma(discharge,[]))).
% 11.25/11.40 tff(1147,plain,
% 11.25/11.40 (~node22(c_e_h_3, c_l, s3, s4)),
% 11.25/11.40 inference(unit_resolution,[status(thm)],[1146, 1140, 912])).
% 11.25/11.40 tff(1148,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_l, s3)), introduced(assumption)).
% 11.25/11.40 tff(1149,assumption,(m_or_h_gate_v_out(c_e_h_3, c_g, s2)), introduced(assumption)).
% 11.25/11.40 tff(1150,assumption,(m_and_h_gate_v_out(c_e_h_3, c_d, s1)), introduced(assumption)).
% 11.25/11.40 tff(1151,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_b, s0)), introduced(assumption)).
% 11.25/11.40 tff(1152,plain,
% 11.25/11.40 (^[I0: $i, I1: $i] : refl((~m_mutex_h_half_v_out(I0, I1, s0)) <=> (~m_mutex_h_half_v_out(I0, I1, s0)))),
% 11.25/11.40 inference(bind,[status(th)],[])).
% 11.25/11.40 tff(1153,plain,
% 11.25/11.40 (![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))),
% 11.25/11.40 inference(quant_intro,[status(thm)],[1152])).
% 11.25/11.40 tff(1154,plain,
% 11.25/11.40 (![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))),
% 11.25/11.40 inference(rewrite,[status(thm)],[])).
% 11.25/11.40 tff(1155,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')).
% 11.25/11.40 tff(1156,plain,
% 11.25/11.40 (![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1155, 1154])).
% 11.25/11.40 tff(1157,plain,(
% 11.25/11.40 ![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))),
% 11.25/11.40 inference(skolemize,[status(sab)],[1156])).
% 11.25/11.40 tff(1158,plain,
% 11.25/11.40 (![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1157, 1153])).
% 11.25/11.40 tff(1159,plain,
% 11.25/11.40 ((~![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s0))),
% 11.25/11.40 inference(quant_inst,[status(thm)],[])).
% 11.25/11.40 tff(1160,plain,
% 11.25/11.40 ($false),
% 11.25/11.40 inference(unit_resolution,[status(thm)],[1159, 1158, 1151])).
% 11.25/11.40 tff(1161,plain,(~m_mutex_h_half_v_out(c_e_h_3, c_b, s0)), inference(lemma,lemma(discharge,[]))).
% 11.25/11.40 tff(1162,plain,
% 11.25/11.40 (^[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)))),
% 11.25/11.40 inference(bind,[status(th)],[])).
% 11.25/11.40 tff(1163,plain,
% 11.25/11.40 (![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))),
% 11.25/11.40 inference(quant_intro,[status(thm)],[1162])).
% 11.25/11.40 tff(1164,plain,
% 11.25/11.40 (![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))),
% 11.25/11.40 inference(rewrite,[status(thm)],[])).
% 11.25/11.40 tff(1165,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')).
% 11.25/11.40 tff(1166,plain,
% 11.25/11.40 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1165, 1164])).
% 11.25/11.40 tff(1167,plain,(
% 11.25/11.40 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))),
% 11.25/11.40 inference(skolemize,[status(sab)],[1166])).
% 11.25/11.40 tff(1168,plain,
% 11.25/11.40 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1167, 1163])).
% 11.25/11.40 tff(1169,plain,
% 11.25/11.40 (((~![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))),
% 11.25/11.40 inference(rewrite,[status(thm)],[])).
% 11.25/11.40 tff(1170,plain,
% 11.25/11.40 ((~![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))),
% 11.25/11.40 inference(quant_inst,[status(thm)],[])).
% 11.25/11.40 tff(1171,plain,
% 11.25/11.40 ((~![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)),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1170, 1169])).
% 11.25/11.40 tff(1172,plain,
% 11.25/11.40 (~m_and_h_gate_v_in1(c_e_h_3, c_d, s0)),
% 11.25/11.40 inference(unit_resolution,[status(thm)],[1171, 1168, 1161])).
% 11.25/11.40 tff(1173,plain,
% 11.25/11.40 (((~![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))),
% 11.25/11.40 inference(rewrite,[status(thm)],[])).
% 11.25/11.40 tff(1174,plain,
% 11.25/11.40 ((~![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))),
% 11.25/11.40 inference(quant_inst,[status(thm)],[])).
% 11.25/11.40 tff(1175,plain,
% 11.25/11.40 ((~![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)),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1174, 1173])).
% 11.25/11.40 tff(1176,plain,
% 11.25/11.40 (~node20(c_e_h_3, c_d, s0)),
% 11.25/11.40 inference(unit_resolution,[status(thm)],[1175, 213, 1172])).
% 11.25/11.40 tff(1177,assumption,(node21(c_e_h_3, c_d, s0, s1)), introduced(assumption)).
% 11.25/11.40 tff(1178,plain,
% 11.25/11.40 (((~![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_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)))),
% 11.25/11.40 inference(rewrite,[status(thm)],[])).
% 11.25/11.40 tff(1179,plain,
% 11.25/11.40 ((~![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_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)))),
% 11.25/11.40 inference(quant_inst,[status(thm)],[])).
% 11.25/11.40 tff(1180,plain,
% 11.25/11.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_d, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s1)) | (~node21(c_e_h_3, c_d, s0, s1))),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1179, 1178])).
% 11.25/11.40 tff(1181,plain,
% 11.25/11.40 ($false),
% 11.25/11.40 inference(unit_resolution,[status(thm)],[1180, 228, 1177, 1176, 1150])).
% 11.25/11.40 tff(1182,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,[]))).
% 11.25/11.40 tff(1183,plain,
% 11.25/11.40 (~node21(c_e_h_3, c_d, s0, s1)),
% 11.25/11.40 inference(unit_resolution,[status(thm)],[1182, 1150])).
% 11.25/11.40 tff(1184,plain,
% 11.25/11.40 (((~![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))),
% 11.25/11.40 inference(rewrite,[status(thm)],[])).
% 11.25/11.40 tff(1185,plain,
% 11.25/11.40 ((~![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))),
% 11.25/11.40 inference(quant_inst,[status(thm)],[])).
% 11.25/11.40 tff(1186,plain,
% 11.25/11.40 ((~![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)),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1185, 1184])).
% 11.25/11.40 tff(1187,plain,
% 11.25/11.40 (node21(c_e_h_3, c_d, s0, s1) | node22(c_e_h_3, c_d, s0, s1)),
% 11.25/11.40 inference(unit_resolution,[status(thm)],[1186, 247, 100])).
% 11.25/11.40 tff(1188,plain,
% 11.25/11.40 (node22(c_e_h_3, c_d, s0, s1)),
% 11.25/11.40 inference(unit_resolution,[status(thm)],[1187, 1183])).
% 11.25/11.40 tff(1189,plain,
% 11.25/11.40 (((~![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_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))),
% 11.25/11.40 inference(rewrite,[status(thm)],[])).
% 11.25/11.40 tff(1190,plain,
% 11.25/11.40 ((~![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_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))),
% 11.25/11.40 inference(quant_inst,[status(thm)],[])).
% 11.25/11.40 tff(1191,plain,
% 11.25/11.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s1)) | (~node22(c_e_h_3, c_d, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0)),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1190, 1189])).
% 11.25/11.40 tff(1192,plain,
% 11.25/11.40 ($false),
% 11.25/11.40 inference(unit_resolution,[status(thm)],[1191, 273, 668, 1188, 1150])).
% 11.25/11.40 tff(1193,plain,(~m_and_h_gate_v_out(c_e_h_3, c_d, s1)), inference(lemma,lemma(discharge,[]))).
% 11.25/11.40 tff(1194,plain,
% 11.25/11.40 (((~![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))),
% 11.25/11.40 inference(rewrite,[status(thm)],[])).
% 11.25/11.40 tff(1195,plain,
% 11.25/11.40 ((~![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))),
% 11.25/11.40 inference(quant_inst,[status(thm)],[])).
% 11.25/11.40 tff(1196,plain,
% 11.25/11.40 ((~![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)),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1195, 1194])).
% 11.25/11.40 tff(1197,plain,
% 11.25/11.40 (~m_or_h_gate_v_in2(c_e_h_3, c_g, s1)),
% 11.25/11.40 inference(unit_resolution,[status(thm)],[1196, 675, 1193])).
% 11.25/11.40 tff(1198,assumption,(m_and_h_gate_v_out(c_e_h_3, c_c, s1)), introduced(assumption)).
% 11.25/11.40 tff(1199,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_a, s0)), introduced(assumption)).
% 11.25/11.40 tff(1200,plain,
% 11.25/11.40 ((~![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s0))),
% 11.25/11.40 inference(quant_inst,[status(thm)],[])).
% 11.25/11.40 tff(1201,plain,
% 11.25/11.40 ($false),
% 11.25/11.40 inference(unit_resolution,[status(thm)],[1200, 1158, 1199])).
% 11.25/11.40 tff(1202,plain,(~m_mutex_h_half_v_out(c_e_h_3, c_a, s0)), inference(lemma,lemma(discharge,[]))).
% 11.25/11.40 tff(1203,plain,
% 11.25/11.40 (^[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)))),
% 11.25/11.40 inference(bind,[status(th)],[])).
% 11.25/11.40 tff(1204,plain,
% 11.25/11.40 (![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))),
% 11.25/11.40 inference(quant_intro,[status(thm)],[1203])).
% 11.25/11.40 tff(1205,plain,
% 11.25/11.40 (![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))),
% 11.25/11.40 inference(rewrite,[status(thm)],[])).
% 11.25/11.40 tff(1206,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')).
% 11.25/11.40 tff(1207,plain,
% 11.25/11.40 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1206, 1205])).
% 11.25/11.40 tff(1208,plain,(
% 11.25/11.40 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))),
% 11.25/11.40 inference(skolemize,[status(sab)],[1207])).
% 11.25/11.40 tff(1209,plain,
% 11.25/11.40 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1208, 1204])).
% 11.25/11.40 tff(1210,plain,
% 11.25/11.40 (((~![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))),
% 11.25/11.40 inference(rewrite,[status(thm)],[])).
% 11.25/11.40 tff(1211,plain,
% 11.25/11.40 ((~![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))),
% 11.25/11.40 inference(quant_inst,[status(thm)],[])).
% 11.25/11.40 tff(1212,plain,
% 11.25/11.40 ((~![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)),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1211, 1210])).
% 11.25/11.40 tff(1213,plain,
% 11.25/11.40 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s0)),
% 11.25/11.40 inference(unit_resolution,[status(thm)],[1212, 1209, 1202])).
% 11.25/11.40 tff(1214,plain,
% 11.25/11.40 (((~![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))),
% 11.25/11.40 inference(rewrite,[status(thm)],[])).
% 11.25/11.40 tff(1215,plain,
% 11.25/11.40 ((~![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))),
% 11.25/11.40 inference(quant_inst,[status(thm)],[])).
% 11.25/11.40 tff(1216,plain,
% 11.25/11.40 ((~![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)),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1215, 1214])).
% 11.25/11.40 tff(1217,plain,
% 11.25/11.40 (~node20(c_e_h_3, c_c, s0)),
% 11.25/11.40 inference(unit_resolution,[status(thm)],[1216, 213, 1213])).
% 11.25/11.40 tff(1218,assumption,(node21(c_e_h_3, c_c, s0, s1)), introduced(assumption)).
% 11.25/11.40 tff(1219,plain,
% 11.25/11.40 (((~![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_3, c_c, s0) | (~node21(c_e_h_3, c_c, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, 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) | (~node21(c_e_h_3, c_c, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1)))),
% 11.25/11.40 inference(rewrite,[status(thm)],[])).
% 11.25/11.40 tff(1220,plain,
% 11.25/11.40 ((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))) <=> (node20(c_e_h_3, c_c, s0) | (~node21(c_e_h_3, c_c, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1)))),
% 11.25/11.40 inference(rewrite,[status(thm)],[])).
% 11.25/11.40 tff(1221,plain,
% 11.25/11.40 (((~![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_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) | (~node21(c_e_h_3, c_c, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1))))),
% 11.25/11.40 inference(monotonicity,[status(thm)],[1220])).
% 11.25/11.40 tff(1222,plain,
% 11.25/11.40 (((~![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_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) | (~node21(c_e_h_3, c_c, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1)))),
% 11.25/11.40 inference(transitivity,[status(thm)],[1221, 1219])).
% 11.25/11.40 tff(1223,plain,
% 11.25/11.40 ((~![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_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)))),
% 11.25/11.40 inference(quant_inst,[status(thm)],[])).
% 11.25/11.40 tff(1224,plain,
% 11.25/11.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_c, s0) | (~node21(c_e_h_3, c_c, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1))),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1223, 1222])).
% 11.25/11.40 tff(1225,plain,
% 11.25/11.40 ($false),
% 11.25/11.40 inference(unit_resolution,[status(thm)],[1224, 228, 1198, 1218, 1217])).
% 11.25/11.40 tff(1226,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,[]))).
% 11.25/11.40 tff(1227,plain,
% 11.25/11.40 (~node21(c_e_h_3, c_c, s0, s1)),
% 11.25/11.40 inference(unit_resolution,[status(thm)],[1226, 1198])).
% 11.25/11.40 tff(1228,plain,
% 11.25/11.40 (((~![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))),
% 11.25/11.40 inference(rewrite,[status(thm)],[])).
% 11.25/11.40 tff(1229,plain,
% 11.25/11.40 ((~![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))),
% 11.25/11.40 inference(quant_inst,[status(thm)],[])).
% 11.25/11.40 tff(1230,plain,
% 11.25/11.40 ((~![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)),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1229, 1228])).
% 11.25/11.40 tff(1231,plain,
% 11.25/11.40 (node21(c_e_h_3, c_c, s0, s1) | node22(c_e_h_3, c_c, s0, s1)),
% 11.25/11.40 inference(unit_resolution,[status(thm)],[1230, 247, 100])).
% 11.25/11.40 tff(1232,plain,
% 11.25/11.40 (node22(c_e_h_3, c_c, s0, s1)),
% 11.25/11.40 inference(unit_resolution,[status(thm)],[1231, 1227])).
% 11.25/11.40 tff(1233,plain,
% 11.25/11.40 (((~![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_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))),
% 11.25/11.40 inference(rewrite,[status(thm)],[])).
% 11.25/11.40 tff(1234,plain,
% 11.25/11.40 ((~![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_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))),
% 11.25/11.40 inference(quant_inst,[status(thm)],[])).
% 11.25/11.40 tff(1235,plain,
% 11.25/11.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1)) | (~node22(c_e_h_3, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0)),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1234, 1233])).
% 11.25/11.40 tff(1236,plain,
% 11.25/11.40 ($false),
% 11.25/11.40 inference(unit_resolution,[status(thm)],[1235, 273, 684, 1198, 1232])).
% 11.25/11.40 tff(1237,plain,(~m_and_h_gate_v_out(c_e_h_3, c_c, s1)), inference(lemma,lemma(discharge,[]))).
% 11.25/11.40 tff(1238,plain,
% 11.25/11.40 (((~![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))),
% 11.25/11.40 inference(rewrite,[status(thm)],[])).
% 11.25/11.40 tff(1239,plain,
% 11.25/11.40 ((~![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))),
% 11.25/11.40 inference(quant_inst,[status(thm)],[])).
% 11.25/11.40 tff(1240,plain,
% 11.25/11.40 ((~![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)),
% 11.25/11.40 inference(modus_ponens,[status(thm)],[1239, 1238])).
% 11.25/11.40 tff(1241,plain,
% 11.25/11.40 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s1)),
% 11.25/11.40 inference(unit_resolution,[status(thm)],[1240, 691, 1237])).
% 11.25/11.40 tff(1242,assumption,(node5(c_e_h_3, c_g, s1, s2)), introduced(assumption)).
% 11.25/11.40 tff(1243,plain,
% 11.25/11.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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_g, s1) | (~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) | (~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_in2(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_in1(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2)))),
% 11.25/11.41 inference(rewrite,[status(thm)],[])).
% 11.25/11.41 tff(1244,plain,
% 11.25/11.41 ((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_in2(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_in1(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2)))),
% 11.25/11.41 inference(rewrite,[status(thm)],[])).
% 11.25/11.41 tff(1245,plain,
% 11.25/11.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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_in2(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_in1(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2))))),
% 11.25/11.41 inference(monotonicity,[status(thm)],[1244])).
% 11.25/11.41 tff(1246,plain,
% 11.25/11.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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_in2(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_in1(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2)))),
% 11.25/11.41 inference(transitivity,[status(thm)],[1245, 1243])).
% 11.25/11.41 tff(1247,plain,
% 11.25/11.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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)))),
% 11.25/11.41 inference(quant_inst,[status(thm)],[])).
% 11.25/11.41 tff(1248,plain,
% 11.25/11.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2))),
% 11.25/11.41 inference(modus_ponens,[status(thm)],[1247, 1246])).
% 11.25/11.41 tff(1249,plain,
% 11.25/11.41 ($false),
% 11.25/11.41 inference(unit_resolution,[status(thm)],[1248, 705, 1242, 1241, 1197, 1149])).
% 11.25/11.41 tff(1250,plain,((~node5(c_e_h_3, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2))), inference(lemma,lemma(discharge,[]))).
% 11.25/11.41 tff(1251,plain,
% 11.25/11.41 (~node5(c_e_h_3, c_g, s1, s2)),
% 11.25/11.41 inference(unit_resolution,[status(thm)],[1250, 1149])).
% 11.25/11.41 tff(1252,plain,
% 11.25/11.41 (((~![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))),
% 11.25/11.41 inference(rewrite,[status(thm)],[])).
% 11.25/11.41 tff(1253,plain,
% 11.25/11.41 ((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))),
% 11.25/11.41 inference(rewrite,[status(thm)],[])).
% 11.25/11.41 tff(1254,plain,
% 11.25/11.41 (((~![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)))),
% 11.25/11.41 inference(monotonicity,[status(thm)],[1253])).
% 11.25/11.41 tff(1255,plain,
% 11.25/11.41 (((~![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))),
% 11.25/11.41 inference(transitivity,[status(thm)],[1254, 1252])).
% 11.25/11.41 tff(1256,plain,
% 11.25/11.41 ((~![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)))),
% 11.25/11.41 inference(quant_inst,[status(thm)],[])).
% 11.25/11.41 tff(1257,plain,
% 11.25/11.41 ((~![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)),
% 11.25/11.41 inference(modus_ponens,[status(thm)],[1256, 1255])).
% 11.25/11.41 tff(1258,plain,
% 11.25/11.41 (node6(c_e_h_3, c_g, s1, s2) | node5(c_e_h_3, c_g, s1, s2)),
% 11.25/11.41 inference(unit_resolution,[status(thm)],[1257, 724, 470])).
% 11.25/11.41 tff(1259,plain,
% 11.25/11.41 (node6(c_e_h_3, c_g, s1, s2)),
% 11.25/11.41 inference(unit_resolution,[status(thm)],[1258, 1251])).
% 11.25/11.41 tff(1260,plain,
% 11.25/11.41 (((~![Y: $i, I0: $i, X: $i, I1: $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)))),
% 11.25/11.41 inference(rewrite,[status(thm)],[])).
% 11.25/11.41 tff(1261,plain,
% 11.25/11.41 (((~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)))),
% 11.25/11.41 inference(rewrite,[status(thm)],[])).
% 11.25/11.41 tff(1262,plain,
% 11.25/11.41 (((~![Y: $i, I0: $i, X: $i, I1: $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))))),
% 11.25/11.41 inference(monotonicity,[status(thm)],[1261])).
% 11.25/11.41 tff(1263,plain,
% 11.25/11.41 (((~![Y: $i, I0: $i, X: $i, I1: $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)))),
% 11.25/11.41 inference(transitivity,[status(thm)],[1262, 1260])).
% 11.25/11.41 tff(1264,plain,
% 11.25/11.41 ((~![Y: $i, I0: $i, X: $i, I1: $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))),
% 11.25/11.41 inference(quant_inst,[status(thm)],[])).
% 11.25/11.41 tff(1265,plain,
% 11.25/11.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | (~node6(c_e_h_3, c_g, s1, s2))),
% 11.25/11.41 inference(modus_ponens,[status(thm)],[1264, 1263])).
% 11.25/11.41 tff(1266,plain,
% 11.25/11.41 ($false),
% 11.25/11.41 inference(unit_resolution,[status(thm)],[1265, 742, 750, 1259, 1149])).
% 11.25/11.41 tff(1267,plain,(~m_or_h_gate_v_out(c_e_h_3, c_g, s2)), inference(lemma,lemma(discharge,[]))).
% 11.25/11.41 tff(1268,plain,
% 11.25/11.41 (((~![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))),
% 11.25/11.41 inference(rewrite,[status(thm)],[])).
% 11.25/11.41 tff(1269,plain,
% 11.25/11.41 ((~![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))),
% 11.25/11.41 inference(quant_inst,[status(thm)],[])).
% 11.25/11.41 tff(1270,plain,
% 11.25/11.41 ((~![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)),
% 11.25/11.41 inference(modus_ponens,[status(thm)],[1269, 1268])).
% 11.25/11.41 tff(1271,plain,
% 11.25/11.41 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s2)),
% 11.25/11.41 inference(unit_resolution,[status(thm)],[1270, 757, 1267])).
% 11.25/11.41 tff(1272,plain,
% 11.25/11.41 (((~![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))),
% 11.25/11.41 inference(rewrite,[status(thm)],[])).
% 11.25/11.41 tff(1273,plain,
% 11.25/11.41 ((~![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))),
% 11.25/11.41 inference(quant_inst,[status(thm)],[])).
% 11.25/11.41 tff(1274,plain,
% 11.25/11.41 ((~![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)),
% 11.25/11.41 inference(modus_ponens,[status(thm)],[1273, 1272])).
% 11.25/11.41 tff(1275,plain,
% 11.25/11.41 (~node20(c_e_h_3, c_k, s2)),
% 11.25/11.41 inference(unit_resolution,[status(thm)],[1274, 213, 1271])).
% 11.25/11.41 tff(1276,assumption,(m_and_h_gate_v_out(c_e_h_3, c_k, s3)), introduced(assumption)).
% 11.25/11.41 tff(1277,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_k, s2)), introduced(assumption)).
% 11.25/11.41 tff(1278,assumption,(~node20(c_e_h_3, c_k, s2)), introduced(assumption)).
% 11.25/11.41 tff(1279,assumption,(node21(c_e_h_3, c_k, s2, s3)), introduced(assumption)).
% 11.25/11.41 tff(1280,plain,
% 11.25/11.41 (((~![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_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) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3)) | (~node21(c_e_h_3, c_k, s2, s3)))),
% 11.25/11.41 inference(rewrite,[status(thm)],[])).
% 11.25/11.41 tff(1281,plain,
% 11.25/11.41 ((~![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_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)))),
% 11.25/11.41 inference(quant_inst,[status(thm)],[])).
% 11.25/11.41 tff(1282,plain,
% 11.25/11.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3)) | (~node21(c_e_h_3, c_k, s2, s3))),
% 11.25/11.41 inference(modus_ponens,[status(thm)],[1281, 1280])).
% 11.25/11.41 tff(1283,plain,
% 11.25/11.41 ($false),
% 11.25/11.41 inference(unit_resolution,[status(thm)],[1282, 228, 1279, 1278, 1276])).
% 11.25/11.41 tff(1284,plain,((~node21(c_e_h_3, c_k, s2, s3)) | node20(c_e_h_3, c_k, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3))), inference(lemma,lemma(discharge,[]))).
% 11.25/11.41 tff(1285,plain,
% 11.25/11.41 (~node21(c_e_h_3, c_k, s2, s3)),
% 11.25/11.41 inference(unit_resolution,[status(thm)],[1284, 1276, 1278])).
% 11.25/11.41 tff(1286,plain,
% 11.25/11.41 (((~![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))),
% 11.25/11.41 inference(rewrite,[status(thm)],[])).
% 11.25/11.41 tff(1287,plain,
% 11.25/11.41 ((~![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))),
% 11.25/11.41 inference(quant_inst,[status(thm)],[])).
% 11.25/11.41 tff(1288,plain,
% 11.25/11.41 ((~![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)),
% 11.25/11.41 inference(modus_ponens,[status(thm)],[1287, 1286])).
% 11.25/11.41 tff(1289,plain,
% 11.25/11.41 (node21(c_e_h_3, c_k, s2, s3) | node22(c_e_h_3, c_k, s2, s3)),
% 11.25/11.41 inference(unit_resolution,[status(thm)],[1288, 247, 604])).
% 11.25/11.41 tff(1290,plain,
% 11.25/11.41 (node22(c_e_h_3, c_k, s2, s3)),
% 11.25/11.41 inference(unit_resolution,[status(thm)],[1289, 1285])).
% 11.25/11.41 tff(1291,plain,
% 11.25/11.41 (((~![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_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))),
% 11.25/11.41 inference(rewrite,[status(thm)],[])).
% 11.25/11.41 tff(1292,plain,
% 11.25/11.41 ((~![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_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))),
% 11.25/11.41 inference(quant_inst,[status(thm)],[])).
% 11.25/11.41 tff(1293,plain,
% 11.25/11.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3)) | (~node22(c_e_h_3, c_k, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_k, s2)),
% 11.25/11.41 inference(modus_ponens,[status(thm)],[1292, 1291])).
% 11.25/11.41 tff(1294,plain,
% 11.25/11.41 ($false),
% 11.25/11.41 inference(unit_resolution,[status(thm)],[1293, 273, 1290, 1277, 1276])).
% 11.25/11.41 tff(1295,plain,((~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) | node20(c_e_h_3, c_k, s2)), inference(lemma,lemma(discharge,[]))).
% 11.25/11.41 tff(1296,plain,
% 11.25/11.41 (~m_and_h_gate_v_out(c_e_h_3, c_k, s3)),
% 11.25/11.41 inference(unit_resolution,[status(thm)],[1295, 816, 1275])).
% 11.25/11.41 tff(1297,plain,
% 11.25/11.41 (((~![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))),
% 11.25/11.41 inference(rewrite,[status(thm)],[])).
% 11.25/11.41 tff(1298,plain,
% 11.25/11.41 ((~![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))),
% 11.25/11.41 inference(quant_inst,[status(thm)],[])).
% 11.25/11.41 tff(1299,plain,
% 11.25/11.41 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s3)) | m_and_h_gate_v_out(c_e_h_3, c_k, s3)),
% 11.25/11.41 inference(modus_ponens,[status(thm)],[1298, 1297])).
% 11.25/11.41 tff(1300,plain,
% 11.25/11.41 ($false),
% 11.25/11.41 inference(unit_resolution,[status(thm)],[1299, 823, 1296, 1148])).
% 11.25/11.41 tff(1301,plain,(~m_and_h_gate_v_in1(c_e_h_3, c_l, s3)), inference(lemma,lemma(discharge,[]))).
% 11.25/11.41 tff(1302,plain,
% 11.25/11.41 (((~![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))),
% 11.25/11.41 inference(rewrite,[status(thm)],[])).
% 11.25/11.41 tff(1303,plain,
% 11.25/11.41 ((~![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))),
% 11.25/11.41 inference(quant_inst,[status(thm)],[])).
% 11.25/11.41 tff(1304,plain,
% 11.25/11.41 ((~![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)),
% 11.25/11.41 inference(modus_ponens,[status(thm)],[1303, 1302])).
% 11.25/11.41 tff(1305,plain,
% 11.25/11.41 (~node20(c_e_h_3, c_l, s3)),
% 11.25/11.41 inference(unit_resolution,[status(thm)],[1304, 213, 1301])).
% 11.25/11.41 tff(1306,assumption,(~node20(c_e_h_3, c_l, s3)), introduced(assumption)).
% 11.25/11.41 tff(1307,assumption,(node21(c_e_h_3, c_l, s3, s4)), introduced(assumption)).
% 11.25/11.41 tff(1308,plain,
% 11.25/11.41 (((~![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_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)))) | 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)))),
% 11.25/11.41 inference(rewrite,[status(thm)],[])).
% 11.25/11.41 tff(1309,plain,
% 11.25/11.41 ((~![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_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)))),
% 11.25/11.41 inference(quant_inst,[status(thm)],[])).
% 11.25/11.41 tff(1310,plain,
% 11.25/11.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | (~node21(c_e_h_3, c_l, s3, s4))),
% 11.25/11.41 inference(modus_ponens,[status(thm)],[1309, 1308])).
% 11.25/11.41 tff(1311,plain,
% 11.25/11.41 ($false),
% 11.25/11.41 inference(unit_resolution,[status(thm)],[1310, 228, 1307, 1306, 1140])).
% 11.25/11.41 tff(1312,plain,((~node21(c_e_h_3, c_l, s3, s4)) | node20(c_e_h_3, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4))), inference(lemma,lemma(discharge,[]))).
% 11.25/11.41 tff(1313,plain,
% 11.25/11.41 (~node21(c_e_h_3, c_l, s3, s4)),
% 11.25/11.41 inference(unit_resolution,[status(thm)],[1312, 1140, 1305])).
% 11.25/11.41 tff(1314,plain,
% 11.25/11.41 (((~![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))),
% 11.25/11.41 inference(rewrite,[status(thm)],[])).
% 11.25/11.41 tff(1315,plain,
% 11.25/11.41 ((~![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))),
% 11.25/11.41 inference(quant_inst,[status(thm)],[])).
% 11.25/11.41 tff(1316,plain,
% 11.25/11.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_l, s3, s4) | node22(c_e_h_3, c_l, s3, s4)),
% 11.25/11.41 inference(modus_ponens,[status(thm)],[1315, 1314])).
% 11.25/11.41 tff(1317,plain,
% 11.25/11.41 (node21(c_e_h_3, c_l, s3, s4) | node22(c_e_h_3, c_l, s3, s4)),
% 11.25/11.41 inference(unit_resolution,[status(thm)],[1316, 247, 1092])).
% 11.25/11.41 tff(1318,plain,
% 11.25/11.41 ($false),
% 11.25/11.41 inference(unit_resolution,[status(thm)],[1317, 1313, 1147])).
% 11.25/11.41 tff(1319,plain,((~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | m_and_h_gate_v_out(c_e_h_3, c_l, s3)), inference(lemma,lemma(discharge,[]))).
% 11.25/11.41 tff(1320,plain,
% 11.25/11.41 (~m_and_h_gate_v_out(c_e_h_3, c_l, s4)),
% 11.25/11.41 inference(unit_resolution,[status(thm)],[1319, 1139])).
% 11.25/11.41 tff(1321,plain,
% 11.25/11.41 (((~![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))),
% 11.25/11.41 inference(rewrite,[status(thm)],[])).
% 11.25/11.41 tff(1322,plain,
% 11.25/11.41 ((~![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))),
% 11.25/11.41 inference(quant_inst,[status(thm)],[])).
% 11.25/11.41 tff(1323,plain,
% 11.25/11.41 ((~![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)),
% 11.25/11.41 inference(modus_ponens,[status(thm)],[1322, 1321])).
% 11.25/11.41 tff(1324,plain,
% 11.25/11.41 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s4)),
% 11.25/11.41 inference(unit_resolution,[status(thm)],[1323, 920, 1320])).
% 11.25/11.41 tff(1325,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_j, s4)), introduced(assumption)).
% 11.25/11.41 tff(1326,assumption,(~m_or_h_gate_v_in2(c_e_h_3, c_j, s4)), introduced(assumption)).
% 11.25/11.41 tff(1327,plain,
% 11.25/11.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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, s4) | m_or_h_gate_v_in1(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_in2(c_e_h_3, c_j, s4) | m_or_h_gate_v_in1(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)))),
% 11.25/11.41 inference(rewrite,[status(thm)],[])).
% 11.25/11.41 tff(1328,plain,
% 11.25/11.41 ((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_in2(c_e_h_3, c_j, s4) | m_or_h_gate_v_in1(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)))),
% 11.25/11.41 inference(rewrite,[status(thm)],[])).
% 11.25/11.41 tff(1329,plain,
% 11.25/11.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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_in2(c_e_h_3, c_j, s4) | m_or_h_gate_v_in1(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))))),
% 11.25/11.41 inference(monotonicity,[status(thm)],[1328])).
% 11.25/11.41 tff(1330,plain,
% 11.25/11.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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_in2(c_e_h_3, c_j, s4) | m_or_h_gate_v_in1(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)))),
% 11.25/11.41 inference(transitivity,[status(thm)],[1329, 1327])).
% 11.25/11.41 tff(1331,plain,
% 11.25/11.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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)))),
% 11.25/11.41 inference(quant_inst,[status(thm)],[])).
% 11.25/11.41 tff(1332,plain,
% 11.25/11.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s4) | m_or_h_gate_v_in1(c_e_h_3, c_j, s4) | (~node5(c_e_h_3, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5))),
% 11.25/11.41 inference(modus_ponens,[status(thm)],[1331, 1330])).
% 11.25/11.41 tff(1333,plain,
% 11.25/11.41 ($false),
% 11.25/11.41 inference(unit_resolution,[status(thm)],[1332, 705, 1124, 1326, 1325, 1125])).
% 11.25/11.41 tff(1334,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_in2(c_e_h_3, c_j, s4) | m_or_h_gate_v_in1(c_e_h_3, c_j, s4)), inference(lemma,lemma(discharge,[]))).
% 11.25/11.41 tff(1335,plain,
% 11.25/11.41 (m_or_h_gate_v_in2(c_e_h_3, c_j, s4)),
% 11.25/11.41 inference(unit_resolution,[status(thm)],[1334, 1324, 1124, 1125])).
% 11.25/11.41 tff(1336,plain,
% 11.25/11.41 (((~![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))),
% 11.25/11.41 inference(rewrite,[status(thm)],[])).
% 11.25/11.41 tff(1337,plain,
% 11.25/11.41 ((~![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))),
% 11.25/11.41 inference(quant_inst,[status(thm)],[])).
% 11.25/11.41 tff(1338,plain,
% 11.25/11.41 ((~![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)),
% 11.25/11.42 inference(modus_ponens,[status(thm)],[1337, 1336])).
% 11.25/11.42 tff(1339,plain,
% 11.25/11.42 (m_cell_v_ack(c_e_h_3, s4)),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1338, 645, 1335])).
% 11.25/11.42 tff(1340,plain,
% 11.25/11.42 (((~![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))),
% 11.25/11.42 inference(rewrite,[status(thm)],[])).
% 11.25/11.42 tff(1341,plain,
% 11.25/11.42 ((~![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))),
% 11.25/11.42 inference(quant_inst,[status(thm)],[])).
% 11.25/11.42 tff(1342,plain,
% 11.25/11.42 ((~![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)),
% 11.25/11.42 inference(modus_ponens,[status(thm)],[1341, 1340])).
% 11.25/11.42 tff(1343,plain,
% 11.25/11.42 (node3(c_e_h_2, c_e_h_3, s4)),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1342, 619, 616])).
% 11.25/11.42 tff(1344,plain,
% 11.25/11.42 (((~![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_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))),
% 11.25/11.42 inference(rewrite,[status(thm)],[])).
% 11.25/11.42 tff(1345,plain,
% 11.25/11.42 ((~![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_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))),
% 11.25/11.42 inference(quant_inst,[status(thm)],[])).
% 11.25/11.42 tff(1346,plain,
% 11.25/11.42 ((~![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_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)),
% 11.25/11.42 inference(modus_ponens,[status(thm)],[1345, 1344])).
% 11.25/11.42 tff(1347,plain,
% 11.25/11.42 ((~m_cell_v_ack(c_e_h_3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_q, s4)),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1346, 633, 1343])).
% 11.25/11.42 tff(1348,plain,
% 11.25/11.42 (m_and_h_gate_v_out(c_e_h_2, c_q, s4)),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1347, 1339])).
% 11.25/11.42 tff(1349,assumption,(m_c_h_element_v_out(c_e_h_2, c_f, s3)), introduced(assumption)).
% 11.25/11.42 tff(1350,assumption,(~m_c_h_element_v_out(c_e_h_2, c_f, s2)), introduced(assumption)).
% 11.25/11.42 tff(1351,assumption,(node15(c_e_h_2, c_f, s2, s3)), introduced(assumption)).
% 11.25/11.42 tff(1352,plain,
% 11.25/11.42 (((~![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_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))),
% 11.25/11.42 inference(rewrite,[status(thm)],[])).
% 11.25/11.42 tff(1353,plain,
% 11.25/11.42 ((~![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_f, s3)) | (~node15(c_e_h_2, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s2))),
% 11.25/11.42 inference(quant_inst,[status(thm)],[])).
% 11.25/11.42 tff(1354,plain,
% 11.25/11.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node15(c_e_h_2, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s2)),
% 11.25/11.42 inference(modus_ponens,[status(thm)],[1353, 1352])).
% 11.25/11.42 tff(1355,plain,
% 11.25/11.42 ($false),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1354, 393, 1350, 1349, 1351])).
% 11.25/11.42 tff(1356,plain,((~node15(c_e_h_2, c_f, s2, s3)) | 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, s3))), inference(lemma,lemma(discharge,[]))).
% 11.25/11.42 tff(1357,plain,
% 11.25/11.42 (~node15(c_e_h_2, c_f, s2, s3)),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1356, 1350, 1349])).
% 11.25/11.42 tff(1358,assumption,(~node15(c_e_h_2, c_f, s2, s3)), introduced(assumption)).
% 11.25/11.42 tff(1359,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_f, s2)), introduced(assumption)).
% 11.25/11.42 tff(1360,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s2)), introduced(assumption)).
% 11.25/11.42 tff(1361,plain,
% 11.25/11.42 (((~![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_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))),
% 11.25/11.42 inference(rewrite,[status(thm)],[])).
% 11.25/11.42 tff(1362,plain,
% 11.25/11.42 ((~![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_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))),
% 11.25/11.42 inference(quant_inst,[status(thm)],[])).
% 11.25/11.42 tff(1363,plain,
% 11.25/11.42 ((~![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_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)),
% 11.25/11.42 inference(modus_ponens,[status(thm)],[1362, 1361])).
% 11.25/11.42 tff(1364,plain,
% 11.25/11.42 ((~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | (~node22(c_e_h_2, c_i, s1, s2))),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1363, 273, 527])).
% 11.25/11.42 tff(1365,plain,
% 11.25/11.42 (~node22(c_e_h_2, c_i, s1, s2)),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1364, 1360])).
% 11.25/11.42 tff(1366,plain,
% 11.25/11.42 (((~![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))),
% 11.25/11.42 inference(rewrite,[status(thm)],[])).
% 11.25/11.42 tff(1367,plain,
% 11.25/11.42 ((~![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))),
% 11.25/11.42 inference(quant_inst,[status(thm)],[])).
% 11.25/11.42 tff(1368,plain,
% 11.25/11.42 ((~![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)),
% 11.25/11.42 inference(modus_ponens,[status(thm)],[1367, 1366])).
% 11.25/11.42 tff(1369,plain,
% 11.25/11.42 (node21(c_e_h_2, c_i, s1, s2)),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1368, 247, 470, 1365])).
% 11.25/11.42 tff(1370,assumption,(m_or_h_gate_v_out(c_e_h_2, c_g, s0)), introduced(assumption)).
% 11.25/11.42 tff(1371,plain,
% 11.25/11.42 ((~![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s0))),
% 11.25/11.42 inference(quant_inst,[status(thm)],[])).
% 11.25/11.42 tff(1372,plain,
% 11.25/11.42 ($false),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1371, 660, 1370])).
% 11.25/11.42 tff(1373,plain,(~m_or_h_gate_v_out(c_e_h_2, c_g, s0)), inference(lemma,lemma(discharge,[]))).
% 11.25/11.42 tff(1374,plain,
% 11.25/11.42 (^[I0: $i, X: $i] : refl(((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X)) <=> ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X)))),
% 11.25/11.42 inference(bind,[status(th)],[])).
% 11.25/11.42 tff(1375,plain,
% 11.25/11.42 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X)) <=> ![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 11.25/11.42 inference(quant_intro,[status(thm)],[1374])).
% 11.25/11.42 tff(1376,plain,
% 11.25/11.42 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X)) <=> ![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 11.25/11.42 inference(rewrite,[status(thm)],[])).
% 11.25/11.42 tff(1377,axiom,(![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_32')).
% 11.25/11.42 tff(1378,plain,
% 11.25/11.42 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 11.25/11.42 inference(modus_ponens,[status(thm)],[1377, 1376])).
% 11.25/11.42 tff(1379,plain,(
% 11.25/11.42 ![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 11.25/11.42 inference(skolemize,[status(sab)],[1378])).
% 11.25/11.42 tff(1380,plain,
% 11.25/11.42 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 11.25/11.42 inference(modus_ponens,[status(thm)],[1379, 1375])).
% 11.25/11.42 tff(1381,plain,
% 11.25/11.42 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s0)) | m_or_h_gate_v_out(c_e_h_2, c_g, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s0)) | m_or_h_gate_v_out(c_e_h_2, c_g, s0))),
% 11.25/11.42 inference(rewrite,[status(thm)],[])).
% 11.25/11.42 tff(1382,plain,
% 11.25/11.42 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s0)) | m_or_h_gate_v_out(c_e_h_2, c_g, s0))),
% 11.25/11.42 inference(quant_inst,[status(thm)],[])).
% 11.25/11.42 tff(1383,plain,
% 11.25/11.42 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s0)) | m_or_h_gate_v_out(c_e_h_2, c_g, s0)),
% 11.25/11.42 inference(modus_ponens,[status(thm)],[1382, 1381])).
% 11.25/11.42 tff(1384,plain,
% 11.25/11.42 (~m_c_h_element_v_in1(c_e_h_2, c_h, s0)),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1383, 1380, 1373])).
% 11.25/11.42 tff(1385,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s0)), introduced(assumption)).
% 11.25/11.42 tff(1386,plain,
% 11.25/11.42 ((~![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s0))),
% 11.25/11.42 inference(quant_inst,[status(thm)],[])).
% 11.25/11.42 tff(1387,plain,
% 11.25/11.42 ($false),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1386, 660, 1385])).
% 11.25/11.42 tff(1388,plain,(~m_or_h_gate_v_out(c_e_h_2, c_j, s0)), inference(lemma,lemma(discharge,[]))).
% 11.25/11.42 tff(1389,plain,
% 11.25/11.42 (((~![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))),
% 11.25/11.42 inference(rewrite,[status(thm)],[])).
% 11.25/11.42 tff(1390,plain,
% 11.25/11.42 ((~![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))),
% 11.25/11.42 inference(quant_inst,[status(thm)],[])).
% 11.25/11.42 tff(1391,plain,
% 11.25/11.42 ((~![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)),
% 11.25/11.42 inference(modus_ponens,[status(thm)],[1390, 1389])).
% 11.25/11.42 tff(1392,plain,
% 11.25/11.42 (~m_c_h_element_v_in2(c_e_h_2, c_h, s0)),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1391, 1117, 1388])).
% 11.25/11.42 tff(1393,plain,
% 11.25/11.42 (((~![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_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))),
% 11.25/11.42 inference(rewrite,[status(thm)],[])).
% 11.25/11.42 tff(1394,plain,
% 11.25/11.42 ((~![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_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))),
% 11.25/11.42 inference(quant_inst,[status(thm)],[])).
% 11.25/11.42 tff(1395,plain,
% 11.25/11.42 ((~![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_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)),
% 11.25/11.42 inference(modus_ponens,[status(thm)],[1394, 1393])).
% 11.25/11.42 tff(1396,plain,
% 11.25/11.42 ((~node16(c_e_h_2, c_h, s0)) | m_c_h_element_v_in2(c_e_h_2, c_h, s0)),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1395, 377, 1384])).
% 11.25/11.42 tff(1397,plain,
% 11.25/11.42 (~node16(c_e_h_2, c_h, s0)),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1396, 1392])).
% 11.25/11.42 tff(1398,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s0)), introduced(assumption)).
% 11.25/11.42 tff(1399,assumption,(~node16(c_e_h_2, c_h, s0)), introduced(assumption)).
% 11.25/11.42 tff(1400,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s1)), introduced(assumption)).
% 11.25/11.42 tff(1401,plain,
% 11.25/11.42 (((~![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_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))),
% 11.25/11.42 inference(rewrite,[status(thm)],[])).
% 11.25/11.42 tff(1402,plain,
% 11.25/11.42 ((~![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_h, s1)) | (~node15(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0))),
% 11.25/11.42 inference(quant_inst,[status(thm)],[])).
% 11.25/11.42 tff(1403,plain,
% 11.25/11.42 ((~![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_h, s1)) | (~node15(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0)),
% 11.25/11.42 inference(modus_ponens,[status(thm)],[1402, 1401])).
% 11.25/11.42 tff(1404,plain,
% 11.25/11.42 ((~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | (~node15(c_e_h_2, c_h, s0, s1))),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1403, 393, 496])).
% 11.25/11.42 tff(1405,plain,
% 11.25/11.42 (~node15(c_e_h_2, c_h, s0, s1)),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1404, 1400])).
% 11.25/11.42 tff(1406,assumption,(~node19(c_e_h_2, c_h, s0, s1)), introduced(assumption)).
% 11.25/11.42 tff(1407,plain,
% 11.25/11.42 (((~![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))),
% 11.25/11.42 inference(rewrite,[status(thm)],[])).
% 11.25/11.42 tff(1408,plain,
% 11.25/11.42 ((~![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))),
% 11.25/11.42 inference(quant_inst,[status(thm)],[])).
% 11.25/11.42 tff(1409,plain,
% 11.25/11.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_2, c_h, s0, s1)),
% 11.25/11.42 inference(modus_ponens,[status(thm)],[1408, 1407])).
% 11.25/11.42 tff(1410,plain,
% 11.25/11.42 ($false),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1409, 312, 100, 1406])).
% 11.25/11.42 tff(1411,plain,(node19(c_e_h_2, c_h, s0, s1)), inference(lemma,lemma(discharge,[]))).
% 11.25/11.42 tff(1412,plain,
% 11.25/11.42 (((~![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)))) | (node15(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)) | node14(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)))) | node15(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)) | node14(c_e_h_2, c_h, s0, s1))),
% 11.25/11.42 inference(rewrite,[status(thm)],[])).
% 11.25/11.42 tff(1413,plain,
% 11.25/11.42 ((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))) <=> (node15(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)) | node14(c_e_h_2, c_h, s0, s1))),
% 11.25/11.42 inference(rewrite,[status(thm)],[])).
% 11.25/11.42 tff(1414,plain,
% 11.25/11.42 (((~![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_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)))) | (node15(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)) | node14(c_e_h_2, c_h, s0, s1)))),
% 11.25/11.42 inference(monotonicity,[status(thm)],[1413])).
% 11.25/11.42 tff(1415,plain,
% 11.25/11.42 (((~![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_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)))) | node15(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)) | node14(c_e_h_2, c_h, s0, s1))),
% 11.25/11.42 inference(transitivity,[status(thm)],[1414, 1412])).
% 11.25/11.42 tff(1416,plain,
% 11.25/11.42 ((~![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_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)))),
% 11.25/11.42 inference(quant_inst,[status(thm)],[])).
% 11.25/11.42 tff(1417,plain,
% 11.25/11.42 ((~![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)))) | node15(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)) | node14(c_e_h_2, c_h, s0, s1)),
% 11.25/11.42 inference(modus_ponens,[status(thm)],[1416, 1415])).
% 11.25/11.42 tff(1418,plain,
% 11.25/11.42 (node15(c_e_h_2, c_h, s0, s1) | node16(c_e_h_2, c_h, s0) | node14(c_e_h_2, c_h, s0, s1)),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1417, 409, 1411])).
% 11.25/11.42 tff(1419,plain,
% 11.25/11.42 (node14(c_e_h_2, c_h, s0, s1)),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1418, 1405, 1399])).
% 11.25/11.42 tff(1420,plain,
% 11.25/11.42 (((~![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_h, s0) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | (~node14(c_e_h_2, 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_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)))),
% 11.25/11.42 inference(rewrite,[status(thm)],[])).
% 11.25/11.42 tff(1421,plain,
% 11.25/11.42 (((~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))) <=> (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)))),
% 11.25/11.42 inference(rewrite,[status(thm)],[])).
% 11.25/11.42 tff(1422,plain,
% 11.25/11.42 (((~![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_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)))) | (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))))),
% 11.25/11.42 inference(monotonicity,[status(thm)],[1421])).
% 11.25/11.42 tff(1423,plain,
% 11.25/11.42 (((~![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_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)))) | 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)))),
% 11.25/11.42 inference(transitivity,[status(thm)],[1422, 1420])).
% 11.25/11.42 tff(1424,plain,
% 11.25/11.42 ((~![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_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)))),
% 11.25/11.42 inference(quant_inst,[status(thm)],[])).
% 11.25/11.42 tff(1425,plain,
% 11.25/11.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | (~node14(c_e_h_2, c_h, s0, s1))),
% 11.25/11.42 inference(modus_ponens,[status(thm)],[1424, 1423])).
% 11.25/11.42 tff(1426,plain,
% 11.25/11.42 ($false),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1425, 427, 1400, 1419, 1398])).
% 11.25/11.42 tff(1427,plain,((~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) | node16(c_e_h_2, c_h, s0)), inference(lemma,lemma(discharge,[]))).
% 11.25/11.42 tff(1428,plain,
% 11.25/11.42 (~m_c_h_element_v_out(c_e_h_2, c_h, s1)),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1427, 1397, 1384])).
% 11.25/11.42 tff(1429,plain,
% 11.25/11.42 (((~![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))),
% 11.25/11.42 inference(rewrite,[status(thm)],[])).
% 11.25/11.42 tff(1430,plain,
% 11.25/11.42 ((~![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))),
% 11.25/11.42 inference(quant_inst,[status(thm)],[])).
% 11.25/11.42 tff(1431,plain,
% 11.25/11.42 ((~![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)),
% 11.25/11.42 inference(modus_ponens,[status(thm)],[1430, 1429])).
% 11.25/11.42 tff(1432,plain,
% 11.25/11.42 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s1)),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1431, 503, 1428])).
% 11.25/11.42 tff(1433,plain,
% 11.25/11.42 (((~![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))),
% 11.25/11.42 inference(rewrite,[status(thm)],[])).
% 11.25/11.42 tff(1434,plain,
% 11.25/11.42 ((~![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))),
% 11.25/11.42 inference(quant_inst,[status(thm)],[])).
% 11.25/11.42 tff(1435,plain,
% 11.25/11.42 ((~![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)),
% 11.25/11.42 inference(modus_ponens,[status(thm)],[1434, 1433])).
% 11.25/11.42 tff(1436,plain,
% 11.25/11.42 (~node20(c_e_h_2, c_i, s1)),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1435, 213, 1432])).
% 11.25/11.42 tff(1437,plain,
% 11.25/11.42 (((~![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_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) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | (~node21(c_e_h_2, c_i, s1, s2)))),
% 11.25/11.42 inference(rewrite,[status(thm)],[])).
% 11.25/11.42 tff(1438,plain,
% 11.25/11.42 ((~![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_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)))),
% 11.25/11.42 inference(quant_inst,[status(thm)],[])).
% 11.25/11.42 tff(1439,plain,
% 11.25/11.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | (~node21(c_e_h_2, c_i, s1, s2))),
% 11.25/11.42 inference(modus_ponens,[status(thm)],[1438, 1437])).
% 11.25/11.42 tff(1440,plain,
% 11.25/11.42 ($false),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1439, 228, 1360, 1436, 1369])).
% 11.25/11.42 tff(1441,plain,(~m_and_h_gate_v_out(c_e_h_2, c_i, s2)), inference(lemma,lemma(discharge,[]))).
% 11.25/11.42 tff(1442,plain,
% 11.25/11.42 (((~![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))),
% 11.25/11.42 inference(rewrite,[status(thm)],[])).
% 11.25/11.42 tff(1443,plain,
% 11.25/11.42 ((~![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))),
% 11.25/11.42 inference(quant_inst,[status(thm)],[])).
% 11.25/11.42 tff(1444,plain,
% 11.25/11.42 ((~![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)),
% 11.25/11.42 inference(modus_ponens,[status(thm)],[1443, 1442])).
% 11.25/11.42 tff(1445,plain,
% 11.25/11.42 (~m_c_h_element_v_in2(c_e_h_2, c_f, s2)),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1444, 345, 1441])).
% 11.25/11.42 tff(1446,plain,
% 11.25/11.42 (((~![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_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))),
% 11.25/11.42 inference(rewrite,[status(thm)],[])).
% 11.25/11.42 tff(1447,plain,
% 11.25/11.42 ((~![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_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))),
% 11.25/11.42 inference(quant_inst,[status(thm)],[])).
% 11.25/11.42 tff(1448,plain,
% 11.25/11.42 ((~![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_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)),
% 11.25/11.42 inference(modus_ponens,[status(thm)],[1447, 1446])).
% 11.25/11.42 tff(1449,plain,
% 11.25/11.42 ((~node16(c_e_h_2, c_f, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2)),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1448, 377, 1445])).
% 11.25/11.42 tff(1450,plain,
% 11.25/11.42 (~node16(c_e_h_2, c_f, s2)),
% 11.25/11.42 inference(unit_resolution,[status(thm)],[1449, 1359])).
% 11.25/11.42 tff(1451,plain,
% 11.25/11.42 (((~![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_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))),
% 11.25/11.43 inference(rewrite,[status(thm)],[])).
% 11.25/11.43 tff(1452,plain,
% 11.25/11.43 ((~![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))),
% 11.25/11.43 inference(quant_inst,[status(thm)],[])).
% 11.25/11.43 tff(1453,plain,
% 11.25/11.43 ((~![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)),
% 11.25/11.43 inference(modus_ponens,[status(thm)],[1452, 1451])).
% 11.25/11.43 tff(1454,plain,
% 11.25/11.43 (node19(c_e_h_2, c_f, s2, s3)),
% 11.25/11.43 inference(unit_resolution,[status(thm)],[1453, 312, 604])).
% 11.25/11.43 tff(1455,plain,
% 11.25/11.43 (((~![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)))) | ((~node19(c_e_h_2, c_f, s2, s3)) | 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))) <=> ((~![Y: $i, I0: $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, s2, s3)) | 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))),
% 11.25/11.43 inference(rewrite,[status(thm)],[])).
% 11.25/11.43 tff(1456,plain,
% 11.25/11.43 ((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))) <=> ((~node19(c_e_h_2, c_f, s2, s3)) | 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))),
% 11.25/11.43 inference(rewrite,[status(thm)],[])).
% 11.25/11.43 tff(1457,plain,
% 11.25/11.43 (((~![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_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)))) | ((~node19(c_e_h_2, c_f, s2, s3)) | 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)))),
% 11.25/11.43 inference(monotonicity,[status(thm)],[1456])).
% 11.25/11.43 tff(1458,plain,
% 11.25/11.43 (((~![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_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)))) | (~node19(c_e_h_2, c_f, s2, s3)) | 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))),
% 11.25/11.43 inference(transitivity,[status(thm)],[1457, 1455])).
% 11.25/11.43 tff(1459,plain,
% 11.25/11.43 ((~![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_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)))),
% 11.25/11.43 inference(quant_inst,[status(thm)],[])).
% 11.25/11.43 tff(1460,plain,
% 11.25/11.43 ((~![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)))) | (~node19(c_e_h_2, c_f, s2, s3)) | 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)),
% 11.25/11.43 inference(modus_ponens,[status(thm)],[1459, 1458])).
% 11.25/11.43 tff(1461,plain,
% 11.25/11.43 (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)),
% 11.25/11.43 inference(unit_resolution,[status(thm)],[1460, 409, 1454])).
% 11.25/11.43 tff(1462,plain,
% 11.25/11.43 (node14(c_e_h_2, c_f, s2, s3)),
% 11.25/11.43 inference(unit_resolution,[status(thm)],[1461, 1450, 1358])).
% 11.25/11.43 tff(1463,plain,
% 11.25/11.43 (((~![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_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)))),
% 11.25/11.43 inference(rewrite,[status(thm)],[])).
% 11.25/11.43 tff(1464,plain,
% 11.25/11.43 (((~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)))),
% 11.25/11.43 inference(rewrite,[status(thm)],[])).
% 11.25/11.43 tff(1465,plain,
% 11.25/11.43 (((~![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_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))))),
% 11.25/11.43 inference(monotonicity,[status(thm)],[1464])).
% 11.25/11.43 tff(1466,plain,
% 11.25/11.43 (((~![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_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)))),
% 11.25/11.43 inference(transitivity,[status(thm)],[1465, 1463])).
% 11.25/11.43 tff(1467,plain,
% 11.25/11.43 ((~![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_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)))),
% 11.25/11.43 inference(quant_inst,[status(thm)],[])).
% 11.25/11.43 tff(1468,plain,
% 11.25/11.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node14(c_e_h_2, c_f, s2, s3))),
% 11.25/11.43 inference(modus_ponens,[status(thm)],[1467, 1466])).
% 11.25/11.43 tff(1469,plain,
% 11.25/11.43 ($false),
% 11.25/11.43 inference(unit_resolution,[status(thm)],[1468, 427, 1349, 1359, 1462])).
% 11.25/11.43 tff(1470,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)), inference(lemma,lemma(discharge,[]))).
% 11.25/11.43 tff(1471,plain,
% 11.25/11.43 (m_c_h_element_v_in1(c_e_h_2, c_f, s2)),
% 11.25/11.43 inference(unit_resolution,[status(thm)],[1470, 1357, 1349])).
% 11.25/11.43 tff(1472,plain,
% 11.25/11.43 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | 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)) | (~node17(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)))) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | (~node17(c_e_h_2, c_f, s2)) | m_c_h_element_v_in2(c_e_h_2, c_f, s2))),
% 11.25/11.43 inference(rewrite,[status(thm)],[])).
% 11.25/11.43 tff(1473,plain,
% 11.25/11.43 (((~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))) <=> ((~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | (~node17(c_e_h_2, c_f, s2)) | m_c_h_element_v_in2(c_e_h_2, c_f, s2))),
% 11.25/11.43 inference(rewrite,[status(thm)],[])).
% 11.25/11.43 tff(1474,plain,
% 11.25/11.43 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | 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)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | (~node17(c_e_h_2, c_f, s2)) | m_c_h_element_v_in2(c_e_h_2, c_f, s2)))),
% 11.25/11.43 inference(monotonicity,[status(thm)],[1473])).
% 11.25/11.43 tff(1475,plain,
% 11.25/11.43 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | 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)))) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | (~node17(c_e_h_2, c_f, s2)) | m_c_h_element_v_in2(c_e_h_2, c_f, s2))),
% 11.25/11.43 inference(transitivity,[status(thm)],[1474, 1472])).
% 11.25/11.43 tff(1476,plain,
% 11.25/11.43 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | 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)))),
% 11.25/11.43 inference(quant_inst,[status(thm)],[])).
% 11.25/11.43 tff(1477,plain,
% 11.25/11.43 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | 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)) | (~node17(c_e_h_2, c_f, s2)) | m_c_h_element_v_in2(c_e_h_2, c_f, s2)),
% 11.25/11.43 inference(modus_ponens,[status(thm)],[1476, 1475])).
% 11.25/11.43 tff(1478,plain,
% 11.25/11.43 ((~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | (~node17(c_e_h_2, c_f, s2))),
% 11.25/11.43 inference(unit_resolution,[status(thm)],[1477, 359, 1445])).
% 11.25/11.43 tff(1479,plain,
% 11.25/11.43 (~node17(c_e_h_2, c_f, s2)),
% 11.25/11.43 inference(unit_resolution,[status(thm)],[1478, 1471])).
% 11.25/11.43 tff(1480,plain,
% 11.25/11.43 (((~![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, s2, s3)) | node17(c_e_h_2, c_f, s2) | 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)))) | (~node19(c_e_h_2, c_f, s2, s3)) | node17(c_e_h_2, c_f, s2) | node18(c_e_h_2, c_f, s2, s3))),
% 11.25/11.43 inference(rewrite,[status(thm)],[])).
% 11.25/11.43 tff(1481,plain,
% 11.25/11.43 ((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))) <=> ((~node19(c_e_h_2, c_f, s2, s3)) | node17(c_e_h_2, c_f, s2) | node18(c_e_h_2, c_f, s2, s3))),
% 11.25/11.43 inference(rewrite,[status(thm)],[])).
% 11.25/11.43 tff(1482,plain,
% 11.25/11.43 (((~![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_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)))) | ((~node19(c_e_h_2, c_f, s2, s3)) | node17(c_e_h_2, c_f, s2) | node18(c_e_h_2, c_f, s2, s3)))),
% 11.25/11.43 inference(monotonicity,[status(thm)],[1481])).
% 11.25/11.43 tff(1483,plain,
% 11.25/11.43 (((~![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_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)))) | (~node19(c_e_h_2, c_f, s2, s3)) | node17(c_e_h_2, c_f, s2) | node18(c_e_h_2, c_f, s2, s3))),
% 11.25/11.43 inference(transitivity,[status(thm)],[1482, 1480])).
% 11.25/11.43 tff(1484,plain,
% 11.25/11.43 ((~![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_f, s2) | node18(c_e_h_2, c_f, s2, s3) | (~node19(c_e_h_2, c_f, s2, s3)))),
% 11.25/11.43 inference(quant_inst,[status(thm)],[])).
% 11.25/11.43 tff(1485,plain,
% 11.25/11.43 ((~![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, s2, s3)) | node17(c_e_h_2, c_f, s2) | node18(c_e_h_2, c_f, s2, s3)),
% 11.25/11.43 inference(modus_ponens,[status(thm)],[1484, 1483])).
% 11.25/11.43 tff(1486,plain,
% 11.25/11.43 (node17(c_e_h_2, c_f, s2) | node18(c_e_h_2, c_f, s2, s3)),
% 11.25/11.43 inference(unit_resolution,[status(thm)],[1485, 326, 1454])).
% 11.25/11.43 tff(1487,plain,
% 11.25/11.43 (node18(c_e_h_2, c_f, s2, s3)),
% 11.25/11.43 inference(unit_resolution,[status(thm)],[1486, 1479])).
% 11.25/11.43 tff(1488,plain,
% 11.25/11.43 (((~![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_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~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, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node18(c_e_h_2, c_f, s2, s3)))),
% 11.25/11.43 inference(rewrite,[status(thm)],[])).
% 11.25/11.43 tff(1489,plain,
% 11.25/11.43 (((~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))) <=> (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, s3)) | (~node18(c_e_h_2, c_f, s2, s3)))),
% 11.25/11.43 inference(rewrite,[status(thm)],[])).
% 11.25/11.43 tff(1490,plain,
% 11.25/11.43 (((~![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_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, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node18(c_e_h_2, c_f, s2, s3))))),
% 11.25/11.43 inference(monotonicity,[status(thm)],[1489])).
% 11.25/11.43 tff(1491,plain,
% 11.25/11.43 (((~![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_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, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node18(c_e_h_2, c_f, s2, s3)))),
% 11.25/11.43 inference(transitivity,[status(thm)],[1490, 1488])).
% 11.25/11.43 tff(1492,plain,
% 11.25/11.43 ((~![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_f, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s2) | (~node18(c_e_h_2, c_f, s2, s3)))),
% 11.25/11.43 inference(quant_inst,[status(thm)],[])).
% 11.25/11.43 tff(1493,plain,
% 11.25/11.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node18(c_e_h_2, c_f, s2, s3))),
% 11.25/11.43 inference(modus_ponens,[status(thm)],[1492, 1491])).
% 11.25/11.43 tff(1494,plain,
% 11.25/11.43 ($false),
% 11.25/11.43 inference(unit_resolution,[status(thm)],[1493, 296, 1350, 1349, 1487])).
% 11.25/11.43 tff(1495,plain,(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, s3))), inference(lemma,lemma(discharge,[]))).
% 11.25/11.43 tff(1496,plain,
% 11.25/11.43 (~m_c_h_element_v_out(c_e_h_2, c_f, s3)),
% 11.25/11.43 inference(unit_resolution,[status(thm)],[1495, 581])).
% 11.25/11.43 tff(1497,plain,
% 11.25/11.43 (((~![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))),
% 11.25/11.43 inference(rewrite,[status(thm)],[])).
% 11.25/11.43 tff(1498,plain,
% 11.25/11.43 ((~![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))),
% 11.25/11.43 inference(quant_inst,[status(thm)],[])).
% 11.25/11.43 tff(1499,plain,
% 11.25/11.43 ((~![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)),
% 11.25/11.43 inference(modus_ponens,[status(thm)],[1498, 1497])).
% 11.25/11.43 tff(1500,plain,
% 11.25/11.43 (~m_and_h_gate_v_in1(c_e_h_2, c_q, s3)),
% 11.25/11.43 inference(unit_resolution,[status(thm)],[1499, 199, 1496])).
% 11.25/11.43 tff(1501,plain,
% 11.25/11.43 (((~![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))),
% 11.25/11.43 inference(rewrite,[status(thm)],[])).
% 11.25/11.43 tff(1502,plain,
% 11.25/11.43 ((~![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))),
% 11.25/11.43 inference(quant_inst,[status(thm)],[])).
% 11.25/11.43 tff(1503,plain,
% 11.25/11.43 ((~![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)),
% 11.25/11.43 inference(modus_ponens,[status(thm)],[1502, 1501])).
% 11.25/11.43 tff(1504,plain,
% 11.25/11.43 (~node20(c_e_h_2, c_q, s3)),
% 11.25/11.43 inference(unit_resolution,[status(thm)],[1503, 213, 1500])).
% 11.25/11.43 tff(1505,assumption,(node21(c_e_h_2, c_q, s3, s4)), introduced(assumption)).
% 11.25/11.43 tff(1506,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s4)), introduced(assumption)).
% 11.25/11.43 tff(1507,plain,
% 11.25/11.43 (((~![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)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | node20(c_e_h_2, c_q, s3) | (~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)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | node20(c_e_h_2, c_q, s3) | (~node21(c_e_h_2, c_q, s3, s4)))),
% 11.25/11.43 inference(rewrite,[status(thm)],[])).
% 11.25/11.43 tff(1508,plain,
% 11.25/11.43 ((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))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | node20(c_e_h_2, c_q, s3) | (~node21(c_e_h_2, c_q, s3, s4)))),
% 11.25/11.43 inference(rewrite,[status(thm)],[])).
% 11.25/11.43 tff(1509,plain,
% 11.25/11.43 (((~![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_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)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | node20(c_e_h_2, c_q, s3) | (~node21(c_e_h_2, c_q, s3, s4))))),
% 11.25/11.43 inference(monotonicity,[status(thm)],[1508])).
% 11.25/11.43 tff(1510,plain,
% 11.25/11.43 (((~![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_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)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | node20(c_e_h_2, c_q, s3) | (~node21(c_e_h_2, c_q, s3, s4)))),
% 11.25/11.43 inference(transitivity,[status(thm)],[1509, 1507])).
% 11.25/11.43 tff(1511,plain,
% 11.25/11.43 ((~![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_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)))),
% 11.25/11.43 inference(quant_inst,[status(thm)],[])).
% 11.25/11.43 tff(1512,plain,
% 11.25/11.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | node20(c_e_h_2, c_q, s3) | (~node21(c_e_h_2, c_q, s3, s4))),
% 11.25/11.43 inference(modus_ponens,[status(thm)],[1511, 1510])).
% 11.25/11.43 tff(1513,plain,
% 11.25/11.43 ($false),
% 11.25/11.43 inference(unit_resolution,[status(thm)],[1512, 228, 1506, 1505, 1504])).
% 11.25/11.43 tff(1514,plain,((~node21(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,[]))).
% 11.25/11.43 tff(1515,plain,
% 11.25/11.43 (~node21(c_e_h_2, c_q, s3, s4)),
% 11.25/11.43 inference(unit_resolution,[status(thm)],[1514, 1348])).
% 11.25/11.43 tff(1516,plain,
% 11.25/11.43 (((~![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))),
% 11.25/11.43 inference(rewrite,[status(thm)],[])).
% 11.25/11.43 tff(1517,plain,
% 11.25/11.43 ((~![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))),
% 11.25/11.43 inference(quant_inst,[status(thm)],[])).
% 11.25/11.43 tff(1518,plain,
% 11.25/11.43 ((~![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)),
% 11.25/11.43 inference(modus_ponens,[status(thm)],[1517, 1516])).
% 11.25/11.43 tff(1519,plain,
% 11.25/11.43 (node21(c_e_h_2, c_q, s3, s4) | node22(c_e_h_2, c_q, s3, s4)),
% 11.25/11.43 inference(unit_resolution,[status(thm)],[1518, 247, 1092])).
% 11.25/11.43 tff(1520,plain,
% 11.25/11.43 (node22(c_e_h_2, c_q, s3, s4)),
% 11.25/11.43 inference(unit_resolution,[status(thm)],[1519, 1515])).
% 11.25/11.43 tff(1521,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_q, s3)), introduced(assumption)).
% 11.25/11.43 tff(1522,plain,
% 11.25/11.43 (((~![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_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))),
% 11.25/11.43 inference(rewrite,[status(thm)],[])).
% 11.25/11.43 tff(1523,plain,
% 11.25/11.43 ((~![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_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))),
% 11.25/11.43 inference(quant_inst,[status(thm)],[])).
% 11.25/11.43 tff(1524,plain,
% 11.25/11.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | (~node22(c_e_h_2, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_q, s3)),
% 11.25/11.43 inference(modus_ponens,[status(thm)],[1523, 1522])).
% 11.25/11.43 tff(1525,plain,
% 11.25/11.43 ($false),
% 11.25/11.43 inference(unit_resolution,[status(thm)],[1524, 273, 1348, 1521, 1520])).
% 11.25/11.43 tff(1526,plain,(m_and_h_gate_v_out(c_e_h_2, c_q, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | (~node5(c_e_h_3, c_j, s4, s5)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3)), inference(lemma,lemma(discharge,[]))).
% 11.25/11.43 tff(1527,plain,
% 11.25/11.43 (~node5(c_e_h_3, c_j, s4, s5)),
% 11.25/11.43 inference(unit_resolution,[status(thm)],[1526, 1124, 609, 926])).
% 11.25/11.43 tff(1528,plain,
% 11.25/11.43 (((~![Y: $i, I0: $i, X: $i, I1: $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)))),
% 11.25/11.43 inference(rewrite,[status(thm)],[])).
% 11.25/11.43 tff(1529,plain,
% 11.25/11.43 (((~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)))),
% 11.25/11.43 inference(rewrite,[status(thm)],[])).
% 11.25/11.43 tff(1530,plain,
% 11.25/11.43 (((~![Y: $i, I0: $i, X: $i, I1: $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))))),
% 11.25/11.43 inference(monotonicity,[status(thm)],[1529])).
% 11.25/11.43 tff(1531,plain,
% 11.25/11.43 (((~![Y: $i, I0: $i, X: $i, I1: $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)))),
% 11.25/11.44 inference(transitivity,[status(thm)],[1530, 1528])).
% 11.25/11.44 tff(1532,plain,
% 11.25/11.44 ((~![Y: $i, I0: $i, X: $i, I1: $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))),
% 11.25/11.44 inference(quant_inst,[status(thm)],[])).
% 11.25/11.44 tff(1533,plain,
% 11.25/11.44 ((~![Y: $i, I0: $i, X: $i, I1: $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))),
% 11.25/11.44 inference(modus_ponens,[status(thm)],[1532, 1531])).
% 11.25/11.44 tff(1534,plain,
% 11.25/11.44 (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))),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1533, 742])).
% 11.25/11.44 tff(1535,plain,
% 11.25/11.44 (~node6(c_e_h_3, c_j, s4, s5)),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1534, 1124, 1108])).
% 11.25/11.44 tff(1536,plain,
% 11.25/11.44 (succ(s4, s5) <=> succ(s4, s5)),
% 11.25/11.44 inference(rewrite,[status(thm)],[])).
% 11.25/11.44 tff(1537,axiom,(succ(s4, s5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound5')).
% 11.25/11.44 tff(1538,plain,
% 11.25/11.44 (succ(s4, s5)),
% 11.25/11.44 inference(modus_ponens,[status(thm)],[1537, 1536])).
% 11.25/11.44 tff(1539,plain,
% 11.25/11.44 (((~![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))),
% 11.25/11.44 inference(rewrite,[status(thm)],[])).
% 11.25/11.44 tff(1540,plain,
% 11.25/11.44 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s4, s5)) | trans(s4, s5))),
% 11.25/11.44 inference(quant_inst,[status(thm)],[])).
% 11.25/11.44 tff(1541,plain,
% 11.25/11.44 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s4, s5)) | trans(s4, s5)),
% 11.25/11.44 inference(modus_ponens,[status(thm)],[1540, 1539])).
% 11.25/11.44 tff(1542,plain,
% 11.25/11.44 (trans(s4, s5)),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1541, 1538, 93])).
% 11.25/11.44 tff(1543,plain,
% 11.25/11.44 (((~![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))),
% 11.25/11.44 inference(rewrite,[status(thm)],[])).
% 11.25/11.44 tff(1544,plain,
% 11.25/11.44 ((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))),
% 11.25/11.44 inference(rewrite,[status(thm)],[])).
% 11.25/11.44 tff(1545,plain,
% 11.25/11.44 (((~![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)))),
% 11.25/11.44 inference(monotonicity,[status(thm)],[1544])).
% 11.25/11.44 tff(1546,plain,
% 11.25/11.44 (((~![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))),
% 11.25/11.44 inference(transitivity,[status(thm)],[1545, 1543])).
% 11.25/11.44 tff(1547,plain,
% 11.25/11.44 ((~![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)))),
% 11.25/11.44 inference(quant_inst,[status(thm)],[])).
% 11.25/11.44 tff(1548,plain,
% 11.25/11.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node6(c_e_h_3, c_j, s4, s5) | node5(c_e_h_3, c_j, s4, s5)),
% 11.25/11.44 inference(modus_ponens,[status(thm)],[1547, 1546])).
% 11.25/11.44 tff(1549,plain,
% 11.25/11.44 (node6(c_e_h_3, c_j, s4, s5) | node5(c_e_h_3, c_j, s4, s5)),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1548, 724, 1542])).
% 11.25/11.44 tff(1550,plain,
% 11.25/11.44 ($false),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1549, 1535, 1527])).
% 11.25/11.44 tff(1551,plain,(~m_or_h_gate_v_out(c_e_h_3, c_j, s5)), inference(lemma,lemma(discharge,[]))).
% 11.25/11.44 tff(1552,plain,
% 11.25/11.44 (((~![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))),
% 11.25/11.44 inference(rewrite,[status(thm)],[])).
% 11.25/11.44 tff(1553,plain,
% 11.25/11.44 ((~![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))),
% 11.25/11.44 inference(quant_inst,[status(thm)],[])).
% 11.25/11.44 tff(1554,plain,
% 11.25/11.44 ((~![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)),
% 11.25/11.44 inference(modus_ponens,[status(thm)],[1553, 1552])).
% 11.25/11.44 tff(1555,plain,
% 11.25/11.44 (~m_c_h_element_v_in2(c_e_h_3, c_h, s5)),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1554, 1117, 1551])).
% 11.25/11.44 tff(1556,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_h, s5)), introduced(assumption)).
% 11.25/11.44 tff(1557,assumption,(~m_user_v_ack(c_e_h_1, c_u, s9)), introduced(assumption)).
% 11.25/11.44 tff(1558,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_h, s4)), introduced(assumption)).
% 11.25/11.44 tff(1559,plain,
% 11.25/11.44 (((~![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))),
% 11.25/11.44 inference(rewrite,[status(thm)],[])).
% 11.25/11.44 tff(1560,plain,
% 11.25/11.44 ((~![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))),
% 11.25/11.44 inference(quant_inst,[status(thm)],[])).
% 11.25/11.44 tff(1561,plain,
% 11.25/11.44 ((~![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)),
% 11.25/11.44 inference(modus_ponens,[status(thm)],[1560, 1559])).
% 11.25/11.44 tff(1562,plain,
% 11.25/11.44 (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1561, 1117, 1076])).
% 11.25/11.44 tff(1563,plain,
% 11.25/11.44 (((~![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))),
% 11.25/11.44 inference(rewrite,[status(thm)],[])).
% 11.25/11.44 tff(1564,plain,
% 11.25/11.44 ((~![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))),
% 11.25/11.44 inference(quant_inst,[status(thm)],[])).
% 11.25/11.44 tff(1565,plain,
% 11.25/11.44 ((~![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)),
% 11.25/11.44 inference(modus_ponens,[status(thm)],[1564, 1563])).
% 11.25/11.44 tff(1566,plain,
% 11.25/11.44 (~m_c_h_element_v_in2(c_e_h_3, c_h, s2)),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1565, 1117, 1038])).
% 11.25/11.44 tff(1567,plain,
% 11.25/11.44 (((~![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))),
% 11.25/11.44 inference(rewrite,[status(thm)],[])).
% 11.25/11.44 tff(1568,plain,
% 11.25/11.44 ((~![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))),
% 11.25/11.44 inference(quant_inst,[status(thm)],[])).
% 11.25/11.44 tff(1569,plain,
% 11.25/11.44 ((~![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)),
% 11.25/11.44 inference(modus_ponens,[status(thm)],[1568, 1567])).
% 11.25/11.44 tff(1570,plain,
% 11.25/11.44 (~m_c_h_element_v_in2(c_e_h_3, c_h, s1)),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1569, 1117, 990])).
% 11.25/11.44 tff(1571,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_h, s1)), introduced(assumption)).
% 11.25/11.44 tff(1572,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s2)), introduced(assumption)).
% 11.25/11.44 tff(1573,assumption,(node18(c_e_h_3, c_h, s1, s2)), introduced(assumption)).
% 11.25/11.44 tff(1574,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s1)), introduced(assumption)).
% 11.25/11.44 tff(1575,assumption,(node14(c_e_h_3, c_h, s0, s1)), introduced(assumption)).
% 11.25/11.44 tff(1576,plain,
% 11.25/11.44 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s0)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s0)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0))),
% 11.25/11.44 inference(rewrite,[status(thm)],[])).
% 11.25/11.44 tff(1577,plain,
% 11.25/11.44 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s0)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0))),
% 11.25/11.44 inference(quant_inst,[status(thm)],[])).
% 11.25/11.44 tff(1578,plain,
% 11.25/11.44 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s0)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0)),
% 11.25/11.44 inference(modus_ponens,[status(thm)],[1577, 1576])).
% 11.25/11.44 tff(1579,plain,
% 11.25/11.44 (~m_c_h_element_v_in1(c_e_h_3, c_h, s0)),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1578, 1380, 663])).
% 11.25/11.44 tff(1580,plain,
% 11.25/11.44 (((~![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_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)))),
% 11.25/11.44 inference(rewrite,[status(thm)],[])).
% 11.25/11.44 tff(1581,plain,
% 11.25/11.44 (((~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)))),
% 11.25/11.44 inference(rewrite,[status(thm)],[])).
% 11.25/11.44 tff(1582,plain,
% 11.25/11.44 (((~![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_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))))),
% 11.25/11.44 inference(monotonicity,[status(thm)],[1581])).
% 11.25/11.44 tff(1583,plain,
% 11.25/11.44 (((~![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_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)))),
% 11.25/11.44 inference(transitivity,[status(thm)],[1582, 1580])).
% 11.25/11.44 tff(1584,plain,
% 11.25/11.44 ((~![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_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)))),
% 11.25/11.44 inference(quant_inst,[status(thm)],[])).
% 11.25/11.44 tff(1585,plain,
% 11.25/11.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~node14(c_e_h_3, c_h, s0, s1))),
% 11.25/11.44 inference(modus_ponens,[status(thm)],[1584, 1583])).
% 11.25/11.44 tff(1586,plain,
% 11.25/11.44 ($false),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1585, 427, 1574, 1579, 1575])).
% 11.25/11.44 tff(1587,plain,((~node14(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,[]))).
% 11.25/11.44 tff(1588,plain,
% 11.25/11.44 (~node14(c_e_h_3, c_h, s0, s1)),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1587, 1574])).
% 11.25/11.44 tff(1589,plain,
% 11.25/11.44 (((~![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))),
% 11.25/11.44 inference(rewrite,[status(thm)],[])).
% 11.25/11.44 tff(1590,plain,
% 11.25/11.44 ((~![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))),
% 11.25/11.44 inference(quant_inst,[status(thm)],[])).
% 11.25/11.44 tff(1591,plain,
% 11.25/11.44 ((~![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)),
% 11.25/11.44 inference(modus_ponens,[status(thm)],[1590, 1589])).
% 11.25/11.44 tff(1592,plain,
% 11.25/11.44 (~m_c_h_element_v_in2(c_e_h_3, c_h, s0)),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1591, 1117, 982])).
% 11.25/11.44 tff(1593,plain,
% 11.25/11.44 (((~![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_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))),
% 11.25/11.44 inference(rewrite,[status(thm)],[])).
% 11.25/11.44 tff(1594,plain,
% 11.25/11.44 ((~![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_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))),
% 11.25/11.44 inference(quant_inst,[status(thm)],[])).
% 11.25/11.44 tff(1595,plain,
% 11.25/11.44 ((~![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_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)),
% 11.25/11.44 inference(modus_ponens,[status(thm)],[1594, 1593])).
% 11.25/11.44 tff(1596,plain,
% 11.25/11.44 ((~node16(c_e_h_3, c_h, s0)) | m_c_h_element_v_in2(c_e_h_3, c_h, s0)),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1595, 377, 1579])).
% 11.25/11.44 tff(1597,plain,
% 11.25/11.44 (~node16(c_e_h_3, c_h, s0)),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1596, 1592])).
% 11.25/11.44 tff(1598,plain,
% 11.25/11.44 (((~![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))),
% 11.25/11.44 inference(rewrite,[status(thm)],[])).
% 11.25/11.44 tff(1599,plain,
% 11.25/11.44 ((~![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))),
% 11.25/11.44 inference(quant_inst,[status(thm)],[])).
% 11.25/11.44 tff(1600,plain,
% 11.25/11.44 ((~![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)),
% 11.25/11.44 inference(modus_ponens,[status(thm)],[1599, 1598])).
% 11.25/11.44 tff(1601,plain,
% 11.25/11.44 (node19(c_e_h_3, c_h, s0, s1)),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1600, 312, 100])).
% 11.25/11.44 tff(1602,plain,
% 11.25/11.44 (((~![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_3, c_h, s0) | (~node19(c_e_h_3, c_h, s0, s1)) | node14(c_e_h_3, c_h, s0, s1) | node15(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)))) | node16(c_e_h_3, c_h, s0) | (~node19(c_e_h_3, c_h, s0, s1)) | node14(c_e_h_3, c_h, s0, s1) | node15(c_e_h_3, c_h, s0, s1))),
% 11.25/11.44 inference(rewrite,[status(thm)],[])).
% 11.25/11.44 tff(1603,plain,
% 11.25/11.44 ((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))) <=> (node16(c_e_h_3, c_h, s0) | (~node19(c_e_h_3, c_h, s0, s1)) | node14(c_e_h_3, c_h, s0, s1) | node15(c_e_h_3, c_h, s0, s1))),
% 11.25/11.44 inference(rewrite,[status(thm)],[])).
% 11.25/11.44 tff(1604,plain,
% 11.25/11.44 (((~![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_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)))) | (node16(c_e_h_3, c_h, s0) | (~node19(c_e_h_3, c_h, s0, s1)) | node14(c_e_h_3, c_h, s0, s1) | node15(c_e_h_3, c_h, s0, s1)))),
% 11.25/11.44 inference(monotonicity,[status(thm)],[1603])).
% 11.25/11.44 tff(1605,plain,
% 11.25/11.44 (((~![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_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)))) | node16(c_e_h_3, c_h, s0) | (~node19(c_e_h_3, c_h, s0, s1)) | node14(c_e_h_3, c_h, s0, s1) | node15(c_e_h_3, c_h, s0, s1))),
% 11.25/11.44 inference(transitivity,[status(thm)],[1604, 1602])).
% 11.25/11.44 tff(1606,plain,
% 11.25/11.44 ((~![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_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)))),
% 11.25/11.44 inference(quant_inst,[status(thm)],[])).
% 11.25/11.44 tff(1607,plain,
% 11.25/11.44 ((~![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_3, c_h, s0) | (~node19(c_e_h_3, c_h, s0, s1)) | node14(c_e_h_3, c_h, s0, s1) | node15(c_e_h_3, c_h, s0, s1)),
% 11.25/11.44 inference(modus_ponens,[status(thm)],[1606, 1605])).
% 11.25/11.44 tff(1608,plain,
% 11.25/11.44 (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)),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1607, 409, 1601])).
% 11.25/11.44 tff(1609,plain,
% 11.25/11.44 (node14(c_e_h_3, c_h, s0, s1) | node15(c_e_h_3, c_h, s0, s1)),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1608, 1597])).
% 11.25/11.44 tff(1610,plain,
% 11.25/11.44 (node15(c_e_h_3, c_h, s0, s1)),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1609, 1588])).
% 11.25/11.44 tff(1611,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s0)), introduced(assumption)).
% 11.25/11.44 tff(1612,plain,
% 11.25/11.44 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s0))),
% 11.25/11.44 inference(quant_inst,[status(thm)],[])).
% 11.25/11.44 tff(1613,plain,
% 11.25/11.44 ($false),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1612, 189, 1611])).
% 11.25/11.44 tff(1614,plain,(~m_c_h_element_v_out(c_e_h_3, c_h, s0)), inference(lemma,lemma(discharge,[]))).
% 11.25/11.44 tff(1615,plain,
% 11.25/11.44 (((~![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_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))),
% 11.25/11.44 inference(rewrite,[status(thm)],[])).
% 11.25/11.44 tff(1616,plain,
% 11.25/11.44 ((~![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_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))),
% 11.25/11.44 inference(quant_inst,[status(thm)],[])).
% 11.25/11.44 tff(1617,plain,
% 11.25/11.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | (~node15(c_e_h_3, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s0)),
% 11.25/11.44 inference(modus_ponens,[status(thm)],[1616, 1615])).
% 11.25/11.44 tff(1618,plain,
% 11.25/11.44 ($false),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1617, 393, 1574, 1614, 1610])).
% 11.25/11.44 tff(1619,plain,(~m_c_h_element_v_out(c_e_h_3, c_h, s1)), inference(lemma,lemma(discharge,[]))).
% 11.25/11.44 tff(1620,plain,
% 11.25/11.44 (((~![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_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, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s1) | (~node18(c_e_h_3, c_h, s1, s2)))),
% 11.25/11.44 inference(rewrite,[status(thm)],[])).
% 11.25/11.44 tff(1621,plain,
% 11.25/11.44 ((~![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_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)))),
% 11.25/11.44 inference(quant_inst,[status(thm)],[])).
% 11.25/11.44 tff(1622,plain,
% 11.25/11.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s1) | (~node18(c_e_h_3, c_h, s1, s2))),
% 11.25/11.44 inference(modus_ponens,[status(thm)],[1621, 1620])).
% 11.25/11.44 tff(1623,plain,
% 11.25/11.44 ($false),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1622, 296, 1619, 1572, 1573])).
% 11.25/11.44 tff(1624,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,[]))).
% 11.25/11.44 tff(1625,plain,
% 11.25/11.44 (~node18(c_e_h_3, c_h, s1, s2)),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1624, 1572])).
% 11.25/11.44 tff(1626,assumption,(~node19(c_e_h_3, c_h, s1, s2)), introduced(assumption)).
% 11.25/11.44 tff(1627,plain,
% 11.25/11.44 (((~![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))),
% 11.25/11.44 inference(rewrite,[status(thm)],[])).
% 11.25/11.44 tff(1628,plain,
% 11.25/11.44 ((~![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))),
% 11.25/11.44 inference(quant_inst,[status(thm)],[])).
% 11.25/11.44 tff(1629,plain,
% 11.25/11.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_3, c_h, s1, s2)),
% 11.25/11.44 inference(modus_ponens,[status(thm)],[1628, 1627])).
% 11.25/11.44 tff(1630,plain,
% 11.25/11.44 ($false),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1629, 312, 470, 1626])).
% 11.25/11.44 tff(1631,plain,(node19(c_e_h_3, c_h, s1, s2)), inference(lemma,lemma(discharge,[]))).
% 11.25/11.44 tff(1632,plain,
% 11.25/11.44 (((~![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_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)))),
% 11.25/11.44 inference(rewrite,[status(thm)],[])).
% 11.25/11.44 tff(1633,plain,
% 11.25/11.44 ((~![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_3, c_h, s1) | node18(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)))),
% 11.25/11.44 inference(quant_inst,[status(thm)],[])).
% 11.25/11.44 tff(1634,plain,
% 11.25/11.44 ((~![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_3, c_h, s1) | node18(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2))),
% 11.25/11.44 inference(modus_ponens,[status(thm)],[1633, 1632])).
% 11.25/11.44 tff(1635,plain,
% 11.25/11.44 (node17(c_e_h_3, c_h, s1) | node18(c_e_h_3, c_h, s1, s2)),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1634, 326, 1631])).
% 11.25/11.44 tff(1636,plain,
% 11.25/11.44 (node17(c_e_h_3, c_h, s1)),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1635, 1625])).
% 11.25/11.44 tff(1637,plain,
% 11.25/11.44 (((~![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_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)))) | (~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)))),
% 11.25/11.44 inference(rewrite,[status(thm)],[])).
% 11.25/11.44 tff(1638,plain,
% 11.25/11.44 ((~![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_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)))),
% 11.25/11.44 inference(quant_inst,[status(thm)],[])).
% 11.25/11.44 tff(1639,plain,
% 11.25/11.44 ((~![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_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))),
% 11.25/11.44 inference(modus_ponens,[status(thm)],[1638, 1637])).
% 11.25/11.44 tff(1640,plain,
% 11.25/11.44 ((~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)),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1639, 359, 1636])).
% 11.25/11.44 tff(1641,plain,
% 11.25/11.44 (~m_c_h_element_v_in1(c_e_h_3, c_h, s1)),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1640, 1571])).
% 11.25/11.44 tff(1642,assumption,(node15(c_e_h_3, c_h, s1, s2)), introduced(assumption)).
% 11.25/11.44 tff(1643,plain,
% 11.25/11.44 (((~![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_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))),
% 11.25/11.44 inference(rewrite,[status(thm)],[])).
% 11.25/11.44 tff(1644,plain,
% 11.25/11.44 ((~![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_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))),
% 11.25/11.44 inference(quant_inst,[status(thm)],[])).
% 11.25/11.44 tff(1645,plain,
% 11.25/11.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node15(c_e_h_3, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s1)),
% 11.25/11.44 inference(modus_ponens,[status(thm)],[1644, 1643])).
% 11.25/11.44 tff(1646,plain,
% 11.25/11.44 ($false),
% 11.25/11.44 inference(unit_resolution,[status(thm)],[1645, 393, 1619, 1572, 1642])).
% 11.25/11.45 tff(1647,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,[]))).
% 11.25/11.45 tff(1648,plain,
% 11.25/11.45 (~node15(c_e_h_3, c_h, s1, s2)),
% 11.25/11.45 inference(unit_resolution,[status(thm)],[1647, 1572])).
% 11.25/11.45 tff(1649,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_h, s1)), introduced(assumption)).
% 11.25/11.45 tff(1650,assumption,(node14(c_e_h_3, c_h, s1, s2)), introduced(assumption)).
% 11.25/11.45 tff(1651,plain,
% 11.25/11.45 (((~![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_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)))),
% 11.25/11.45 inference(rewrite,[status(thm)],[])).
% 11.25/11.45 tff(1652,plain,
% 11.25/11.45 (((~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)))),
% 11.25/11.45 inference(rewrite,[status(thm)],[])).
% 11.25/11.45 tff(1653,plain,
% 11.25/11.45 (((~![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_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))))),
% 11.25/11.45 inference(monotonicity,[status(thm)],[1652])).
% 11.25/11.45 tff(1654,plain,
% 11.25/11.45 (((~![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_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)))),
% 11.25/11.45 inference(transitivity,[status(thm)],[1653, 1651])).
% 11.25/11.45 tff(1655,plain,
% 11.25/11.45 ((~![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_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)))),
% 11.25/11.45 inference(quant_inst,[status(thm)],[])).
% 11.25/11.45 tff(1656,plain,
% 11.25/11.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node14(c_e_h_3, c_h, s1, s2))),
% 11.25/11.45 inference(modus_ponens,[status(thm)],[1655, 1654])).
% 11.25/11.45 tff(1657,plain,
% 11.25/11.45 ($false),
% 11.25/11.45 inference(unit_resolution,[status(thm)],[1656, 427, 1572, 1650, 1649])).
% 11.25/11.45 tff(1658,plain,((~node14(c_e_h_3, c_h, s1, s2)) | (~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)), inference(lemma,lemma(discharge,[]))).
% 11.25/11.45 tff(1659,plain,
% 11.25/11.45 (~node14(c_e_h_3, c_h, s1, s2)),
% 11.25/11.45 inference(unit_resolution,[status(thm)],[1658, 1641, 1572])).
% 11.25/11.45 tff(1660,plain,
% 11.25/11.45 (((~![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_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) | 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)))),
% 11.25/11.45 inference(rewrite,[status(thm)],[])).
% 11.25/11.45 tff(1661,plain,
% 11.25/11.45 ((~![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_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)))),
% 11.25/11.45 inference(quant_inst,[status(thm)],[])).
% 11.25/11.45 tff(1662,plain,
% 11.25/11.45 ((~![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_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))),
% 11.25/11.45 inference(modus_ponens,[status(thm)],[1661, 1660])).
% 11.25/11.45 tff(1663,plain,
% 11.25/11.45 (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)),
% 11.25/11.45 inference(unit_resolution,[status(thm)],[1662, 409, 1631])).
% 11.25/11.45 tff(1664,plain,
% 11.25/11.45 (node16(c_e_h_3, c_h, s1)),
% 11.25/11.45 inference(unit_resolution,[status(thm)],[1663, 1659, 1648])).
% 11.25/11.45 tff(1665,plain,
% 11.25/11.45 (((~![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_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))),
% 11.25/11.45 inference(rewrite,[status(thm)],[])).
% 11.25/11.45 tff(1666,plain,
% 11.25/11.45 ((~![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_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))),
% 11.25/11.45 inference(quant_inst,[status(thm)],[])).
% 11.25/11.45 tff(1667,plain,
% 11.25/11.45 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | m_c_h_element_v_in2(c_e_h_3, c_h, s1)),
% 11.25/11.45 inference(modus_ponens,[status(thm)],[1666, 1665])).
% 11.25/11.45 tff(1668,plain,
% 11.25/11.45 ($false),
% 11.25/11.45 inference(unit_resolution,[status(thm)],[1667, 377, 1664, 1571, 1641])).
% 11.25/11.45 tff(1669,plain,(m_c_h_element_v_in2(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2))), inference(lemma,lemma(discharge,[]))).
% 11.25/11.45 tff(1670,plain,
% 11.25/11.45 (~m_c_h_element_v_out(c_e_h_3, c_h, s2)),
% 11.25/11.45 inference(unit_resolution,[status(thm)],[1669, 1570])).
% 11.25/11.45 tff(1671,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s3)), introduced(assumption)).
% 11.25/11.45 tff(1672,assumption,(~m_c_h_element_v_out(c_e_h_3, c_h, s2)), introduced(assumption)).
% 11.25/11.45 tff(1673,plain,
% 11.25/11.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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)))),
% 11.25/11.45 inference(rewrite,[status(thm)],[])).
% 11.25/11.45 tff(1674,plain,
% 11.25/11.45 (((~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)))),
% 11.25/11.45 inference(rewrite,[status(thm)],[])).
% 11.25/11.45 tff(1675,plain,
% 11.25/11.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))))),
% 11.25/11.45 inference(monotonicity,[status(thm)],[1674])).
% 11.25/11.45 tff(1676,plain,
% 11.25/11.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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)))),
% 11.25/11.45 inference(transitivity,[status(thm)],[1675, 1673])).
% 11.25/11.45 tff(1677,plain,
% 11.25/11.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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)))),
% 11.25/11.45 inference(quant_inst,[status(thm)],[])).
% 11.25/11.45 tff(1678,plain,
% 11.25/11.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 11.25/11.45 inference(modus_ponens,[status(thm)],[1677, 1676])).
% 11.25/11.45 tff(1679,plain,
% 11.25/11.45 (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))),
% 11.25/11.45 inference(unit_resolution,[status(thm)],[1678, 296])).
% 11.25/11.45 tff(1680,plain,
% 11.25/11.45 (~node18(c_e_h_3, c_h, s2, s3)),
% 11.25/11.45 inference(unit_resolution,[status(thm)],[1679, 1671, 1672])).
% 11.25/11.45 tff(1681,assumption,(~node19(c_e_h_3, c_h, s2, s3)), introduced(assumption)).
% 11.25/11.45 tff(1682,plain,
% 11.25/11.45 (((~![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))),
% 11.25/11.45 inference(rewrite,[status(thm)],[])).
% 11.25/11.45 tff(1683,plain,
% 11.25/11.45 ((~![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))),
% 11.25/11.45 inference(quant_inst,[status(thm)],[])).
% 11.25/11.45 tff(1684,plain,
% 11.25/11.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_3, c_h, s2, s3)),
% 11.25/11.45 inference(modus_ponens,[status(thm)],[1683, 1682])).
% 11.25/11.45 tff(1685,plain,
% 11.25/11.45 ($false),
% 11.25/11.45 inference(unit_resolution,[status(thm)],[1684, 312, 604, 1681])).
% 11.25/11.45 tff(1686,plain,(node19(c_e_h_3, c_h, s2, s3)), inference(lemma,lemma(discharge,[]))).
% 11.25/11.45 tff(1687,plain,
% 11.25/11.45 (((~![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_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)) | node17(c_e_h_3, c_h, 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_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)) | node17(c_e_h_3, c_h, s2))),
% 11.25/11.45 inference(rewrite,[status(thm)],[])).
% 11.25/11.45 tff(1688,plain,
% 11.25/11.45 ((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))) <=> (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))),
% 11.25/11.45 inference(rewrite,[status(thm)],[])).
% 11.25/11.45 tff(1689,plain,
% 11.25/11.45 (((~![Y: $i, 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)))) | (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)))),
% 11.25/11.45 inference(monotonicity,[status(thm)],[1688])).
% 11.25/11.45 tff(1690,plain,
% 11.25/11.45 (((~![Y: $i, 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)))) | 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))),
% 11.25/11.45 inference(transitivity,[status(thm)],[1689, 1687])).
% 11.25/11.45 tff(1691,plain,
% 11.25/11.45 ((~![Y: $i, 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)))),
% 11.25/11.45 inference(quant_inst,[status(thm)],[])).
% 11.25/11.45 tff(1692,plain,
% 11.25/11.45 ((~![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_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)) | node17(c_e_h_3, c_h, s2)),
% 11.25/11.45 inference(modus_ponens,[status(thm)],[1691, 1690])).
% 11.25/11.45 tff(1693,plain,
% 11.25/11.45 (node18(c_e_h_3, c_h, s2, s3) | node17(c_e_h_3, c_h, s2)),
% 11.25/11.45 inference(unit_resolution,[status(thm)],[1692, 326, 1686])).
% 11.25/11.45 tff(1694,plain,
% 11.25/11.45 (node17(c_e_h_3, c_h, s2)),
% 11.25/11.45 inference(unit_resolution,[status(thm)],[1693, 1680])).
% 11.25/11.45 tff(1695,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_h, s2)), introduced(assumption)).
% 11.25/11.45 tff(1696,plain,
% 11.25/11.45 (((~![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_in2(c_e_h_3, c_h, s2) | (~m_c_h_element_v_in1(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)))) | 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)) | (~node17(c_e_h_3, c_h, s2)))),
% 11.25/11.45 inference(rewrite,[status(thm)],[])).
% 11.25/11.45 tff(1697,plain,
% 11.25/11.45 (((~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))) <=> (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)) | (~node17(c_e_h_3, c_h, s2)))),
% 11.25/11.45 inference(rewrite,[status(thm)],[])).
% 11.25/11.45 tff(1698,plain,
% 11.25/11.45 (((~![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_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)))) | (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)) | (~node17(c_e_h_3, c_h, s2))))),
% 11.25/11.45 inference(monotonicity,[status(thm)],[1697])).
% 11.25/11.45 tff(1699,plain,
% 11.25/11.45 (((~![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_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)))) | 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)) | (~node17(c_e_h_3, c_h, s2)))),
% 11.25/11.45 inference(transitivity,[status(thm)],[1698, 1696])).
% 11.25/11.45 tff(1700,plain,
% 11.25/11.45 ((~![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_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)))),
% 11.25/11.45 inference(quant_inst,[status(thm)],[])).
% 11.25/11.45 tff(1701,plain,
% 11.25/11.45 ((~![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_in2(c_e_h_3, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s2)) | (~node17(c_e_h_3, c_h, s2))),
% 11.25/11.45 inference(modus_ponens,[status(thm)],[1700, 1699])).
% 11.25/11.45 tff(1702,plain,
% 11.25/11.45 ((~m_c_h_element_v_in1(c_e_h_3, c_h, s2)) | (~node17(c_e_h_3, c_h, s2))),
% 11.25/11.45 inference(unit_resolution,[status(thm)],[1701, 359, 1695])).
% 11.25/11.45 tff(1703,plain,
% 11.25/11.45 (~m_c_h_element_v_in1(c_e_h_3, c_h, s2)),
% 11.25/11.45 inference(unit_resolution,[status(thm)],[1702, 1694])).
% 11.25/11.45 tff(1704,plain,
% 11.25/11.45 (((~![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_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)))),
% 11.25/11.45 inference(rewrite,[status(thm)],[])).
% 11.25/11.45 tff(1705,plain,
% 11.25/11.45 (((~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)))),
% 11.25/11.45 inference(rewrite,[status(thm)],[])).
% 11.25/11.45 tff(1706,plain,
% 11.25/11.45 (((~![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_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))))),
% 11.25/11.45 inference(monotonicity,[status(thm)],[1705])).
% 11.25/11.45 tff(1707,plain,
% 11.25/11.45 (((~![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_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)))),
% 11.25/11.45 inference(transitivity,[status(thm)],[1706, 1704])).
% 11.25/11.45 tff(1708,plain,
% 11.25/11.45 ((~![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_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)))),
% 11.25/11.45 inference(quant_inst,[status(thm)],[])).
% 11.25/11.45 tff(1709,plain,
% 11.25/11.45 ((~![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_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))),
% 11.25/11.45 inference(modus_ponens,[status(thm)],[1708, 1707])).
% 11.25/11.45 tff(1710,plain,
% 11.25/11.45 (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))),
% 11.25/11.45 inference(unit_resolution,[status(thm)],[1709, 427])).
% 11.25/11.45 tff(1711,plain,
% 11.25/11.45 (~node14(c_e_h_3, c_h, s2, s3)),
% 11.25/11.45 inference(unit_resolution,[status(thm)],[1710, 1703, 1671])).
% 11.25/11.45 tff(1712,plain,
% 11.25/11.45 (((~![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_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))),
% 11.25/11.45 inference(rewrite,[status(thm)],[])).
% 11.25/11.45 tff(1713,plain,
% 11.25/11.45 ((~![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_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))),
% 11.25/11.45 inference(quant_inst,[status(thm)],[])).
% 11.25/11.45 tff(1714,plain,
% 11.25/11.45 ((~![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_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)),
% 11.25/11.45 inference(modus_ponens,[status(thm)],[1713, 1712])).
% 11.25/11.45 tff(1715,plain,
% 11.25/11.45 ((~node16(c_e_h_3, c_h, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s2)),
% 11.25/11.45 inference(unit_resolution,[status(thm)],[1714, 377, 1695])).
% 11.31/11.45 tff(1716,plain,
% 11.31/11.45 (~node16(c_e_h_3, c_h, s2)),
% 11.31/11.45 inference(unit_resolution,[status(thm)],[1715, 1703])).
% 11.31/11.45 tff(1717,plain,
% 11.31/11.45 (((~![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_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))) <=> ((~![Y: $i, I0: $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, 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))),
% 11.31/11.45 inference(rewrite,[status(thm)],[])).
% 11.31/11.45 tff(1718,plain,
% 11.31/11.45 ((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))) <=> (node14(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))),
% 11.31/11.45 inference(rewrite,[status(thm)],[])).
% 11.31/11.45 tff(1719,plain,
% 11.31/11.45 (((~![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_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)))) | (node14(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)))),
% 11.31/11.45 inference(monotonicity,[status(thm)],[1718])).
% 11.31/11.45 tff(1720,plain,
% 11.31/11.45 (((~![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_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)))) | node14(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))),
% 11.31/11.45 inference(transitivity,[status(thm)],[1719, 1717])).
% 11.31/11.45 tff(1721,plain,
% 11.31/11.45 ((~![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_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)))),
% 11.31/11.45 inference(quant_inst,[status(thm)],[])).
% 11.31/11.45 tff(1722,plain,
% 11.31/11.45 ((~![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_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)),
% 11.31/11.45 inference(modus_ponens,[status(thm)],[1721, 1720])).
% 11.31/11.45 tff(1723,plain,
% 11.31/11.45 (node14(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)),
% 11.31/11.45 inference(unit_resolution,[status(thm)],[1722, 409, 1686])).
% 11.31/11.45 tff(1724,plain,
% 11.31/11.45 (node15(c_e_h_3, c_h, s2, s3)),
% 11.31/11.45 inference(unit_resolution,[status(thm)],[1723, 1716, 1711])).
% 11.31/11.45 tff(1725,plain,
% 11.31/11.45 (((~![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_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))),
% 11.31/11.45 inference(rewrite,[status(thm)],[])).
% 11.31/11.45 tff(1726,plain,
% 11.31/11.45 ((~![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_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))),
% 11.31/11.45 inference(quant_inst,[status(thm)],[])).
% 11.31/11.45 tff(1727,plain,
% 11.31/11.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node15(c_e_h_3, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s2)),
% 11.31/11.46 inference(modus_ponens,[status(thm)],[1726, 1725])).
% 11.31/11.46 tff(1728,plain,
% 11.31/11.46 ($false),
% 11.31/11.46 inference(unit_resolution,[status(thm)],[1727, 393, 1671, 1672, 1724])).
% 11.31/11.46 tff(1729,plain,((~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) | m_c_h_element_v_in2(c_e_h_3, c_h, s2)), inference(lemma,lemma(discharge,[]))).
% 11.31/11.46 tff(1730,plain,
% 11.31/11.46 ((~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | m_c_h_element_v_in2(c_e_h_3, c_h, s2)),
% 11.31/11.46 inference(unit_resolution,[status(thm)],[1729, 1670])).
% 11.31/11.46 tff(1731,plain,
% 11.31/11.46 (~m_c_h_element_v_out(c_e_h_3, c_h, s3)),
% 11.31/11.46 inference(unit_resolution,[status(thm)],[1730, 1566])).
% 11.31/11.46 tff(1732,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s4)), introduced(assumption)).
% 11.31/11.46 tff(1733,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_h, s3)), introduced(assumption)).
% 11.31/11.46 tff(1734,assumption,(~m_c_h_element_v_out(c_e_h_3, c_h, s3)), introduced(assumption)).
% 11.31/11.46 tff(1735,assumption,(node18(c_e_h_3, c_h, s3, s4)), introduced(assumption)).
% 11.31/11.46 tff(1736,plain,
% 11.31/11.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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)))),
% 11.31/11.46 inference(rewrite,[status(thm)],[])).
% 11.31/11.46 tff(1737,plain,
% 11.31/11.46 (((~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)))),
% 11.31/11.46 inference(rewrite,[status(thm)],[])).
% 11.31/11.46 tff(1738,plain,
% 11.31/11.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))))),
% 11.31/11.46 inference(monotonicity,[status(thm)],[1737])).
% 11.31/11.46 tff(1739,plain,
% 11.31/11.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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)))),
% 11.31/11.46 inference(transitivity,[status(thm)],[1738, 1736])).
% 11.31/11.46 tff(1740,plain,
% 11.31/11.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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)))),
% 11.31/11.46 inference(quant_inst,[status(thm)],[])).
% 11.31/11.46 tff(1741,plain,
% 11.31/11.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node18(c_e_h_3, c_h, s3, s4))),
% 11.31/11.46 inference(modus_ponens,[status(thm)],[1740, 1739])).
% 11.31/11.46 tff(1742,plain,
% 11.31/11.46 ($false),
% 11.31/11.46 inference(unit_resolution,[status(thm)],[1741, 296, 1732, 1734, 1735])).
% 11.31/11.46 tff(1743,plain,((~node18(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_out(c_e_h_3, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 11.31/11.46 tff(1744,plain,
% 11.31/11.46 (~node18(c_e_h_3, c_h, s3, s4)),
% 11.31/11.46 inference(unit_resolution,[status(thm)],[1743, 1732, 1734])).
% 11.31/11.46 tff(1745,plain,
% 11.31/11.46 (((~![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))),
% 11.31/11.46 inference(rewrite,[status(thm)],[])).
% 11.31/11.46 tff(1746,plain,
% 11.31/11.46 ((~![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))),
% 11.31/11.46 inference(quant_inst,[status(thm)],[])).
% 11.31/11.46 tff(1747,plain,
% 11.31/11.46 ((~![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)),
% 11.31/11.46 inference(modus_ponens,[status(thm)],[1746, 1745])).
% 11.31/11.46 tff(1748,plain,
% 11.31/11.46 (node19(c_e_h_3, c_h, s3, s4)),
% 11.31/11.46 inference(unit_resolution,[status(thm)],[1747, 312, 1092])).
% 11.31/11.46 tff(1749,plain,
% 11.31/11.46 (((~![Y: $i, 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) | (~node19(c_e_h_3, c_h, s3, s4)) | node18(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) | (~node19(c_e_h_3, c_h, s3, s4)) | node18(c_e_h_3, c_h, s3, s4))),
% 11.31/11.46 inference(rewrite,[status(thm)],[])).
% 11.31/11.46 tff(1750,plain,
% 11.31/11.46 ((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))) <=> (node17(c_e_h_3, c_h, s3) | (~node19(c_e_h_3, c_h, s3, s4)) | node18(c_e_h_3, c_h, s3, s4))),
% 11.31/11.46 inference(rewrite,[status(thm)],[])).
% 11.31/11.46 tff(1751,plain,
% 11.31/11.46 (((~![Y: $i, 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) | (~node19(c_e_h_3, c_h, s3, s4)) | node18(c_e_h_3, c_h, s3, s4)))),
% 11.31/11.46 inference(monotonicity,[status(thm)],[1750])).
% 11.31/11.46 tff(1752,plain,
% 11.31/11.46 (((~![Y: $i, 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) | (~node19(c_e_h_3, c_h, s3, s4)) | node18(c_e_h_3, c_h, s3, s4))),
% 11.31/11.46 inference(transitivity,[status(thm)],[1751, 1749])).
% 11.31/11.46 tff(1753,plain,
% 11.31/11.46 ((~![Y: $i, 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)))),
% 11.31/11.46 inference(quant_inst,[status(thm)],[])).
% 11.31/11.46 tff(1754,plain,
% 11.31/11.46 ((~![Y: $i, 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) | (~node19(c_e_h_3, c_h, s3, s4)) | node18(c_e_h_3, c_h, s3, s4)),
% 11.31/11.46 inference(modus_ponens,[status(thm)],[1753, 1752])).
% 11.31/11.46 tff(1755,plain,
% 11.31/11.46 (node17(c_e_h_3, c_h, s3) | node18(c_e_h_3, c_h, s3, s4)),
% 11.31/11.46 inference(unit_resolution,[status(thm)],[1754, 326, 1748])).
% 11.31/11.46 tff(1756,plain,
% 11.31/11.46 (node17(c_e_h_3, c_h, s3)),
% 11.31/11.46 inference(unit_resolution,[status(thm)],[1755, 1744])).
% 11.31/11.46 tff(1757,plain,
% 11.31/11.46 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, 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)) | (~node17(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] : ((~m_c_h_element_v_in1(I0, 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)) | (~node17(c_e_h_3, c_h, s3)) | m_c_h_element_v_in2(c_e_h_3, c_h, s3))),
% 11.31/11.46 inference(rewrite,[status(thm)],[])).
% 11.31/11.46 tff(1758,plain,
% 11.31/11.46 (((~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_in1(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))),
% 11.31/11.46 inference(rewrite,[status(thm)],[])).
% 11.31/11.46 tff(1759,plain,
% 11.31/11.46 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, 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_in1(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)))),
% 11.31/11.46 inference(monotonicity,[status(thm)],[1758])).
% 11.31/11.46 tff(1760,plain,
% 11.31/11.46 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, 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_in1(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))),
% 11.31/11.46 inference(transitivity,[status(thm)],[1759, 1757])).
% 11.31/11.46 tff(1761,plain,
% 11.31/11.46 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, 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)))),
% 11.31/11.46 inference(quant_inst,[status(thm)],[])).
% 11.31/11.46 tff(1762,plain,
% 11.31/11.46 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, 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)) | (~node17(c_e_h_3, c_h, s3)) | m_c_h_element_v_in2(c_e_h_3, c_h, s3)),
% 11.31/11.46 inference(modus_ponens,[status(thm)],[1761, 1760])).
% 11.31/11.46 tff(1763,plain,
% 11.31/11.46 ((~m_c_h_element_v_in1(c_e_h_3, c_h, s3)) | (~node17(c_e_h_3, c_h, s3))),
% 11.31/11.46 inference(unit_resolution,[status(thm)],[1762, 359, 1733])).
% 11.31/11.46 tff(1764,plain,
% 11.31/11.46 (~m_c_h_element_v_in1(c_e_h_3, c_h, s3)),
% 11.31/11.46 inference(unit_resolution,[status(thm)],[1763, 1756])).
% 11.31/11.46 tff(1765,assumption,(~node15(c_e_h_3, c_h, s3, s4)), introduced(assumption)).
% 11.31/11.46 tff(1766,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_h, s3)), introduced(assumption)).
% 11.31/11.46 tff(1767,plain,
% 11.31/11.46 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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))),
% 11.31/11.46 inference(rewrite,[status(thm)],[])).
% 11.31/11.46 tff(1768,plain,
% 11.31/11.46 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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))),
% 11.31/11.46 inference(quant_inst,[status(thm)],[])).
% 11.31/11.46 tff(1769,plain,
% 11.31/11.46 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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)),
% 11.31/11.46 inference(modus_ponens,[status(thm)],[1768, 1767])).
% 11.31/11.46 tff(1770,plain,
% 11.31/11.46 ((~node16(c_e_h_3, c_h, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3)),
% 11.31/11.46 inference(unit_resolution,[status(thm)],[1769, 377, 1733])).
% 11.31/11.46 tff(1771,plain,
% 11.31/11.46 (~node16(c_e_h_3, c_h, s3)),
% 11.31/11.46 inference(unit_resolution,[status(thm)],[1770, 1766])).
% 11.31/11.46 tff(1772,plain,
% 11.31/11.46 (((~![Y: $i, I0: $i, X: $i, I1: $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) | (~node19(c_e_h_3, c_h, s3, s4)) | node15(c_e_h_3, c_h, s3, s4) | node14(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) | (~node19(c_e_h_3, c_h, s3, s4)) | node15(c_e_h_3, c_h, s3, s4) | node14(c_e_h_3, c_h, s3, s4))),
% 11.32/11.46 inference(rewrite,[status(thm)],[])).
% 11.32/11.46 tff(1773,plain,
% 11.32/11.46 ((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) | (~node19(c_e_h_3, c_h, s3, s4)) | node15(c_e_h_3, c_h, s3, s4) | node14(c_e_h_3, c_h, s3, s4))),
% 11.32/11.46 inference(rewrite,[status(thm)],[])).
% 11.32/11.46 tff(1774,plain,
% 11.32/11.46 (((~![Y: $i, I0: $i, X: $i, I1: $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) | (~node19(c_e_h_3, c_h, s3, s4)) | node15(c_e_h_3, c_h, s3, s4) | node14(c_e_h_3, c_h, s3, s4)))),
% 11.32/11.46 inference(monotonicity,[status(thm)],[1773])).
% 11.32/11.46 tff(1775,plain,
% 11.32/11.46 (((~![Y: $i, I0: $i, X: $i, I1: $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) | (~node19(c_e_h_3, c_h, s3, s4)) | node15(c_e_h_3, c_h, s3, s4) | node14(c_e_h_3, c_h, s3, s4))),
% 11.32/11.46 inference(transitivity,[status(thm)],[1774, 1772])).
% 11.32/11.46 tff(1776,plain,
% 11.32/11.46 ((~![Y: $i, I0: $i, X: $i, I1: $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)))),
% 11.32/11.46 inference(quant_inst,[status(thm)],[])).
% 11.32/11.46 tff(1777,plain,
% 11.32/11.46 ((~![Y: $i, I0: $i, X: $i, I1: $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) | (~node19(c_e_h_3, c_h, s3, s4)) | node15(c_e_h_3, c_h, s3, s4) | node14(c_e_h_3, c_h, s3, s4)),
% 11.32/11.46 inference(modus_ponens,[status(thm)],[1776, 1775])).
% 11.32/11.46 tff(1778,plain,
% 11.32/11.46 (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)),
% 11.32/11.46 inference(unit_resolution,[status(thm)],[1777, 409, 1748])).
% 11.32/11.46 tff(1779,plain,
% 11.32/11.46 (node14(c_e_h_3, c_h, s3, s4)),
% 11.32/11.46 inference(unit_resolution,[status(thm)],[1778, 1771, 1765])).
% 11.32/11.46 tff(1780,plain,
% 11.32/11.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_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, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~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_in1(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node14(c_e_h_3, c_h, s3, s4)))),
% 11.32/11.46 inference(rewrite,[status(thm)],[])).
% 11.32/11.46 tff(1781,plain,
% 11.32/11.46 (((~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_in1(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node14(c_e_h_3, c_h, s3, s4)))),
% 11.32/11.46 inference(rewrite,[status(thm)],[])).
% 11.32/11.46 tff(1782,plain,
% 11.32/11.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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_in1(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node14(c_e_h_3, c_h, s3, s4))))),
% 11.32/11.46 inference(monotonicity,[status(thm)],[1781])).
% 11.32/11.46 tff(1783,plain,
% 11.32/11.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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_in1(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node14(c_e_h_3, c_h, s3, s4)))),
% 11.32/11.46 inference(transitivity,[status(thm)],[1782, 1780])).
% 11.32/11.46 tff(1784,plain,
% 11.32/11.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))),
% 11.32/11.46 inference(quant_inst,[status(thm)],[])).
% 11.32/11.46 tff(1785,plain,
% 11.32/11.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node14(c_e_h_3, c_h, s3, s4))),
% 11.32/11.46 inference(modus_ponens,[status(thm)],[1784, 1783])).
% 11.32/11.46 tff(1786,plain,
% 11.32/11.46 ($false),
% 11.32/11.46 inference(unit_resolution,[status(thm)],[1785, 427, 1732, 1766, 1779])).
% 11.32/11.46 tff(1787,plain,(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)) | node15(c_e_h_3, c_h, s3, s4) | m_c_h_element_v_in2(c_e_h_3, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 11.32/11.46 tff(1788,plain,
% 11.32/11.46 (node15(c_e_h_3, c_h, s3, s4)),
% 11.32/11.46 inference(unit_resolution,[status(thm)],[1787, 1764, 1733, 1732])).
% 11.32/11.46 tff(1789,plain,
% 11.32/11.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 11.32/11.46 inference(rewrite,[status(thm)],[])).
% 11.32/11.46 tff(1790,plain,
% 11.32/11.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 11.32/11.46 inference(quant_inst,[status(thm)],[])).
% 11.32/11.46 tff(1791,plain,
% 11.32/11.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node15(c_e_h_3, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s3)),
% 11.32/11.46 inference(modus_ponens,[status(thm)],[1790, 1789])).
% 11.32/11.46 tff(1792,plain,
% 11.32/11.46 ($false),
% 11.32/11.46 inference(unit_resolution,[status(thm)],[1791, 393, 1732, 1734, 1788])).
% 11.32/11.46 tff(1793,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, s3) | m_c_h_element_v_in2(c_e_h_3, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 11.32/11.46 tff(1794,plain,
% 11.32/11.46 ((~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)),
% 11.32/11.46 inference(unit_resolution,[status(thm)],[1793, 1731])).
% 11.32/11.46 tff(1795,plain,
% 11.32/11.46 (~m_c_h_element_v_out(c_e_h_3, c_h, s4)),
% 11.32/11.46 inference(unit_resolution,[status(thm)],[1794, 1562])).
% 11.32/11.46 tff(1796,assumption,(~m_c_h_element_v_out(c_e_h_3, c_h, s4)), introduced(assumption)).
% 11.32/11.46 tff(1797,plain,
% 11.32/11.46 (((~![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_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))),
% 11.32/11.46 inference(rewrite,[status(thm)],[])).
% 11.32/11.46 tff(1798,plain,
% 11.32/11.46 ((~![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_3, c_i, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s4))),
% 11.32/11.46 inference(quant_inst,[status(thm)],[])).
% 11.32/11.46 tff(1799,plain,
% 11.32/11.46 ((~![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_3, c_i, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s4)),
% 11.32/11.46 inference(modus_ponens,[status(thm)],[1798, 1797])).
% 11.32/11.46 tff(1800,plain,
% 11.32/11.46 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s4)),
% 11.32/11.46 inference(unit_resolution,[status(thm)],[1799, 503, 1796])).
% 11.32/11.46 tff(1801,plain,
% 11.32/11.46 (((~![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))),
% 11.32/11.46 inference(rewrite,[status(thm)],[])).
% 11.32/11.46 tff(1802,plain,
% 11.32/11.46 ((~![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))),
% 11.32/11.46 inference(quant_inst,[status(thm)],[])).
% 11.32/11.46 tff(1803,plain,
% 11.32/11.46 ((~![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)),
% 11.32/11.46 inference(modus_ponens,[status(thm)],[1802, 1801])).
% 11.32/11.46 tff(1804,plain,
% 11.32/11.46 (~node20(c_e_h_3, c_i, s4)),
% 11.32/11.46 inference(unit_resolution,[status(thm)],[1803, 213, 1800])).
% 11.32/11.46 tff(1805,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s3)), introduced(assumption)).
% 11.32/11.46 tff(1806,plain,
% 11.32/11.46 (((~![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_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))),
% 11.32/11.46 inference(rewrite,[status(thm)],[])).
% 11.32/11.46 tff(1807,plain,
% 11.32/11.46 ((~![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_3, c_i, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s2))),
% 11.32/11.46 inference(quant_inst,[status(thm)],[])).
% 11.32/11.46 tff(1808,plain,
% 11.32/11.46 ((~![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_3, c_i, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s2)),
% 11.32/11.46 inference(modus_ponens,[status(thm)],[1807, 1806])).
% 11.32/11.46 tff(1809,plain,
% 11.32/11.46 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s2)),
% 11.32/11.46 inference(unit_resolution,[status(thm)],[1808, 503, 1670])).
% 11.32/11.46 tff(1810,plain,
% 11.32/11.46 (((~![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))),
% 11.32/11.46 inference(rewrite,[status(thm)],[])).
% 11.32/11.46 tff(1811,plain,
% 11.32/11.46 ((~![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))),
% 11.32/11.46 inference(quant_inst,[status(thm)],[])).
% 11.32/11.46 tff(1812,plain,
% 11.32/11.46 ((~![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)),
% 11.32/11.46 inference(modus_ponens,[status(thm)],[1811, 1810])).
% 11.32/11.46 tff(1813,plain,
% 11.32/11.46 (~node20(c_e_h_3, c_i, s2)),
% 11.32/11.46 inference(unit_resolution,[status(thm)],[1812, 213, 1809])).
% 11.32/11.46 tff(1814,assumption,(node21(c_e_h_3, c_i, s2, s3)), introduced(assumption)).
% 11.32/11.46 tff(1815,assumption,(~node20(c_e_h_3, c_i, s2)), introduced(assumption)).
% 11.32/11.46 tff(1816,plain,
% 11.32/11.46 (((~![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_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)))),
% 11.32/11.47 inference(rewrite,[status(thm)],[])).
% 11.32/11.47 tff(1817,plain,
% 11.32/11.47 ((~![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_i, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | (~node21(c_e_h_3, c_i, s2, s3)))),
% 11.32/11.47 inference(quant_inst,[status(thm)],[])).
% 11.32/11.47 tff(1818,plain,
% 11.32/11.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | (~node21(c_e_h_3, c_i, s2, s3))),
% 11.32/11.47 inference(modus_ponens,[status(thm)],[1817, 1816])).
% 11.32/11.47 tff(1819,plain,
% 11.32/11.47 ($false),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1818, 228, 1805, 1815, 1814])).
% 11.32/11.47 tff(1820,plain,((~node21(c_e_h_3, c_i, s2, s3)) | (~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,[]))).
% 11.32/11.47 tff(1821,plain,
% 11.32/11.47 ((~node21(c_e_h_3, c_i, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s3))),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1820, 1813])).
% 11.32/11.47 tff(1822,plain,
% 11.32/11.47 (~node21(c_e_h_3, c_i, s2, s3)),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1821, 1805])).
% 11.32/11.47 tff(1823,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s2)), introduced(assumption)).
% 11.32/11.47 tff(1824,plain,
% 11.32/11.47 (((~![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))),
% 11.32/11.47 inference(rewrite,[status(thm)],[])).
% 11.32/11.47 tff(1825,plain,
% 11.32/11.47 ((~![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))),
% 11.32/11.47 inference(quant_inst,[status(thm)],[])).
% 11.32/11.47 tff(1826,plain,
% 11.32/11.47 ((~![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)),
% 11.32/11.47 inference(modus_ponens,[status(thm)],[1825, 1824])).
% 11.32/11.47 tff(1827,plain,
% 11.32/11.47 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s1)),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1826, 503, 1619])).
% 11.32/11.47 tff(1828,plain,
% 11.32/11.47 (((~![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))),
% 11.32/11.47 inference(rewrite,[status(thm)],[])).
% 11.32/11.47 tff(1829,plain,
% 11.32/11.47 ((~![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))),
% 11.32/11.47 inference(quant_inst,[status(thm)],[])).
% 11.32/11.47 tff(1830,plain,
% 11.32/11.47 ((~![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)),
% 11.32/11.47 inference(modus_ponens,[status(thm)],[1829, 1828])).
% 11.32/11.47 tff(1831,plain,
% 11.32/11.47 (~node20(c_e_h_3, c_i, s1)),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1830, 213, 1827])).
% 11.32/11.47 tff(1832,assumption,(node21(c_e_h_3, c_i, s1, s2)), introduced(assumption)).
% 11.32/11.47 tff(1833,assumption,(~node20(c_e_h_3, c_i, s1)), introduced(assumption)).
% 11.32/11.47 tff(1834,plain,
% 11.32/11.47 (((~![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_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) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2)) | (~node21(c_e_h_3, c_i, s1, s2)))),
% 11.32/11.47 inference(rewrite,[status(thm)],[])).
% 11.32/11.47 tff(1835,plain,
% 11.32/11.47 ((~![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_i, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2)) | (~node21(c_e_h_3, c_i, s1, s2)))),
% 11.32/11.47 inference(quant_inst,[status(thm)],[])).
% 11.32/11.47 tff(1836,plain,
% 11.32/11.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2)) | (~node21(c_e_h_3, c_i, s1, s2))),
% 11.32/11.47 inference(modus_ponens,[status(thm)],[1835, 1834])).
% 11.32/11.47 tff(1837,plain,
% 11.32/11.47 ($false),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1836, 228, 1823, 1833, 1832])).
% 11.32/11.47 tff(1838,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,[]))).
% 11.32/11.47 tff(1839,plain,
% 11.32/11.47 ((~node21(c_e_h_3, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2))),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1838, 1831])).
% 11.32/11.47 tff(1840,plain,
% 11.32/11.47 (~node21(c_e_h_3, c_i, s1, s2)),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1839, 1823])).
% 11.32/11.47 tff(1841,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s1)), introduced(assumption)).
% 11.32/11.47 tff(1842,assumption,(node21(c_e_h_3, c_i, s0, s1)), introduced(assumption)).
% 11.32/11.47 tff(1843,plain,
% 11.32/11.47 (((~![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))),
% 11.32/11.47 inference(rewrite,[status(thm)],[])).
% 11.32/11.47 tff(1844,plain,
% 11.32/11.47 ((~![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))),
% 11.32/11.47 inference(quant_inst,[status(thm)],[])).
% 11.32/11.47 tff(1845,plain,
% 11.32/11.47 ((~![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)),
% 11.32/11.47 inference(modus_ponens,[status(thm)],[1844, 1843])).
% 11.32/11.47 tff(1846,plain,
% 11.32/11.47 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s0)),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1845, 503, 1614])).
% 11.32/11.47 tff(1847,plain,
% 11.32/11.47 (((~![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))),
% 11.32/11.47 inference(rewrite,[status(thm)],[])).
% 11.32/11.47 tff(1848,plain,
% 11.32/11.47 ((~![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))),
% 11.32/11.47 inference(quant_inst,[status(thm)],[])).
% 11.32/11.47 tff(1849,plain,
% 11.32/11.47 ((~![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)),
% 11.32/11.47 inference(modus_ponens,[status(thm)],[1848, 1847])).
% 11.32/11.47 tff(1850,plain,
% 11.32/11.47 (~node20(c_e_h_3, c_i, s0)),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1849, 213, 1846])).
% 11.32/11.47 tff(1851,plain,
% 11.32/11.47 (((~![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_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)))),
% 11.32/11.47 inference(rewrite,[status(thm)],[])).
% 11.32/11.47 tff(1852,plain,
% 11.32/11.47 ((~![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_i, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1)) | (~node21(c_e_h_3, c_i, s0, s1)))),
% 11.32/11.47 inference(quant_inst,[status(thm)],[])).
% 11.32/11.47 tff(1853,plain,
% 11.32/11.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1)) | (~node21(c_e_h_3, c_i, s0, s1))),
% 11.32/11.47 inference(modus_ponens,[status(thm)],[1852, 1851])).
% 11.32/11.47 tff(1854,plain,
% 11.32/11.47 ($false),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1853, 228, 1841, 1850, 1842])).
% 11.32/11.47 tff(1855,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,[]))).
% 11.32/11.47 tff(1856,plain,
% 11.32/11.47 (~node21(c_e_h_3, c_i, s0, s1)),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1855, 1841])).
% 11.32/11.47 tff(1857,plain,
% 11.32/11.47 (((~![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))),
% 11.32/11.47 inference(rewrite,[status(thm)],[])).
% 11.32/11.47 tff(1858,plain,
% 11.32/11.47 ((~![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))),
% 11.32/11.47 inference(quant_inst,[status(thm)],[])).
% 11.32/11.47 tff(1859,plain,
% 11.32/11.47 ((~![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)),
% 11.32/11.47 inference(modus_ponens,[status(thm)],[1858, 1857])).
% 11.32/11.47 tff(1860,plain,
% 11.32/11.47 (node21(c_e_h_3, c_i, s0, s1) | node22(c_e_h_3, c_i, s0, s1)),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1859, 247, 100])).
% 11.32/11.47 tff(1861,plain,
% 11.32/11.47 (node22(c_e_h_3, c_i, s0, s1)),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1860, 1856])).
% 11.32/11.47 tff(1862,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s0)), introduced(assumption)).
% 11.32/11.47 tff(1863,plain,
% 11.32/11.47 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s0))),
% 11.32/11.47 inference(quant_inst,[status(thm)],[])).
% 11.32/11.47 tff(1864,plain,
% 11.32/11.47 ($false),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1863, 260, 1862])).
% 11.32/11.47 tff(1865,plain,(~m_and_h_gate_v_out(c_e_h_3, c_i, s0)), inference(lemma,lemma(discharge,[]))).
% 11.32/11.47 tff(1866,plain,
% 11.32/11.47 (((~![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_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))),
% 11.32/11.47 inference(rewrite,[status(thm)],[])).
% 11.32/11.47 tff(1867,plain,
% 11.32/11.47 ((~![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_i, s1)) | (~node22(c_e_h_3, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0))),
% 11.32/11.47 inference(quant_inst,[status(thm)],[])).
% 11.32/11.47 tff(1868,plain,
% 11.32/11.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1)) | (~node22(c_e_h_3, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0)),
% 11.32/11.47 inference(modus_ponens,[status(thm)],[1867, 1866])).
% 11.32/11.47 tff(1869,plain,
% 11.32/11.47 ($false),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1868, 273, 1865, 1841, 1861])).
% 11.32/11.47 tff(1870,plain,(~m_and_h_gate_v_out(c_e_h_3, c_i, s1)), inference(lemma,lemma(discharge,[]))).
% 11.32/11.47 tff(1871,assumption,(node22(c_e_h_3, c_i, s1, s2)), introduced(assumption)).
% 11.32/11.47 tff(1872,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s1)), introduced(assumption)).
% 11.32/11.47 tff(1873,plain,
% 11.32/11.47 (((~![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_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))),
% 11.32/11.47 inference(rewrite,[status(thm)],[])).
% 11.32/11.47 tff(1874,plain,
% 11.32/11.47 ((~![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_i, s2)) | (~node22(c_e_h_3, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1))),
% 11.32/11.47 inference(quant_inst,[status(thm)],[])).
% 11.32/11.47 tff(1875,plain,
% 11.32/11.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2)) | (~node22(c_e_h_3, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1)),
% 11.32/11.47 inference(modus_ponens,[status(thm)],[1874, 1873])).
% 11.32/11.47 tff(1876,plain,
% 11.32/11.47 ($false),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1875, 273, 1872, 1823, 1871])).
% 11.32/11.47 tff(1877,plain,((~node22(c_e_h_3, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2))), inference(lemma,lemma(discharge,[]))).
% 11.32/11.47 tff(1878,plain,
% 11.32/11.47 ((~node22(c_e_h_3, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2))),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1877, 1870])).
% 11.32/11.47 tff(1879,plain,
% 11.32/11.47 (~node22(c_e_h_3, c_i, s1, s2)),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1878, 1823])).
% 11.32/11.47 tff(1880,plain,
% 11.32/11.47 (((~![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))),
% 11.32/11.47 inference(rewrite,[status(thm)],[])).
% 11.32/11.47 tff(1881,plain,
% 11.32/11.47 ((~![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))),
% 11.32/11.47 inference(quant_inst,[status(thm)],[])).
% 11.32/11.47 tff(1882,plain,
% 11.32/11.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_i, s1, s2) | node22(c_e_h_3, c_i, s1, s2)),
% 11.32/11.47 inference(modus_ponens,[status(thm)],[1881, 1880])).
% 11.32/11.47 tff(1883,plain,
% 11.32/11.47 (node21(c_e_h_3, c_i, s1, s2) | node22(c_e_h_3, c_i, s1, s2)),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1882, 247, 470])).
% 11.32/11.47 tff(1884,plain,
% 11.32/11.47 ($false),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1883, 1879, 1840])).
% 11.32/11.47 tff(1885,plain,(~m_and_h_gate_v_out(c_e_h_3, c_i, s2)), inference(lemma,lemma(discharge,[]))).
% 11.32/11.47 tff(1886,assumption,(node22(c_e_h_3, c_i, s2, s3)), introduced(assumption)).
% 11.32/11.47 tff(1887,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s2)), introduced(assumption)).
% 11.32/11.47 tff(1888,plain,
% 11.32/11.47 (((~![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_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))),
% 11.32/11.47 inference(rewrite,[status(thm)],[])).
% 11.32/11.47 tff(1889,plain,
% 11.32/11.47 ((~![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_i, s3)) | (~node22(c_e_h_3, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2))),
% 11.32/11.47 inference(quant_inst,[status(thm)],[])).
% 11.32/11.47 tff(1890,plain,
% 11.32/11.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | (~node22(c_e_h_3, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2)),
% 11.32/11.47 inference(modus_ponens,[status(thm)],[1889, 1888])).
% 11.32/11.47 tff(1891,plain,
% 11.32/11.47 ($false),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1890, 273, 1805, 1887, 1886])).
% 11.32/11.47 tff(1892,plain,((~node22(c_e_h_3, c_i, s2, s3)) | (~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, s2)), inference(lemma,lemma(discharge,[]))).
% 11.32/11.47 tff(1893,plain,
% 11.32/11.47 ((~node22(c_e_h_3, c_i, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s3))),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1892, 1885])).
% 11.32/11.47 tff(1894,plain,
% 11.32/11.47 (~node22(c_e_h_3, c_i, s2, s3)),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1893, 1805])).
% 11.32/11.47 tff(1895,plain,
% 11.32/11.47 (((~![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))),
% 11.32/11.47 inference(rewrite,[status(thm)],[])).
% 11.32/11.47 tff(1896,plain,
% 11.32/11.47 ((~![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))),
% 11.32/11.47 inference(quant_inst,[status(thm)],[])).
% 11.32/11.47 tff(1897,plain,
% 11.32/11.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_i, s2, s3) | node22(c_e_h_3, c_i, s2, s3)),
% 11.32/11.47 inference(modus_ponens,[status(thm)],[1896, 1895])).
% 11.32/11.47 tff(1898,plain,
% 11.32/11.47 (node21(c_e_h_3, c_i, s2, s3) | node22(c_e_h_3, c_i, s2, s3)),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1897, 247, 604])).
% 11.32/11.47 tff(1899,plain,
% 11.32/11.47 ($false),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1898, 1894, 1822])).
% 11.32/11.47 tff(1900,plain,(~m_and_h_gate_v_out(c_e_h_3, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 11.32/11.47 tff(1901,plain,
% 11.32/11.47 (((~![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))),
% 11.32/11.47 inference(rewrite,[status(thm)],[])).
% 11.32/11.47 tff(1902,plain,
% 11.32/11.47 ((~![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))),
% 11.32/11.47 inference(quant_inst,[status(thm)],[])).
% 11.32/11.47 tff(1903,plain,
% 11.32/11.47 ((~![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)),
% 11.32/11.47 inference(modus_ponens,[status(thm)],[1902, 1901])).
% 11.32/11.47 tff(1904,plain,
% 11.32/11.47 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s3)),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1903, 503, 1731])).
% 11.32/11.47 tff(1905,plain,
% 11.32/11.47 (((~![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))),
% 11.32/11.47 inference(rewrite,[status(thm)],[])).
% 11.32/11.47 tff(1906,plain,
% 11.32/11.47 ((~![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))),
% 11.32/11.47 inference(quant_inst,[status(thm)],[])).
% 11.32/11.47 tff(1907,plain,
% 11.32/11.47 ((~![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)),
% 11.32/11.47 inference(modus_ponens,[status(thm)],[1906, 1905])).
% 11.32/11.47 tff(1908,plain,
% 11.32/11.47 (~node20(c_e_h_3, c_i, s3)),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1907, 213, 1904])).
% 11.32/11.47 tff(1909,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s3)), introduced(assumption)).
% 11.32/11.47 tff(1910,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s4)), introduced(assumption)).
% 11.32/11.47 tff(1911,assumption,(node22(c_e_h_3, c_i, s3, s4)), introduced(assumption)).
% 11.32/11.47 tff(1912,plain,
% 11.32/11.47 (((~![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_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))),
% 11.32/11.47 inference(rewrite,[status(thm)],[])).
% 11.32/11.47 tff(1913,plain,
% 11.32/11.47 ((~![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_i, s4)) | (~node22(c_e_h_3, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3))),
% 11.32/11.47 inference(quant_inst,[status(thm)],[])).
% 11.32/11.47 tff(1914,plain,
% 11.32/11.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | (~node22(c_e_h_3, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3)),
% 11.32/11.47 inference(modus_ponens,[status(thm)],[1913, 1912])).
% 11.32/11.47 tff(1915,plain,
% 11.32/11.47 ($false),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1914, 273, 1910, 1909, 1911])).
% 11.32/11.47 tff(1916,plain,((~node22(c_e_h_3, c_i, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 11.32/11.47 tff(1917,plain,
% 11.32/11.47 (~node22(c_e_h_3, c_i, s3, s4)),
% 11.32/11.47 inference(unit_resolution,[status(thm)],[1916, 1910, 1909])).
% 11.32/11.47 tff(1918,assumption,(~node20(c_e_h_3, c_i, s3)), introduced(assumption)).
% 11.32/11.47 tff(1919,assumption,(node21(c_e_h_3, c_i, s3, s4)), introduced(assumption)).
% 11.32/11.47 tff(1920,plain,
% 11.32/11.47 (((~![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_i, s3) | (~node21(c_e_h_3, c_i, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, 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) | (~node21(c_e_h_3, c_i, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)))),
% 11.32/11.47 inference(rewrite,[status(thm)],[])).
% 11.32/11.47 tff(1921,plain,
% 11.32/11.47 ((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))) <=> (node20(c_e_h_3, c_i, s3) | (~node21(c_e_h_3, c_i, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)))),
% 11.32/11.47 inference(rewrite,[status(thm)],[])).
% 11.32/11.47 tff(1922,plain,
% 11.32/11.47 (((~![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_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) | (~node21(c_e_h_3, c_i, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4))))),
% 11.32/11.47 inference(monotonicity,[status(thm)],[1921])).
% 11.32/11.47 tff(1923,plain,
% 11.32/11.47 (((~![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_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) | (~node21(c_e_h_3, c_i, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)))),
% 11.32/11.47 inference(transitivity,[status(thm)],[1922, 1920])).
% 11.32/11.47 tff(1924,plain,
% 11.32/11.47 ((~![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_i, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | (~node21(c_e_h_3, c_i, s3, s4)))),
% 11.32/11.47 inference(quant_inst,[status(thm)],[])).
% 11.32/11.47 tff(1925,plain,
% 11.32/11.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s3) | (~node21(c_e_h_3, c_i, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4))),
% 11.32/11.48 inference(modus_ponens,[status(thm)],[1924, 1923])).
% 11.32/11.48 tff(1926,plain,
% 11.32/11.48 ($false),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[1925, 228, 1910, 1919, 1918])).
% 11.32/11.48 tff(1927,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,[]))).
% 11.32/11.48 tff(1928,plain,
% 11.32/11.48 (~node21(c_e_h_3, c_i, s3, s4)),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[1927, 1910, 1918])).
% 11.32/11.48 tff(1929,plain,
% 11.32/11.48 (((~![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))),
% 11.32/11.48 inference(rewrite,[status(thm)],[])).
% 11.32/11.48 tff(1930,plain,
% 11.32/11.48 ((~![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))),
% 11.32/11.48 inference(quant_inst,[status(thm)],[])).
% 11.32/11.48 tff(1931,plain,
% 11.32/11.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_i, s3, s4) | node22(c_e_h_3, c_i, s3, s4)),
% 11.32/11.48 inference(modus_ponens,[status(thm)],[1930, 1929])).
% 11.32/11.48 tff(1932,plain,
% 11.32/11.48 (node21(c_e_h_3, c_i, s3, s4) | node22(c_e_h_3, c_i, s3, s4)),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[1931, 247, 1092])).
% 11.32/11.48 tff(1933,plain,
% 11.32/11.48 ($false),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[1932, 1928, 1917])).
% 11.32/11.48 tff(1934,plain,((~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | node20(c_e_h_3, c_i, s3) | m_and_h_gate_v_out(c_e_h_3, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 11.32/11.48 tff(1935,plain,
% 11.32/11.48 (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[1934, 1908, 1900])).
% 11.32/11.48 tff(1936,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s4)), introduced(assumption)).
% 11.32/11.48 tff(1937,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s5)), introduced(assumption)).
% 11.32/11.48 tff(1938,plain,
% 11.32/11.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, 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))),
% 11.32/11.48 inference(rewrite,[status(thm)],[])).
% 11.32/11.48 tff(1939,plain,
% 11.32/11.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, 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))),
% 11.32/11.48 inference(quant_inst,[status(thm)],[])).
% 11.32/11.48 tff(1940,plain,
% 11.32/11.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, 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)),
% 11.32/11.48 inference(modus_ponens,[status(thm)],[1939, 1938])).
% 11.32/11.48 tff(1941,plain,
% 11.32/11.48 ((~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)),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[1940, 273])).
% 11.32/11.48 tff(1942,plain,
% 11.32/11.48 (~node22(c_e_h_3, c_i, s4, s5)),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[1941, 1937, 1936])).
% 11.32/11.48 tff(1943,assumption,(~node20(c_e_h_3, c_i, s4)), introduced(assumption)).
% 11.32/11.48 tff(1944,plain,
% 11.32/11.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, 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, s5)) | node20(c_e_h_3, c_i, s4) | (~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)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | node20(c_e_h_3, c_i, s4) | (~node21(c_e_h_3, c_i, s4, s5)))),
% 11.32/11.48 inference(rewrite,[status(thm)],[])).
% 11.32/11.48 tff(1945,plain,
% 11.32/11.48 ((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))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | node20(c_e_h_3, c_i, s4) | (~node21(c_e_h_3, c_i, s4, s5)))),
% 11.32/11.48 inference(rewrite,[status(thm)],[])).
% 11.32/11.48 tff(1946,plain,
% 11.32/11.48 (((~![Y: $i, I0: $i, X: $i, 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)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | node20(c_e_h_3, c_i, s4) | (~node21(c_e_h_3, c_i, s4, s5))))),
% 11.32/11.48 inference(monotonicity,[status(thm)],[1945])).
% 11.32/11.48 tff(1947,plain,
% 11.32/11.48 (((~![Y: $i, I0: $i, X: $i, 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)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | node20(c_e_h_3, c_i, s4) | (~node21(c_e_h_3, c_i, s4, s5)))),
% 11.32/11.48 inference(transitivity,[status(thm)],[1946, 1944])).
% 11.32/11.48 tff(1948,plain,
% 11.32/11.48 ((~![Y: $i, I0: $i, X: $i, 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)))),
% 11.32/11.48 inference(quant_inst,[status(thm)],[])).
% 11.32/11.48 tff(1949,plain,
% 11.32/11.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, 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, s5)) | node20(c_e_h_3, c_i, s4) | (~node21(c_e_h_3, c_i, s4, s5))),
% 11.32/11.48 inference(modus_ponens,[status(thm)],[1948, 1947])).
% 11.32/11.48 tff(1950,plain,
% 11.32/11.48 ((~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | node20(c_e_h_3, c_i, s4) | (~node21(c_e_h_3, c_i, s4, s5))),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[1949, 228])).
% 11.32/11.48 tff(1951,plain,
% 11.32/11.48 (~node21(c_e_h_3, c_i, s4, s5)),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[1950, 1937, 1943])).
% 11.32/11.48 tff(1952,plain,
% 11.32/11.48 (((~![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))),
% 11.32/11.48 inference(rewrite,[status(thm)],[])).
% 11.32/11.48 tff(1953,plain,
% 11.32/11.48 ((~![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))),
% 11.32/11.48 inference(quant_inst,[status(thm)],[])).
% 11.32/11.48 tff(1954,plain,
% 11.32/11.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_i, s4, s5) | node22(c_e_h_3, c_i, s4, s5)),
% 11.32/11.48 inference(modus_ponens,[status(thm)],[1953, 1952])).
% 11.32/11.48 tff(1955,plain,
% 11.32/11.48 ($false),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[1954, 247, 1542, 1951, 1942])).
% 11.32/11.48 tff(1956,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,[]))).
% 11.32/11.48 tff(1957,plain,
% 11.32/11.48 ((~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | node20(c_e_h_3, c_i, s4)),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[1956, 1935])).
% 11.32/11.48 tff(1958,plain,
% 11.32/11.48 (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[1957, 1804])).
% 11.32/11.48 tff(1959,plain,
% 11.32/11.48 (^[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)))),
% 11.32/11.48 inference(bind,[status(th)],[])).
% 11.32/11.48 tff(1960,plain,
% 11.32/11.48 (![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))),
% 11.32/11.48 inference(quant_intro,[status(thm)],[1959])).
% 11.32/11.48 tff(1961,plain,
% 11.32/11.48 (![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))),
% 11.32/11.48 inference(rewrite,[status(thm)],[])).
% 11.32/11.48 tff(1962,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')).
% 11.32/11.48 tff(1963,plain,
% 11.32/11.48 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 11.32/11.48 inference(modus_ponens,[status(thm)],[1962, 1961])).
% 11.32/11.48 tff(1964,plain,(
% 11.32/11.48 ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 11.32/11.48 inference(skolemize,[status(sab)],[1963])).
% 11.32/11.48 tff(1965,plain,
% 11.32/11.48 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 11.32/11.48 inference(modus_ponens,[status(thm)],[1964, 1960])).
% 11.32/11.48 tff(1966,plain,
% 11.32/11.48 (((~![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))),
% 11.32/11.48 inference(rewrite,[status(thm)],[])).
% 11.32/11.48 tff(1967,plain,
% 11.32/11.48 ((~![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))),
% 11.32/11.48 inference(quant_inst,[status(thm)],[])).
% 11.32/11.48 tff(1968,plain,
% 11.32/11.48 ((~![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)),
% 11.32/11.48 inference(modus_ponens,[status(thm)],[1967, 1966])).
% 11.32/11.48 tff(1969,plain,
% 11.32/11.48 (~m_c_h_element_v_in2(c_e_h_3, c_e, s5)),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[1968, 1965, 1958])).
% 11.32/11.48 tff(1970,assumption,(m_c_h_element_v_in2(c_e_h_3, c_e, s3)), introduced(assumption)).
% 11.32/11.48 tff(1971,plain,
% 11.32/11.48 (((~![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))),
% 11.32/11.48 inference(rewrite,[status(thm)],[])).
% 11.32/11.48 tff(1972,plain,
% 11.32/11.48 ((~![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))),
% 11.32/11.48 inference(quant_inst,[status(thm)],[])).
% 11.32/11.48 tff(1973,plain,
% 11.32/11.48 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3)),
% 11.32/11.48 inference(modus_ponens,[status(thm)],[1972, 1971])).
% 11.32/11.48 tff(1974,plain,
% 11.32/11.48 ($false),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[1973, 1965, 1909, 1970])).
% 11.32/11.48 tff(1975,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 11.32/11.48 tff(1976,plain,
% 11.32/11.48 (~m_c_h_element_v_in2(c_e_h_3, c_e, s3)),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[1975, 1900])).
% 11.32/11.48 tff(1977,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s2)), introduced(assumption)).
% 11.32/11.48 tff(1978,plain,
% 11.32/11.48 (^[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)))),
% 11.32/11.48 inference(bind,[status(th)],[])).
% 11.32/11.48 tff(1979,plain,
% 11.32/11.48 (![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))),
% 11.32/11.48 inference(quant_intro,[status(thm)],[1978])).
% 11.32/11.48 tff(1980,plain,
% 11.32/11.48 (![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))),
% 11.32/11.48 inference(rewrite,[status(thm)],[])).
% 11.32/11.48 tff(1981,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')).
% 11.32/11.48 tff(1982,plain,
% 11.32/11.48 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 11.32/11.48 inference(modus_ponens,[status(thm)],[1981, 1980])).
% 11.32/11.48 tff(1983,plain,(
% 11.32/11.48 ![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 11.32/11.48 inference(skolemize,[status(sab)],[1982])).
% 11.32/11.48 tff(1984,plain,
% 11.32/11.48 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 11.32/11.48 inference(modus_ponens,[status(thm)],[1983, 1979])).
% 11.32/11.48 tff(1985,plain,
% 11.32/11.48 (((~![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_3, c_e, s1)) | m_and_h_gate_v_out(c_e_h_3, 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_3, c_e, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1))),
% 11.32/11.48 inference(rewrite,[status(thm)],[])).
% 11.32/11.48 tff(1986,plain,
% 11.32/11.48 ((~![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_3, c_e, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1))),
% 11.32/11.48 inference(quant_inst,[status(thm)],[])).
% 11.32/11.48 tff(1987,plain,
% 11.32/11.48 ((~![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_3, c_e, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1)),
% 11.32/11.48 inference(modus_ponens,[status(thm)],[1986, 1985])).
% 11.32/11.48 tff(1988,plain,
% 11.32/11.48 (~m_c_h_element_v_in1(c_e_h_3, c_e, s1)),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[1987, 1984, 1237])).
% 11.32/11.48 tff(1989,plain,
% 11.32/11.48 (((~![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)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~node14(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] : ((~node14(I0, I1, X, Y)) | m_c_h_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) | (~node14(c_e_h_3, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)))),
% 11.32/11.48 inference(rewrite,[status(thm)],[])).
% 11.32/11.48 tff(1990,plain,
% 11.32/11.48 (((~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) | (~node14(c_e_h_3, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)))),
% 11.32/11.48 inference(rewrite,[status(thm)],[])).
% 11.32/11.48 tff(1991,plain,
% 11.32/11.48 (((~![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_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) | (~node14(c_e_h_3, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2))))),
% 11.32/11.48 inference(monotonicity,[status(thm)],[1990])).
% 11.32/11.48 tff(1992,plain,
% 11.32/11.48 (((~![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_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) | (~node14(c_e_h_3, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)))),
% 11.32/11.48 inference(transitivity,[status(thm)],[1991, 1989])).
% 11.32/11.48 tff(1993,plain,
% 11.32/11.48 ((~![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_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)))),
% 11.32/11.48 inference(quant_inst,[status(thm)],[])).
% 11.32/11.48 tff(1994,plain,
% 11.32/11.48 ((~![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)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~node14(c_e_h_3, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2))),
% 11.32/11.48 inference(modus_ponens,[status(thm)],[1993, 1992])).
% 11.32/11.48 tff(1995,plain,
% 11.32/11.48 (m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~node14(c_e_h_3, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2))),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[1994, 427])).
% 11.32/11.48 tff(1996,plain,
% 11.32/11.48 ((~node14(c_e_h_3, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2))),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[1995, 1988])).
% 11.32/11.48 tff(1997,plain,
% 11.32/11.48 (~node14(c_e_h_3, c_e, s1, s2)),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[1996, 1977])).
% 11.32/11.48 tff(1998,plain,
% 11.32/11.48 (((~![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))),
% 11.32/11.48 inference(rewrite,[status(thm)],[])).
% 11.32/11.48 tff(1999,plain,
% 11.32/11.48 ((~![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))),
% 11.32/11.48 inference(quant_inst,[status(thm)],[])).
% 11.32/11.48 tff(2000,plain,
% 11.32/11.48 ((~![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)),
% 11.32/11.48 inference(modus_ponens,[status(thm)],[1999, 1998])).
% 11.32/11.48 tff(2001,plain,
% 11.32/11.48 (~m_c_h_element_v_in2(c_e_h_3, c_e, s1)),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[2000, 1965, 1870])).
% 11.32/11.48 tff(2002,plain,
% 11.32/11.48 (((~![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_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))),
% 11.32/11.48 inference(rewrite,[status(thm)],[])).
% 11.32/11.48 tff(2003,plain,
% 11.32/11.48 ((~![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_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))),
% 11.32/11.48 inference(quant_inst,[status(thm)],[])).
% 11.32/11.48 tff(2004,plain,
% 11.32/11.48 ((~![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_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)),
% 11.32/11.48 inference(modus_ponens,[status(thm)],[2003, 2002])).
% 11.32/11.48 tff(2005,plain,
% 11.32/11.48 ((~node16(c_e_h_3, c_e, s1)) | m_c_h_element_v_in2(c_e_h_3, c_e, s1)),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[2004, 377, 1988])).
% 11.32/11.48 tff(2006,plain,
% 11.32/11.48 (~node16(c_e_h_3, c_e, s1)),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[2005, 2001])).
% 11.32/11.48 tff(2007,plain,
% 11.32/11.48 (((~![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))),
% 11.32/11.48 inference(rewrite,[status(thm)],[])).
% 11.32/11.48 tff(2008,plain,
% 11.32/11.48 ((~![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))),
% 11.32/11.48 inference(quant_inst,[status(thm)],[])).
% 11.32/11.48 tff(2009,plain,
% 11.32/11.48 ((~![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)),
% 11.32/11.48 inference(modus_ponens,[status(thm)],[2008, 2007])).
% 11.32/11.48 tff(2010,plain,
% 11.32/11.48 (node19(c_e_h_3, c_e, s1, s2)),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[2009, 312, 470])).
% 11.32/11.48 tff(2011,plain,
% 11.32/11.48 (((~![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_3, c_e, s1) | node14(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))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $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) | (~node19(c_e_h_3, c_e, s1, s2)) | node15(c_e_h_3, c_e, s1, s2))),
% 11.32/11.48 inference(rewrite,[status(thm)],[])).
% 11.32/11.48 tff(2012,plain,
% 11.32/11.48 ((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))) <=> (node16(c_e_h_3, c_e, s1) | node14(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))),
% 11.32/11.48 inference(rewrite,[status(thm)],[])).
% 11.32/11.48 tff(2013,plain,
% 11.32/11.48 (((~![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_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)))) | (node16(c_e_h_3, c_e, s1) | node14(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)))),
% 11.32/11.48 inference(monotonicity,[status(thm)],[2012])).
% 11.32/11.48 tff(2014,plain,
% 11.32/11.48 (((~![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_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)))) | node16(c_e_h_3, c_e, s1) | node14(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))),
% 11.32/11.48 inference(transitivity,[status(thm)],[2013, 2011])).
% 11.32/11.48 tff(2015,plain,
% 11.32/11.48 ((~![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_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)))),
% 11.32/11.48 inference(quant_inst,[status(thm)],[])).
% 11.32/11.48 tff(2016,plain,
% 11.32/11.48 ((~![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_3, c_e, s1) | node14(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)),
% 11.32/11.48 inference(modus_ponens,[status(thm)],[2015, 2014])).
% 11.32/11.48 tff(2017,plain,
% 11.32/11.48 (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)),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[2016, 409, 2010])).
% 11.32/11.48 tff(2018,plain,
% 11.32/11.48 (node14(c_e_h_3, c_e, s1, s2) | node15(c_e_h_3, c_e, s1, s2)),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[2017, 2006])).
% 11.32/11.48 tff(2019,plain,
% 11.32/11.48 (node15(c_e_h_3, c_e, s1, s2)),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[2018, 1997])).
% 11.32/11.48 tff(2020,plain,
% 11.32/11.48 (((~![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_3, c_e, s0)) | m_and_h_gate_v_out(c_e_h_3, 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_3, c_e, s0)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0))),
% 11.32/11.48 inference(rewrite,[status(thm)],[])).
% 11.32/11.48 tff(2021,plain,
% 11.32/11.48 ((~![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_3, c_e, s0)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0))),
% 11.32/11.48 inference(quant_inst,[status(thm)],[])).
% 11.32/11.48 tff(2022,plain,
% 11.32/11.48 ((~![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_3, c_e, s0)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0)),
% 11.32/11.48 inference(modus_ponens,[status(thm)],[2021, 2020])).
% 11.32/11.48 tff(2023,plain,
% 11.32/11.48 (~m_c_h_element_v_in1(c_e_h_3, c_e, s0)),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[2022, 1984, 684])).
% 11.32/11.48 tff(2024,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s1)), introduced(assumption)).
% 11.32/11.48 tff(2025,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s0)), introduced(assumption)).
% 11.32/11.48 tff(2026,plain,
% 11.32/11.48 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s0))),
% 11.32/11.48 inference(quant_inst,[status(thm)],[])).
% 11.32/11.48 tff(2027,plain,
% 11.32/11.48 ($false),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[2026, 189, 2025])).
% 11.32/11.48 tff(2028,plain,(~m_c_h_element_v_out(c_e_h_3, c_e, s0)), inference(lemma,lemma(discharge,[]))).
% 11.32/11.48 tff(2029,assumption,(node15(c_e_h_3, c_e, s0, s1)), introduced(assumption)).
% 11.32/11.48 tff(2030,plain,
% 11.32/11.48 (((~![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_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))),
% 11.32/11.48 inference(rewrite,[status(thm)],[])).
% 11.32/11.48 tff(2031,plain,
% 11.32/11.48 ((~![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_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))),
% 11.32/11.48 inference(quant_inst,[status(thm)],[])).
% 11.32/11.48 tff(2032,plain,
% 11.32/11.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | (~node15(c_e_h_3, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s0)),
% 11.32/11.48 inference(modus_ponens,[status(thm)],[2031, 2030])).
% 11.32/11.48 tff(2033,plain,
% 11.32/11.48 ($false),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[2032, 393, 2024, 2029, 2028])).
% 11.32/11.48 tff(2034,plain,((~node15(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,[]))).
% 11.32/11.48 tff(2035,plain,
% 11.32/11.48 (~node15(c_e_h_3, c_e, s0, s1)),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[2034, 2024])).
% 11.32/11.48 tff(2036,plain,
% 11.32/11.48 (((~![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))),
% 11.32/11.48 inference(rewrite,[status(thm)],[])).
% 11.32/11.48 tff(2037,plain,
% 11.32/11.48 ((~![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))),
% 11.32/11.48 inference(quant_inst,[status(thm)],[])).
% 11.32/11.48 tff(2038,plain,
% 11.32/11.48 ((~![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)),
% 11.32/11.48 inference(modus_ponens,[status(thm)],[2037, 2036])).
% 11.32/11.48 tff(2039,plain,
% 11.32/11.48 (~m_c_h_element_v_in2(c_e_h_3, c_e, s0)),
% 11.32/11.48 inference(unit_resolution,[status(thm)],[2038, 1965, 1865])).
% 11.32/11.48 tff(2040,plain,
% 11.32/11.48 (((~![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_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))),
% 11.32/11.49 inference(rewrite,[status(thm)],[])).
% 11.32/11.49 tff(2041,plain,
% 11.32/11.49 ((~![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_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))),
% 11.32/11.49 inference(quant_inst,[status(thm)],[])).
% 11.32/11.49 tff(2042,plain,
% 11.32/11.49 ((~![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_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)),
% 11.32/11.49 inference(modus_ponens,[status(thm)],[2041, 2040])).
% 11.32/11.49 tff(2043,plain,
% 11.32/11.49 ((~node16(c_e_h_3, c_e, s0)) | m_c_h_element_v_in2(c_e_h_3, c_e, s0)),
% 11.32/11.49 inference(unit_resolution,[status(thm)],[2042, 377, 2023])).
% 11.32/11.49 tff(2044,plain,
% 11.32/11.49 (~node16(c_e_h_3, c_e, s0)),
% 11.32/11.49 inference(unit_resolution,[status(thm)],[2043, 2039])).
% 11.32/11.49 tff(2045,plain,
% 11.32/11.49 (((~![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))),
% 11.32/11.49 inference(rewrite,[status(thm)],[])).
% 11.32/11.49 tff(2046,plain,
% 11.32/11.49 ((~![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))),
% 11.32/11.49 inference(quant_inst,[status(thm)],[])).
% 11.32/11.49 tff(2047,plain,
% 11.32/11.49 ((~![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)),
% 11.32/11.49 inference(modus_ponens,[status(thm)],[2046, 2045])).
% 11.32/11.49 tff(2048,plain,
% 11.32/11.49 (node19(c_e_h_3, c_e, s0, s1)),
% 11.32/11.49 inference(unit_resolution,[status(thm)],[2047, 312, 100])).
% 11.32/11.49 tff(2049,plain,
% 11.32/11.49 (((~![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)))) | (node14(c_e_h_3, c_e, s0, s1) | node15(c_e_h_3, c_e, s0, s1) | node16(c_e_h_3, c_e, s0) | (~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)))) | node14(c_e_h_3, c_e, s0, s1) | node15(c_e_h_3, c_e, s0, s1) | node16(c_e_h_3, c_e, s0) | (~node19(c_e_h_3, c_e, s0, s1)))),
% 11.32/11.49 inference(rewrite,[status(thm)],[])).
% 11.32/11.49 tff(2050,plain,
% 11.32/11.49 ((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))) <=> (node14(c_e_h_3, c_e, s0, s1) | node15(c_e_h_3, c_e, s0, s1) | node16(c_e_h_3, c_e, s0) | (~node19(c_e_h_3, c_e, s0, s1)))),
% 11.32/11.49 inference(rewrite,[status(thm)],[])).
% 11.32/11.49 tff(2051,plain,
% 11.32/11.49 (((~![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_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)))) | (node14(c_e_h_3, c_e, s0, s1) | node15(c_e_h_3, c_e, s0, s1) | node16(c_e_h_3, c_e, s0) | (~node19(c_e_h_3, c_e, s0, s1))))),
% 11.32/11.49 inference(monotonicity,[status(thm)],[2050])).
% 11.32/11.49 tff(2052,plain,
% 11.32/11.49 (((~![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_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)))) | node14(c_e_h_3, c_e, s0, s1) | node15(c_e_h_3, c_e, s0, s1) | node16(c_e_h_3, c_e, s0) | (~node19(c_e_h_3, c_e, s0, s1)))),
% 11.32/11.49 inference(transitivity,[status(thm)],[2051, 2049])).
% 11.32/11.49 tff(2053,plain,
% 11.32/11.49 ((~![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_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)))),
% 11.32/11.49 inference(quant_inst,[status(thm)],[])).
% 11.32/11.49 tff(2054,plain,
% 11.32/11.49 ((~![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)))) | node14(c_e_h_3, c_e, s0, s1) | node15(c_e_h_3, c_e, s0, s1) | node16(c_e_h_3, c_e, s0) | (~node19(c_e_h_3, c_e, s0, s1))),
% 11.32/11.49 inference(modus_ponens,[status(thm)],[2053, 2052])).
% 11.32/11.49 tff(2055,plain,
% 11.32/11.49 (node14(c_e_h_3, c_e, s0, s1) | node15(c_e_h_3, c_e, s0, s1) | node16(c_e_h_3, c_e, s0)),
% 11.32/11.49 inference(unit_resolution,[status(thm)],[2054, 409, 2048])).
% 11.32/11.49 tff(2056,plain,
% 11.32/11.49 (node14(c_e_h_3, c_e, s0, s1) | node15(c_e_h_3, c_e, s0, s1)),
% 11.32/11.49 inference(unit_resolution,[status(thm)],[2055, 2044])).
% 11.32/11.49 tff(2057,plain,
% 11.32/11.49 (node14(c_e_h_3, c_e, s0, s1)),
% 11.32/11.49 inference(unit_resolution,[status(thm)],[2056, 2035])).
% 11.32/11.49 tff(2058,plain,
% 11.32/11.49 (((~![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_out(c_e_h_3, c_e, s1)) | (~node14(c_e_h_3, c_e, s0, 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)))) | (~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_in1(c_e_h_3, c_e, s0))),
% 11.32/11.49 inference(rewrite,[status(thm)],[])).
% 11.32/11.49 tff(2059,plain,
% 11.32/11.49 (((~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))) <=> ((~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_in1(c_e_h_3, c_e, s0))),
% 11.32/11.49 inference(rewrite,[status(thm)],[])).
% 11.32/11.49 tff(2060,plain,
% 11.32/11.49 (((~![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_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)))) | ((~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_in1(c_e_h_3, c_e, s0)))),
% 11.32/11.49 inference(monotonicity,[status(thm)],[2059])).
% 11.32/11.49 tff(2061,plain,
% 11.32/11.49 (((~![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_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)))) | (~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_in1(c_e_h_3, c_e, s0))),
% 11.32/11.49 inference(transitivity,[status(thm)],[2060, 2058])).
% 11.32/11.49 tff(2062,plain,
% 11.32/11.49 ((~![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_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)))),
% 11.32/11.49 inference(quant_inst,[status(thm)],[])).
% 11.32/11.49 tff(2063,plain,
% 11.32/11.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | (~node14(c_e_h_3, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0)),
% 11.32/11.49 inference(modus_ponens,[status(thm)],[2062, 2061])).
% 11.32/11.49 tff(2064,plain,
% 11.32/11.49 ($false),
% 11.32/11.49 inference(unit_resolution,[status(thm)],[2063, 427, 2024, 2057, 2023])).
% 11.32/11.49 tff(2065,plain,(~m_c_h_element_v_out(c_e_h_3, c_e, s1)), inference(lemma,lemma(discharge,[]))).
% 11.32/11.49 tff(2066,plain,
% 11.32/11.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 11.32/11.49 inference(rewrite,[status(thm)],[])).
% 11.32/11.49 tff(2067,plain,
% 11.32/11.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 11.32/11.49 inference(quant_inst,[status(thm)],[])).
% 11.32/11.49 tff(2068,plain,
% 11.32/11.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node15(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s1)),
% 11.32/11.49 inference(modus_ponens,[status(thm)],[2067, 2066])).
% 11.32/11.49 tff(2069,plain,
% 11.32/11.49 ($false),
% 11.32/11.49 inference(unit_resolution,[status(thm)],[2068, 393, 2065, 1977, 2019])).
% 11.32/11.49 tff(2070,plain,(~m_c_h_element_v_out(c_e_h_3, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 11.32/11.49 tff(2071,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s3)), introduced(assumption)).
% 11.32/11.49 tff(2072,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s2)), introduced(assumption)).
% 11.32/11.49 tff(2073,plain,
% 11.32/11.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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)))),
% 11.32/11.49 inference(rewrite,[status(thm)],[])).
% 11.32/11.49 tff(2074,plain,
% 11.32/11.49 (((~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)))),
% 11.32/11.49 inference(rewrite,[status(thm)],[])).
% 11.32/11.49 tff(2075,plain,
% 11.32/11.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))))),
% 11.32/11.49 inference(monotonicity,[status(thm)],[2074])).
% 11.32/11.49 tff(2076,plain,
% 11.32/11.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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)))),
% 11.32/11.49 inference(transitivity,[status(thm)],[2075, 2073])).
% 11.32/11.49 tff(2077,plain,
% 11.32/11.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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)))),
% 11.32/11.49 inference(quant_inst,[status(thm)],[])).
% 11.32/11.49 tff(2078,plain,
% 11.32/11.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 11.32/11.49 inference(modus_ponens,[status(thm)],[2077, 2076])).
% 11.32/11.49 tff(2079,plain,
% 11.32/11.49 (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))),
% 11.32/11.49 inference(unit_resolution,[status(thm)],[2078, 296])).
% 11.32/11.49 tff(2080,plain,
% 11.32/11.49 (~node18(c_e_h_3, c_e, s2, s3)),
% 11.32/11.49 inference(unit_resolution,[status(thm)],[2079, 2072, 2071])).
% 11.32/11.49 tff(2081,assumption,(~node19(c_e_h_3, c_e, s2, s3)), introduced(assumption)).
% 11.32/11.49 tff(2082,plain,
% 11.32/11.49 (((~![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))),
% 11.32/11.49 inference(rewrite,[status(thm)],[])).
% 11.32/11.49 tff(2083,plain,
% 11.32/11.49 ((~![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))),
% 11.32/11.49 inference(quant_inst,[status(thm)],[])).
% 11.32/11.49 tff(2084,plain,
% 11.32/11.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_3, c_e, s2, s3)),
% 11.32/11.49 inference(modus_ponens,[status(thm)],[2083, 2082])).
% 11.32/11.49 tff(2085,plain,
% 11.32/11.49 ($false),
% 11.32/11.49 inference(unit_resolution,[status(thm)],[2084, 312, 604, 2081])).
% 11.32/11.49 tff(2086,plain,(node19(c_e_h_3, c_e, s2, s3)), inference(lemma,lemma(discharge,[]))).
% 11.32/11.49 tff(2087,plain,
% 11.32/11.49 (((~![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_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)))),
% 11.32/11.49 inference(rewrite,[status(thm)],[])).
% 11.32/11.49 tff(2088,plain,
% 11.32/11.49 ((~![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_3, c_e, s2) | node18(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)))),
% 11.32/11.49 inference(quant_inst,[status(thm)],[])).
% 11.32/11.49 tff(2089,plain,
% 11.32/11.49 ((~![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_3, c_e, s2) | node18(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3))),
% 11.32/11.49 inference(modus_ponens,[status(thm)],[2088, 2087])).
% 11.32/11.49 tff(2090,plain,
% 11.32/11.49 (node17(c_e_h_3, c_e, s2) | node18(c_e_h_3, c_e, s2, s3)),
% 11.32/11.49 inference(unit_resolution,[status(thm)],[2089, 326, 2086])).
% 11.32/11.49 tff(2091,plain,
% 11.32/11.49 (node17(c_e_h_3, c_e, s2)),
% 11.32/11.49 inference(unit_resolution,[status(thm)],[2090, 2080])).
% 11.32/11.49 tff(2092,plain,
% 11.32/11.49 (((~![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))),
% 11.32/11.49 inference(rewrite,[status(thm)],[])).
% 11.32/11.49 tff(2093,plain,
% 11.32/11.49 ((~![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))),
% 11.32/11.49 inference(quant_inst,[status(thm)],[])).
% 11.32/11.49 tff(2094,plain,
% 11.32/11.49 ((~![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)),
% 11.32/11.49 inference(modus_ponens,[status(thm)],[2093, 2092])).
% 11.32/11.49 tff(2095,plain,
% 11.32/11.49 (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)),
% 11.32/11.49 inference(unit_resolution,[status(thm)],[2094, 1965, 1885])).
% 11.32/11.49 tff(2096,plain,
% 11.32/11.49 (((~![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_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)))) | (~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)))),
% 11.32/11.49 inference(rewrite,[status(thm)],[])).
% 11.32/11.49 tff(2097,plain,
% 11.32/11.49 ((~![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_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)))),
% 11.32/11.49 inference(quant_inst,[status(thm)],[])).
% 11.32/11.49 tff(2098,plain,
% 11.32/11.49 ((~![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_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))),
% 11.32/11.49 inference(modus_ponens,[status(thm)],[2097, 2096])).
% 11.32/11.49 tff(2099,plain,
% 11.32/11.49 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~node17(c_e_h_3, c_e, s2))),
% 11.32/11.49 inference(unit_resolution,[status(thm)],[2098, 359, 2095])).
% 11.32/11.49 tff(2100,plain,
% 11.32/11.49 (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)),
% 11.32/11.49 inference(unit_resolution,[status(thm)],[2099, 2091])).
% 11.32/11.49 tff(2101,assumption,(node15(c_e_h_3, c_e, s2, s3)), introduced(assumption)).
% 11.32/11.49 tff(2102,plain,
% 11.32/11.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 11.32/11.49 inference(rewrite,[status(thm)],[])).
% 11.32/11.49 tff(2103,plain,
% 11.32/11.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 11.32/11.49 inference(quant_inst,[status(thm)],[])).
% 11.32/11.49 tff(2104,plain,
% 11.32/11.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | (~node15(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2)),
% 11.32/11.49 inference(modus_ponens,[status(thm)],[2103, 2102])).
% 11.32/11.49 tff(2105,plain,
% 11.32/11.49 ($false),
% 11.32/11.49 inference(unit_resolution,[status(thm)],[2104, 393, 2072, 2071, 2101])).
% 11.32/11.49 tff(2106,plain,((~node15(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))), inference(lemma,lemma(discharge,[]))).
% 11.32/11.49 tff(2107,plain,
% 11.32/11.49 (~node15(c_e_h_3, c_e, s2, s3)),
% 11.32/11.49 inference(unit_resolution,[status(thm)],[2106, 2072, 2071])).
% 11.32/11.49 tff(2108,assumption,(node16(c_e_h_3, c_e, s2)), introduced(assumption)).
% 11.32/11.49 tff(2109,assumption,(node17(c_e_h_3, c_e, s2)), introduced(assumption)).
% 11.32/11.49 tff(2110,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s2)), introduced(assumption)).
% 11.32/11.49 tff(2111,plain,
% 11.32/11.49 (((~![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_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))),
% 11.32/11.49 inference(rewrite,[status(thm)],[])).
% 11.32/11.49 tff(2112,plain,
% 11.32/11.49 ((~![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_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))),
% 11.32/11.49 inference(quant_inst,[status(thm)],[])).
% 11.32/11.49 tff(2113,plain,
% 11.32/11.49 ((~![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_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)),
% 11.32/11.49 inference(modus_ponens,[status(thm)],[2112, 2111])).
% 11.32/11.49 tff(2114,plain,
% 11.32/11.49 (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)),
% 11.32/11.49 inference(unit_resolution,[status(thm)],[2113, 377, 2108])).
% 11.32/11.49 tff(2115,plain,
% 11.32/11.49 (m_c_h_element_v_in2(c_e_h_3, c_e, s2)),
% 11.32/11.49 inference(unit_resolution,[status(thm)],[2114, 2110])).
% 11.32/11.49 tff(2116,plain,
% 11.32/11.49 (^[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))))),
% 11.32/11.49 inference(bind,[status(th)],[])).
% 11.32/11.49 tff(2117,plain,
% 11.32/11.49 (![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))) <=> ![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 11.32/11.49 inference(quant_intro,[status(thm)],[2116])).
% 11.32/11.49 tff(2118,plain,
% 11.32/11.49 (![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))) <=> ![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 11.32/11.49 inference(rewrite,[status(thm)],[])).
% 11.32/11.49 tff(2119,plain,
% 11.32/11.49 (^[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)))))),
% 11.32/11.49 inference(bind,[status(th)],[])).
% 11.32/11.49 tff(2120,plain,
% 11.32/11.49 (![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))) <=> ![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 11.32/11.49 inference(quant_intro,[status(thm)],[2119])).
% 11.32/11.49 tff(2121,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')).
% 11.32/11.49 tff(2122,plain,
% 11.32/11.49 (![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)))),
% 11.32/11.49 inference(modus_ponens,[status(thm)],[2121, 2120])).
% 11.32/11.49 tff(2123,plain,
% 11.32/11.49 (![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)))),
% 11.32/11.49 inference(modus_ponens,[status(thm)],[2122, 2118])).
% 11.32/11.49 tff(2124,plain,(
% 11.32/11.49 ![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)))),
% 11.32/11.49 inference(skolemize,[status(sab)],[2123])).
% 11.32/11.49 tff(2125,plain,
% 11.32/11.49 (![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)))),
% 11.32/11.49 inference(modus_ponens,[status(thm)],[2124, 2117])).
% 11.32/11.49 tff(2126,plain,
% 11.32/11.49 (((~![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_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)))) | 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)))),
% 11.32/11.49 inference(rewrite,[status(thm)],[])).
% 11.32/11.49 tff(2127,plain,
% 11.32/11.49 ((~![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_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)))),
% 11.32/11.49 inference(quant_inst,[status(thm)],[])).
% 11.32/11.49 tff(2128,plain,
% 11.32/11.49 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | (~node17(c_e_h_3, c_e, s2))),
% 11.32/11.49 inference(modus_ponens,[status(thm)],[2127, 2126])).
% 11.32/11.49 tff(2129,plain,
% 11.32/11.49 (m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2))),
% 11.32/11.49 inference(unit_resolution,[status(thm)],[2128, 2125, 2109])).
% 11.32/11.49 tff(2130,plain,
% 11.32/11.49 ($false),
% 11.32/11.49 inference(unit_resolution,[status(thm)],[2129, 2115, 2110])).
% 11.32/11.49 tff(2131,plain,(m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~node17(c_e_h_3, c_e, s2)) | (~node16(c_e_h_3, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 11.32/11.49 tff(2132,plain,
% 11.32/11.49 (m_c_h_element_v_in1(c_e_h_3, c_e, s2)),
% 11.32/11.49 inference(unit_resolution,[status(thm)],[2131, 2109, 2108])).
% 11.32/11.49 tff(2133,plain,
% 11.32/11.49 (^[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))))),
% 11.32/11.49 inference(bind,[status(th)],[])).
% 11.32/11.49 tff(2134,plain,
% 11.32/11.49 (![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))) <=> ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))),
% 11.32/11.49 inference(quant_intro,[status(thm)],[2133])).
% 11.32/11.49 tff(2135,plain,
% 11.32/11.49 (![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))) <=> ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))),
% 11.32/11.49 inference(rewrite,[status(thm)],[])).
% 11.32/11.49 tff(2136,plain,
% 11.32/11.49 (^[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))))),
% 11.32/11.49 inference(bind,[status(th)],[])).
% 11.32/11.49 tff(2137,plain,
% 11.32/11.49 (![I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X))) | (~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)))),
% 11.32/11.49 inference(quant_intro,[status(thm)],[2136])).
% 11.32/11.49 tff(2138,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')).
% 11.32/11.49 tff(2139,plain,
% 11.32/11.49 (![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)))),
% 11.32/11.49 inference(modus_ponens,[status(thm)],[2138, 2137])).
% 11.32/11.49 tff(2140,plain,
% 11.32/11.49 (![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)))),
% 11.32/11.49 inference(modus_ponens,[status(thm)],[2139, 2135])).
% 11.32/11.49 tff(2141,plain,(
% 11.32/11.49 ![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)))),
% 11.32/11.49 inference(skolemize,[status(sab)],[2140])).
% 11.32/11.49 tff(2142,plain,
% 11.32/11.49 (![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)))),
% 11.32/11.49 inference(modus_ponens,[status(thm)],[2141, 2134])).
% 11.32/11.49 tff(2143,plain,
% 11.32/11.49 (((~![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)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~node16(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)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~node16(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)))),
% 11.32/11.49 inference(rewrite,[status(thm)],[])).
% 11.32/11.50 tff(2144,plain,
% 11.32/11.50 (((~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))) <=> ((~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~node16(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)))),
% 11.32/11.50 inference(rewrite,[status(thm)],[])).
% 11.32/11.50 tff(2145,plain,
% 11.32/11.50 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~node16(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2))))),
% 11.32/11.50 inference(monotonicity,[status(thm)],[2144])).
% 11.32/11.50 tff(2146,plain,
% 11.32/11.50 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~node16(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)))),
% 11.32/11.50 inference(transitivity,[status(thm)],[2145, 2143])).
% 11.32/11.50 tff(2147,plain,
% 11.32/11.50 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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)))),
% 11.32/11.50 inference(quant_inst,[status(thm)],[])).
% 11.32/11.50 tff(2148,plain,
% 11.32/11.50 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~node16(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2))),
% 11.32/11.50 inference(modus_ponens,[status(thm)],[2147, 2146])).
% 11.32/11.50 tff(2149,plain,
% 11.32/11.50 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2))),
% 11.32/11.50 inference(unit_resolution,[status(thm)],[2148, 2142, 2108])).
% 11.32/11.50 tff(2150,plain,
% 11.32/11.50 (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)),
% 11.32/11.50 inference(unit_resolution,[status(thm)],[2149, 2132])).
% 11.32/11.50 tff(2151,plain,
% 11.32/11.50 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2)),
% 11.32/11.50 inference(unit_resolution,[status(thm)],[2098, 359, 2109])).
% 11.32/11.50 tff(2152,plain,
% 11.32/11.50 ($false),
% 11.32/11.50 inference(unit_resolution,[status(thm)],[2151, 2150, 2132])).
% 11.32/11.50 tff(2153,plain,((~node17(c_e_h_3, c_e, s2)) | (~node16(c_e_h_3, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 11.32/11.50 tff(2154,plain,
% 11.32/11.50 (~node16(c_e_h_3, c_e, s2)),
% 11.32/11.50 inference(unit_resolution,[status(thm)],[2153, 2091])).
% 11.32/11.50 tff(2155,plain,
% 11.32/11.50 (((~![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)))) | (node15(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2) | node14(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)))) | node15(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2) | node14(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)))),
% 11.32/11.50 inference(rewrite,[status(thm)],[])).
% 11.32/11.50 tff(2156,plain,
% 11.32/11.50 ((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))) <=> (node15(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2) | node14(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)))),
% 11.32/11.50 inference(rewrite,[status(thm)],[])).
% 11.32/11.50 tff(2157,plain,
% 11.32/11.50 (((~![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_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)))) | (node15(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2) | node14(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3))))),
% 11.32/11.50 inference(monotonicity,[status(thm)],[2156])).
% 11.32/11.50 tff(2158,plain,
% 11.32/11.50 (((~![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_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)))) | node15(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2) | node14(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)))),
% 11.32/11.50 inference(transitivity,[status(thm)],[2157, 2155])).
% 11.32/11.50 tff(2159,plain,
% 11.32/11.50 ((~![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_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)))),
% 11.32/11.50 inference(quant_inst,[status(thm)],[])).
% 11.32/11.50 tff(2160,plain,
% 11.32/11.50 ((~![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)))) | node15(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2) | node14(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3))),
% 11.32/11.50 inference(modus_ponens,[status(thm)],[2159, 2158])).
% 11.32/11.50 tff(2161,plain,
% 11.32/11.50 (node15(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2) | node14(c_e_h_3, c_e, s2, s3)),
% 11.32/11.50 inference(unit_resolution,[status(thm)],[2160, 409, 2086])).
% 11.32/11.50 tff(2162,plain,
% 11.32/11.50 (node14(c_e_h_3, c_e, s2, s3)),
% 11.32/11.50 inference(unit_resolution,[status(thm)],[2161, 2154, 2107])).
% 11.32/11.50 tff(2163,assumption,(node14(c_e_h_3, c_e, s2, s3)), introduced(assumption)).
% 11.32/11.50 tff(2164,plain,
% 11.32/11.50 (((~![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_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~node14(c_e_h_3, 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_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~node14(c_e_h_3, c_e, s2, s3)))),
% 11.32/11.50 inference(rewrite,[status(thm)],[])).
% 11.32/11.50 tff(2165,plain,
% 11.32/11.50 (((~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))) <=> ((~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) | (~node14(c_e_h_3, c_e, s2, s3)))),
% 11.32/11.50 inference(rewrite,[status(thm)],[])).
% 11.32/11.50 tff(2166,plain,
% 11.32/11.50 (((~![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_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)))) | ((~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) | (~node14(c_e_h_3, c_e, s2, s3))))),
% 11.32/11.50 inference(monotonicity,[status(thm)],[2165])).
% 11.32/11.50 tff(2167,plain,
% 11.32/11.50 (((~![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_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)))) | (~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) | (~node14(c_e_h_3, c_e, s2, s3)))),
% 11.32/11.50 inference(transitivity,[status(thm)],[2166, 2164])).
% 11.32/11.50 tff(2168,plain,
% 11.32/11.50 ((~![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_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)))),
% 11.32/11.50 inference(quant_inst,[status(thm)],[])).
% 11.32/11.50 tff(2169,plain,
% 11.32/11.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~node14(c_e_h_3, c_e, s2, s3))),
% 11.32/11.50 inference(modus_ponens,[status(thm)],[2168, 2167])).
% 11.32/11.50 tff(2170,plain,
% 11.32/11.50 ($false),
% 11.32/11.50 inference(unit_resolution,[status(thm)],[2169, 427, 2071, 2163, 2110])).
% 11.32/11.50 tff(2171,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,[]))).
% 11.32/11.50 tff(2172,plain,
% 11.32/11.50 ($false),
% 11.32/11.50 inference(unit_resolution,[status(thm)],[2171, 2162, 2100, 2071])).
% 11.32/11.50 tff(2173,plain,(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))), inference(lemma,lemma(discharge,[]))).
% 11.32/11.50 tff(2174,plain,
% 11.32/11.50 (~m_c_h_element_v_out(c_e_h_3, c_e, s3)),
% 11.32/11.50 inference(unit_resolution,[status(thm)],[2173, 2070])).
% 11.32/11.50 tff(2175,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s4)), introduced(assumption)).
% 11.32/11.50 tff(2176,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s3)), introduced(assumption)).
% 11.32/11.50 tff(2177,assumption,(node18(c_e_h_3, c_e, s3, s4)), introduced(assumption)).
% 11.32/11.50 tff(2178,plain,
% 11.32/11.50 (((~![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)))) | ((~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)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $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, 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)))),
% 11.32/11.50 inference(rewrite,[status(thm)],[])).
% 11.32/11.50 tff(2179,plain,
% 11.32/11.50 (((~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))) <=> ((~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)))),
% 11.32/11.50 inference(rewrite,[status(thm)],[])).
% 11.32/11.50 tff(2180,plain,
% 11.32/11.50 (((~![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_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)))) | ((~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))))),
% 11.32/11.50 inference(monotonicity,[status(thm)],[2179])).
% 11.32/11.50 tff(2181,plain,
% 11.32/11.50 (((~![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_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)))) | (~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)))),
% 11.32/11.50 inference(transitivity,[status(thm)],[2180, 2178])).
% 11.32/11.50 tff(2182,plain,
% 11.32/11.50 ((~![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_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)))),
% 11.32/11.50 inference(quant_inst,[status(thm)],[])).
% 11.32/11.50 tff(2183,plain,
% 11.32/11.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_3, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4))),
% 11.32/11.50 inference(modus_ponens,[status(thm)],[2182, 2181])).
% 11.32/11.50 tff(2184,plain,
% 11.32/11.50 ($false),
% 11.32/11.50 inference(unit_resolution,[status(thm)],[2183, 296, 2175, 2176, 2177])).
% 11.32/11.50 tff(2185,plain,((~node18(c_e_h_3, c_e, s3, s4)) | (~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)), inference(lemma,lemma(discharge,[]))).
% 11.32/11.50 tff(2186,plain,
% 11.32/11.50 (~node18(c_e_h_3, c_e, s3, s4)),
% 11.32/11.50 inference(unit_resolution,[status(thm)],[2185, 2176, 2175])).
% 11.32/11.50 tff(2187,assumption,(~node19(c_e_h_3, c_e, s3, s4)), introduced(assumption)).
% 11.32/11.50 tff(2188,plain,
% 11.32/11.50 (((~![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))),
% 11.32/11.50 inference(rewrite,[status(thm)],[])).
% 11.32/11.50 tff(2189,plain,
% 11.32/11.50 ((~![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))),
% 11.32/11.50 inference(quant_inst,[status(thm)],[])).
% 11.32/11.50 tff(2190,plain,
% 11.32/11.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_3, c_e, s3, s4)),
% 11.32/11.50 inference(modus_ponens,[status(thm)],[2189, 2188])).
% 11.32/11.50 tff(2191,plain,
% 11.32/11.50 ($false),
% 11.32/11.50 inference(unit_resolution,[status(thm)],[2190, 312, 1092, 2187])).
% 11.32/11.50 tff(2192,plain,(node19(c_e_h_3, c_e, s3, s4)), inference(lemma,lemma(discharge,[]))).
% 11.32/11.50 tff(2193,plain,
% 11.32/11.50 (((~![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_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)))),
% 11.32/11.50 inference(rewrite,[status(thm)],[])).
% 11.32/11.50 tff(2194,plain,
% 11.32/11.50 ((~![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_3, c_e, s3) | node18(c_e_h_3, c_e, s3, s4) | (~node19(c_e_h_3, c_e, s3, s4)))),
% 11.32/11.50 inference(quant_inst,[status(thm)],[])).
% 11.32/11.50 tff(2195,plain,
% 11.32/11.50 ((~![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_3, c_e, s3) | node18(c_e_h_3, c_e, s3, s4) | (~node19(c_e_h_3, c_e, s3, s4))),
% 11.32/11.50 inference(modus_ponens,[status(thm)],[2194, 2193])).
% 11.32/11.50 tff(2196,plain,
% 11.32/11.50 (node17(c_e_h_3, c_e, s3) | node18(c_e_h_3, c_e, s3, s4)),
% 11.32/11.50 inference(unit_resolution,[status(thm)],[2195, 326, 2192])).
% 11.32/11.50 tff(2197,plain,
% 11.32/11.50 (node17(c_e_h_3, c_e, s3)),
% 11.32/11.50 inference(unit_resolution,[status(thm)],[2196, 2186])).
% 11.32/11.50 tff(2198,assumption,(~node14(c_e_h_3, c_e, s3, s4)), introduced(assumption)).
% 11.32/11.50 tff(2199,assumption,(node15(c_e_h_3, c_e, s3, s4)), introduced(assumption)).
% 11.32/11.50 tff(2200,plain,
% 11.32/11.50 (((~![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_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))),
% 11.32/11.50 inference(rewrite,[status(thm)],[])).
% 11.32/11.50 tff(2201,plain,
% 11.32/11.50 ((~![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_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))),
% 11.32/11.50 inference(quant_inst,[status(thm)],[])).
% 11.32/11.50 tff(2202,plain,
% 11.32/11.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | (~node15(c_e_h_3, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3)),
% 11.32/11.50 inference(modus_ponens,[status(thm)],[2201, 2200])).
% 11.32/11.50 tff(2203,plain,
% 11.32/11.50 ($false),
% 11.32/11.50 inference(unit_resolution,[status(thm)],[2202, 393, 2175, 2176, 2199])).
% 11.36/11.50 tff(2204,plain,((~node15(c_e_h_3, c_e, s3, s4)) | (~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)), inference(lemma,lemma(discharge,[]))).
% 11.36/11.50 tff(2205,plain,
% 11.36/11.50 (~node15(c_e_h_3, c_e, s3, s4)),
% 11.36/11.50 inference(unit_resolution,[status(thm)],[2204, 2176, 2175])).
% 11.36/11.50 tff(2206,plain,
% 11.36/11.50 (((~![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)))) | (node15(c_e_h_3, c_e, s3, s4) | node16(c_e_h_3, c_e, s3) | (~node19(c_e_h_3, c_e, s3, s4)) | node14(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)))) | node15(c_e_h_3, c_e, s3, s4) | node16(c_e_h_3, c_e, s3) | (~node19(c_e_h_3, c_e, s3, s4)) | node14(c_e_h_3, c_e, s3, s4))),
% 11.36/11.50 inference(rewrite,[status(thm)],[])).
% 11.36/11.50 tff(2207,plain,
% 11.36/11.50 ((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))) <=> (node15(c_e_h_3, c_e, s3, s4) | node16(c_e_h_3, c_e, s3) | (~node19(c_e_h_3, c_e, s3, s4)) | node14(c_e_h_3, c_e, s3, s4))),
% 11.36/11.50 inference(rewrite,[status(thm)],[])).
% 11.36/11.50 tff(2208,plain,
% 11.36/11.50 (((~![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_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)))) | (node15(c_e_h_3, c_e, s3, s4) | node16(c_e_h_3, c_e, s3) | (~node19(c_e_h_3, c_e, s3, s4)) | node14(c_e_h_3, c_e, s3, s4)))),
% 11.36/11.50 inference(monotonicity,[status(thm)],[2207])).
% 11.36/11.50 tff(2209,plain,
% 11.36/11.50 (((~![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_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)))) | node15(c_e_h_3, c_e, s3, s4) | node16(c_e_h_3, c_e, s3) | (~node19(c_e_h_3, c_e, s3, s4)) | node14(c_e_h_3, c_e, s3, s4))),
% 11.36/11.50 inference(transitivity,[status(thm)],[2208, 2206])).
% 11.36/11.50 tff(2210,plain,
% 11.36/11.50 ((~![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_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)))),
% 11.36/11.50 inference(quant_inst,[status(thm)],[])).
% 11.36/11.50 tff(2211,plain,
% 11.36/11.50 ((~![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)))) | node15(c_e_h_3, c_e, s3, s4) | node16(c_e_h_3, c_e, s3) | (~node19(c_e_h_3, c_e, s3, s4)) | node14(c_e_h_3, c_e, s3, s4)),
% 11.36/11.50 inference(modus_ponens,[status(thm)],[2210, 2209])).
% 11.36/11.50 tff(2212,plain,
% 11.36/11.50 (node15(c_e_h_3, c_e, s3, s4) | node16(c_e_h_3, c_e, s3) | node14(c_e_h_3, c_e, s3, s4)),
% 11.36/11.50 inference(unit_resolution,[status(thm)],[2211, 409, 2192])).
% 11.36/11.50 tff(2213,plain,
% 11.36/11.50 (node16(c_e_h_3, c_e, s3)),
% 11.36/11.50 inference(unit_resolution,[status(thm)],[2212, 2205, 2198])).
% 11.36/11.50 tff(2214,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s3)), introduced(assumption)).
% 11.36/11.50 tff(2215,assumption,(node16(c_e_h_3, c_e, s3)), introduced(assumption)).
% 11.36/11.50 tff(2216,plain,
% 11.36/11.50 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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))),
% 11.36/11.50 inference(rewrite,[status(thm)],[])).
% 11.36/11.50 tff(2217,plain,
% 11.36/11.50 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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))),
% 11.36/11.50 inference(quant_inst,[status(thm)],[])).
% 11.36/11.50 tff(2218,plain,
% 11.36/11.50 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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)),
% 11.36/11.50 inference(modus_ponens,[status(thm)],[2217, 2216])).
% 11.36/11.50 tff(2219,plain,
% 11.36/11.50 (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)),
% 11.36/11.50 inference(unit_resolution,[status(thm)],[2218, 377, 2215])).
% 11.36/11.50 tff(2220,plain,
% 11.36/11.50 (m_c_h_element_v_in2(c_e_h_3, c_e, s3)),
% 11.36/11.50 inference(unit_resolution,[status(thm)],[2219, 2214])).
% 11.36/11.50 tff(2221,assumption,(node17(c_e_h_3, c_e, s3)), introduced(assumption)).
% 11.36/11.50 tff(2222,plain,
% 11.36/11.50 (((~![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_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))),
% 11.36/11.50 inference(rewrite,[status(thm)],[])).
% 11.36/11.50 tff(2223,plain,
% 11.36/11.50 ((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))),
% 11.36/11.50 inference(rewrite,[status(thm)],[])).
% 11.36/11.50 tff(2224,plain,
% 11.36/11.50 (((~![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_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)))),
% 11.36/11.50 inference(monotonicity,[status(thm)],[2223])).
% 11.36/11.50 tff(2225,plain,
% 11.36/11.50 (((~![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_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))),
% 11.36/11.50 inference(transitivity,[status(thm)],[2224, 2222])).
% 11.36/11.50 tff(2226,plain,
% 11.36/11.50 ((~![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_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)))),
% 11.36/11.50 inference(quant_inst,[status(thm)],[])).
% 11.36/11.50 tff(2227,plain,
% 11.36/11.50 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s3)),
% 11.36/11.50 inference(modus_ponens,[status(thm)],[2226, 2225])).
% 11.36/11.50 tff(2228,plain,
% 11.36/11.50 ((~m_c_h_element_v_in2(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s3)),
% 11.36/11.50 inference(unit_resolution,[status(thm)],[2227, 2125, 2221])).
% 11.36/11.50 tff(2229,plain,
% 11.36/11.50 ($false),
% 11.36/11.50 inference(unit_resolution,[status(thm)],[2228, 2220, 2214])).
% 11.36/11.50 tff(2230,plain,(m_c_h_element_v_in1(c_e_h_3, c_e, s3) | (~node17(c_e_h_3, c_e, s3)) | (~node16(c_e_h_3, c_e, s3))), inference(lemma,lemma(discharge,[]))).
% 11.36/11.50 tff(2231,plain,
% 11.36/11.50 (m_c_h_element_v_in1(c_e_h_3, c_e, s3)),
% 11.36/11.50 inference(unit_resolution,[status(thm)],[2230, 2197, 2213])).
% 11.36/11.50 tff(2232,plain,
% 11.36/11.50 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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_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] : ((~node16(I0, 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_in2(c_e_h_3, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s3)))),
% 11.36/11.51 inference(rewrite,[status(thm)],[])).
% 11.36/11.51 tff(2233,plain,
% 11.36/11.51 (((~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))) <=> ((~node16(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)))),
% 11.36/11.51 inference(rewrite,[status(thm)],[])).
% 11.36/11.51 tff(2234,plain,
% 11.36/11.51 (((~![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_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_in2(c_e_h_3, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s3))))),
% 11.36/11.51 inference(monotonicity,[status(thm)],[2233])).
% 11.36/11.51 tff(2235,plain,
% 11.36/11.51 (((~![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_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_in2(c_e_h_3, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s3)))),
% 11.36/11.51 inference(transitivity,[status(thm)],[2234, 2232])).
% 11.36/11.51 tff(2236,plain,
% 11.36/11.51 ((~![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_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)))),
% 11.36/11.51 inference(quant_inst,[status(thm)],[])).
% 11.36/11.51 tff(2237,plain,
% 11.36/11.51 ((~![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_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))),
% 11.36/11.51 inference(modus_ponens,[status(thm)],[2236, 2235])).
% 11.36/11.51 tff(2238,plain,
% 11.36/11.51 ((~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))),
% 11.36/11.51 inference(unit_resolution,[status(thm)],[2237, 2142, 2213])).
% 11.36/11.51 tff(2239,plain,
% 11.36/11.51 (~m_c_h_element_v_in2(c_e_h_3, c_e, s3)),
% 11.36/11.51 inference(unit_resolution,[status(thm)],[2238, 2231])).
% 11.36/11.51 tff(2240,plain,
% 11.36/11.51 (((~![I0: $i, X: $i, 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_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] : ((~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_in1(c_e_h_3, c_e, s3)) | m_c_h_element_v_in2(c_e_h_3, c_e, s3))),
% 11.36/11.51 inference(rewrite,[status(thm)],[])).
% 11.36/11.51 tff(2241,plain,
% 11.36/11.51 (((~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_in1(c_e_h_3, c_e, s3)) | m_c_h_element_v_in2(c_e_h_3, c_e, s3))),
% 11.36/11.51 inference(rewrite,[status(thm)],[])).
% 11.36/11.51 tff(2242,plain,
% 11.36/11.51 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, 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_in1(c_e_h_3, c_e, s3)) | m_c_h_element_v_in2(c_e_h_3, c_e, s3)))),
% 11.36/11.51 inference(monotonicity,[status(thm)],[2241])).
% 11.36/11.51 tff(2243,plain,
% 11.36/11.51 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, 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_in1(c_e_h_3, c_e, s3)) | m_c_h_element_v_in2(c_e_h_3, c_e, s3))),
% 11.36/11.51 inference(transitivity,[status(thm)],[2242, 2240])).
% 11.36/11.51 tff(2244,plain,
% 11.36/11.51 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, 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)))),
% 11.36/11.51 inference(quant_inst,[status(thm)],[])).
% 11.36/11.51 tff(2245,plain,
% 11.36/11.51 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s3)) | m_c_h_element_v_in2(c_e_h_3, c_e, s3)),
% 11.36/11.51 inference(modus_ponens,[status(thm)],[2244, 2243])).
% 11.36/11.51 tff(2246,plain,
% 11.36/11.51 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s3)) | m_c_h_element_v_in2(c_e_h_3, c_e, s3)),
% 11.36/11.51 inference(unit_resolution,[status(thm)],[2245, 359, 2197])).
% 11.36/11.51 tff(2247,plain,
% 11.36/11.51 ($false),
% 11.36/11.51 inference(unit_resolution,[status(thm)],[2246, 2239, 2231])).
% 11.36/11.51 tff(2248,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)) | node14(c_e_h_3, c_e, s3, s4)), inference(lemma,lemma(discharge,[]))).
% 11.36/11.51 tff(2249,plain,
% 11.36/11.51 (node14(c_e_h_3, c_e, s3, s4)),
% 11.36/11.51 inference(unit_resolution,[status(thm)],[2248, 2176, 2175])).
% 11.36/11.51 tff(2250,assumption,(node14(c_e_h_3, c_e, s3, s4)), introduced(assumption)).
% 11.36/11.51 tff(2251,plain,
% 11.36/11.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_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)))),
% 11.36/11.51 inference(rewrite,[status(thm)],[])).
% 11.36/11.51 tff(2252,plain,
% 11.36/11.51 (((~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)))),
% 11.36/11.51 inference(rewrite,[status(thm)],[])).
% 11.36/11.51 tff(2253,plain,
% 11.36/11.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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))))),
% 11.36/11.51 inference(monotonicity,[status(thm)],[2252])).
% 11.36/11.51 tff(2254,plain,
% 11.36/11.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))),
% 11.36/11.51 inference(transitivity,[status(thm)],[2253, 2251])).
% 11.36/11.51 tff(2255,plain,
% 11.36/11.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))),
% 11.36/11.51 inference(quant_inst,[status(thm)],[])).
% 11.36/11.51 tff(2256,plain,
% 11.36/11.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s3) | (~node14(c_e_h_3, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4))),
% 11.36/11.51 inference(modus_ponens,[status(thm)],[2255, 2254])).
% 11.36/11.51 tff(2257,plain,
% 11.36/11.51 ($false),
% 11.36/11.51 inference(unit_resolution,[status(thm)],[2256, 427, 2175, 2250, 2214])).
% 11.36/11.51 tff(2258,plain,((~node14(c_e_h_3, c_e, s3, s4)) | (~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)), inference(lemma,lemma(discharge,[]))).
% 11.36/11.51 tff(2259,plain,
% 11.36/11.51 (m_c_h_element_v_in1(c_e_h_3, c_e, s3)),
% 11.36/11.51 inference(unit_resolution,[status(thm)],[2258, 2249, 2175])).
% 11.36/11.51 tff(2260,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_e, s3)), introduced(assumption)).
% 11.36/11.51 tff(2261,plain,
% 11.36/11.51 ((~node17(c_e_h_3, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s3))),
% 11.36/11.51 inference(unit_resolution,[status(thm)],[2245, 359, 2260])).
% 11.36/11.51 tff(2262,plain,
% 11.36/11.51 ($false),
% 11.36/11.51 inference(unit_resolution,[status(thm)],[2261, 2259, 2197])).
% 11.36/11.51 tff(2263,plain,(m_c_h_element_v_out(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_out(c_e_h_3, c_e, s4))), inference(lemma,lemma(discharge,[]))).
% 11.36/11.51 tff(2264,plain,
% 11.36/11.51 (m_c_h_element_v_in2(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4))),
% 11.36/11.51 inference(unit_resolution,[status(thm)],[2263, 2174])).
% 11.36/11.51 tff(2265,plain,
% 11.36/11.51 (~m_c_h_element_v_out(c_e_h_3, c_e, s4)),
% 11.36/11.51 inference(unit_resolution,[status(thm)],[2264, 1976])).
% 11.36/11.51 tff(2266,plain,
% 11.36/11.51 (((~![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))),
% 11.36/11.51 inference(rewrite,[status(thm)],[])).
% 11.36/11.51 tff(2267,plain,
% 11.36/11.51 ((~![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))),
% 11.36/11.51 inference(quant_inst,[status(thm)],[])).
% 11.36/11.51 tff(2268,plain,
% 11.36/11.51 ((~![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)),
% 11.36/11.51 inference(modus_ponens,[status(thm)],[2267, 2266])).
% 11.36/11.51 tff(2269,plain,
% 11.36/11.51 (~m_c_h_element_v_in2(c_e_h_3, c_e, s4)),
% 11.36/11.51 inference(unit_resolution,[status(thm)],[2268, 1965, 1935])).
% 11.36/11.51 tff(2270,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s5)), introduced(assumption)).
% 11.36/11.51 tff(2271,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s4)), introduced(assumption)).
% 11.36/11.51 tff(2272,assumption,(node18(c_e_h_3, c_e, s4, s5)), introduced(assumption)).
% 11.36/11.51 tff(2273,plain,
% 11.36/11.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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, s5)) | (~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) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | (~node18(c_e_h_3, c_e, s4, s5)))),
% 11.36/11.51 inference(rewrite,[status(thm)],[])).
% 11.36/11.51 tff(2274,plain,
% 11.36/11.51 (((~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) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | (~node18(c_e_h_3, c_e, s4, s5)))),
% 11.36/11.51 inference(rewrite,[status(thm)],[])).
% 11.36/11.51 tff(2275,plain,
% 11.36/11.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | (~node18(c_e_h_3, c_e, s4, s5))))),
% 11.36/11.51 inference(monotonicity,[status(thm)],[2274])).
% 11.36/11.51 tff(2276,plain,
% 11.36/11.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | (~node18(c_e_h_3, c_e, s4, s5)))),
% 11.36/11.51 inference(transitivity,[status(thm)],[2275, 2273])).
% 11.36/11.51 tff(2277,plain,
% 11.36/11.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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)))),
% 11.36/11.51 inference(quant_inst,[status(thm)],[])).
% 11.36/11.51 tff(2278,plain,
% 11.36/11.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | (~node18(c_e_h_3, c_e, s4, s5))),
% 11.36/11.51 inference(modus_ponens,[status(thm)],[2277, 2276])).
% 11.36/11.51 tff(2279,plain,
% 11.36/11.51 ($false),
% 11.36/11.51 inference(unit_resolution,[status(thm)],[2278, 296, 2271, 2270, 2272])).
% 11.36/11.51 tff(2280,plain,((~node18(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,[]))).
% 11.36/11.51 tff(2281,plain,
% 11.36/11.51 (~node18(c_e_h_3, c_e, s4, s5)),
% 11.36/11.51 inference(unit_resolution,[status(thm)],[2280, 2271, 2270])).
% 11.36/11.51 tff(2282,plain,
% 11.36/11.51 (((~![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))),
% 11.36/11.51 inference(rewrite,[status(thm)],[])).
% 11.36/11.51 tff(2283,plain,
% 11.36/11.51 ((~![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))),
% 11.36/11.51 inference(quant_inst,[status(thm)],[])).
% 11.36/11.51 tff(2284,plain,
% 11.36/11.51 ((~![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)),
% 11.36/11.51 inference(modus_ponens,[status(thm)],[2283, 2282])).
% 11.36/11.51 tff(2285,plain,
% 11.36/11.51 (node19(c_e_h_3, c_e, s4, s5)),
% 11.36/11.51 inference(unit_resolution,[status(thm)],[2284, 312, 1542])).
% 11.36/11.51 tff(2286,plain,
% 11.36/11.51 (((~![Y: $i, 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))),
% 11.36/11.51 inference(rewrite,[status(thm)],[])).
% 11.36/11.51 tff(2287,plain,
% 11.36/11.51 ((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))),
% 11.36/11.51 inference(rewrite,[status(thm)],[])).
% 11.36/11.51 tff(2288,plain,
% 11.36/11.51 (((~![Y: $i, 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)))),
% 11.36/11.51 inference(monotonicity,[status(thm)],[2287])).
% 11.36/11.51 tff(2289,plain,
% 11.36/11.51 (((~![Y: $i, 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))),
% 11.36/11.51 inference(transitivity,[status(thm)],[2288, 2286])).
% 11.36/11.51 tff(2290,plain,
% 11.36/11.51 ((~![Y: $i, 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)))),
% 11.36/11.51 inference(quant_inst,[status(thm)],[])).
% 11.36/11.51 tff(2291,plain,
% 11.36/11.51 ((~![Y: $i, 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)),
% 11.36/11.51 inference(modus_ponens,[status(thm)],[2290, 2289])).
% 11.36/11.51 tff(2292,plain,
% 11.36/11.51 (node17(c_e_h_3, c_e, s4) | node18(c_e_h_3, c_e, s4, s5)),
% 11.36/11.51 inference(unit_resolution,[status(thm)],[2291, 326, 2285])).
% 11.36/11.51 tff(2293,plain,
% 11.36/11.51 (node17(c_e_h_3, c_e, s4)),
% 11.36/11.51 inference(unit_resolution,[status(thm)],[2292, 2281])).
% 11.36/11.51 tff(2294,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_e, s4)), introduced(assumption)).
% 11.36/11.51 tff(2295,plain,
% 11.36/11.51 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, 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_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)))),
% 11.36/11.51 inference(rewrite,[status(thm)],[])).
% 11.36/11.51 tff(2296,plain,
% 11.36/11.51 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, 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)))),
% 11.36/11.51 inference(quant_inst,[status(thm)],[])).
% 11.36/11.51 tff(2297,plain,
% 11.36/11.51 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, 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))),
% 11.36/11.51 inference(modus_ponens,[status(thm)],[2296, 2295])).
% 11.36/11.51 tff(2298,plain,
% 11.36/11.51 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s4)) | (~node17(c_e_h_3, c_e, s4))),
% 11.36/11.51 inference(unit_resolution,[status(thm)],[2297, 359, 2294])).
% 11.36/11.51 tff(2299,plain,
% 11.36/11.51 (~m_c_h_element_v_in1(c_e_h_3, c_e, s4)),
% 11.36/11.51 inference(unit_resolution,[status(thm)],[2298, 2293])).
% 11.36/11.51 tff(2300,plain,
% 11.36/11.51 (((~![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_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))),
% 11.36/11.51 inference(rewrite,[status(thm)],[])).
% 11.36/11.51 tff(2301,plain,
% 11.36/11.51 ((~![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_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))),
% 11.36/11.51 inference(quant_inst,[status(thm)],[])).
% 11.36/11.51 tff(2302,plain,
% 11.36/11.51 ((~![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_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)),
% 11.36/11.51 inference(modus_ponens,[status(thm)],[2301, 2300])).
% 11.36/11.51 tff(2303,plain,
% 11.36/11.51 ((~node16(c_e_h_3, c_e, s4)) | m_c_h_element_v_in1(c_e_h_3, c_e, s4)),
% 11.36/11.51 inference(unit_resolution,[status(thm)],[2302, 377, 2294])).
% 11.36/11.51 tff(2304,plain,
% 11.36/11.51 (~node16(c_e_h_3, c_e, s4)),
% 11.36/11.51 inference(unit_resolution,[status(thm)],[2303, 2299])).
% 11.36/11.51 tff(2305,assumption,(node14(c_e_h_3, c_e, s4, s5)), introduced(assumption)).
% 11.36/11.51 tff(2306,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s4)), introduced(assumption)).
% 11.36/11.51 tff(2307,plain,
% 11.36/11.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_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, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | (~node14(c_e_h_3, 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_in1(c_e_h_3, c_e, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | (~node14(c_e_h_3, c_e, s4, s5)))),
% 11.36/11.51 inference(rewrite,[status(thm)],[])).
% 11.36/11.51 tff(2308,plain,
% 11.36/11.51 (((~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))) <=> (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)) | (~node14(c_e_h_3, c_e, s4, s5)))),
% 11.36/11.51 inference(rewrite,[status(thm)],[])).
% 11.36/11.51 tff(2309,plain,
% 11.36/11.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))) | (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)) | (~node14(c_e_h_3, c_e, s4, s5))))),
% 11.36/11.51 inference(monotonicity,[status(thm)],[2308])).
% 11.36/11.51 tff(2310,plain,
% 11.36/11.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))) | 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)) | (~node14(c_e_h_3, c_e, s4, s5)))),
% 11.36/11.51 inference(transitivity,[status(thm)],[2309, 2307])).
% 11.36/11.51 tff(2311,plain,
% 11.36/11.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))),
% 11.36/11.51 inference(quant_inst,[status(thm)],[])).
% 11.36/11.51 tff(2312,plain,
% 11.36/11.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | (~node14(c_e_h_3, c_e, s4, s5))),
% 11.36/11.51 inference(modus_ponens,[status(thm)],[2311, 2310])).
% 11.36/11.51 tff(2313,plain,
% 11.36/11.51 ($false),
% 11.36/11.51 inference(unit_resolution,[status(thm)],[2312, 427, 2306, 2270, 2305])).
% 11.36/11.51 tff(2314,plain,((~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))), inference(lemma,lemma(discharge,[]))).
% 11.36/11.51 tff(2315,plain,
% 11.36/11.51 (~node14(c_e_h_3, c_e, s4, s5)),
% 11.36/11.51 inference(unit_resolution,[status(thm)],[2314, 2299, 2270])).
% 11.36/11.51 tff(2316,plain,
% 11.36/11.51 (((~![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)))) | (node14(c_e_h_3, c_e, s4, s5) | node16(c_e_h_3, c_e, s4) | (~node19(c_e_h_3, c_e, s4, s5)) | node15(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)))) | node14(c_e_h_3, c_e, s4, s5) | node16(c_e_h_3, c_e, s4) | (~node19(c_e_h_3, c_e, s4, s5)) | node15(c_e_h_3, c_e, s4, s5))),
% 11.36/11.51 inference(rewrite,[status(thm)],[])).
% 11.36/11.51 tff(2317,plain,
% 11.36/11.51 ((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))) <=> (node14(c_e_h_3, c_e, s4, s5) | node16(c_e_h_3, c_e, s4) | (~node19(c_e_h_3, c_e, s4, s5)) | node15(c_e_h_3, c_e, s4, s5))),
% 11.36/11.52 inference(rewrite,[status(thm)],[])).
% 11.36/11.52 tff(2318,plain,
% 11.36/11.52 (((~![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)))) | (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)))) | (node14(c_e_h_3, c_e, s4, s5) | node16(c_e_h_3, c_e, s4) | (~node19(c_e_h_3, c_e, s4, s5)) | node15(c_e_h_3, c_e, s4, s5)))),
% 11.36/11.52 inference(monotonicity,[status(thm)],[2317])).
% 11.36/11.52 tff(2319,plain,
% 11.36/11.52 (((~![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)))) | (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)))) | node14(c_e_h_3, c_e, s4, s5) | node16(c_e_h_3, c_e, s4) | (~node19(c_e_h_3, c_e, s4, s5)) | node15(c_e_h_3, c_e, s4, s5))),
% 11.36/11.52 inference(transitivity,[status(thm)],[2318, 2316])).
% 11.36/11.52 tff(2320,plain,
% 11.36/11.52 ((~![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)))) | (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)))),
% 11.36/11.52 inference(quant_inst,[status(thm)],[])).
% 11.36/11.52 tff(2321,plain,
% 11.36/11.52 ((~![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_3, c_e, s4, s5) | node16(c_e_h_3, c_e, s4) | (~node19(c_e_h_3, c_e, s4, s5)) | node15(c_e_h_3, c_e, s4, s5)),
% 11.36/11.52 inference(modus_ponens,[status(thm)],[2320, 2319])).
% 11.36/11.52 tff(2322,plain,
% 11.36/11.52 (node14(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)),
% 11.36/11.52 inference(unit_resolution,[status(thm)],[2321, 409, 2285])).
% 11.36/11.52 tff(2323,plain,
% 11.36/11.52 (node15(c_e_h_3, c_e, s4, s5)),
% 11.36/11.52 inference(unit_resolution,[status(thm)],[2322, 2315, 2304])).
% 11.36/11.52 tff(2324,plain,
% 11.36/11.52 (((~![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_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))),
% 11.36/11.52 inference(rewrite,[status(thm)],[])).
% 11.36/11.52 tff(2325,plain,
% 11.36/11.52 ((~![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_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))),
% 11.36/11.52 inference(quant_inst,[status(thm)],[])).
% 11.36/11.52 tff(2326,plain,
% 11.36/11.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | (~node15(c_e_h_3, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s4)),
% 11.36/11.52 inference(modus_ponens,[status(thm)],[2325, 2324])).
% 11.36/11.52 tff(2327,plain,
% 11.36/11.52 ($false),
% 11.36/11.52 inference(unit_resolution,[status(thm)],[2326, 393, 2271, 2270, 2323])).
% 11.36/11.52 tff(2328,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,[]))).
% 11.36/11.52 tff(2329,plain,
% 11.36/11.52 (~m_c_h_element_v_out(c_e_h_3, c_e, s5)),
% 11.36/11.52 inference(unit_resolution,[status(thm)],[2328, 2269, 2265])).
% 11.36/11.52 tff(2330,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s6)), introduced(assumption)).
% 11.36/11.52 tff(2331,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s5)), introduced(assumption)).
% 11.36/11.52 tff(2332,assumption,(node18(c_e_h_3, c_e, s5, s6)), introduced(assumption)).
% 11.36/11.52 tff(2333,plain,
% 11.36/11.52 (((~![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_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)))),
% 11.36/11.52 inference(rewrite,[status(thm)],[])).
% 11.36/11.52 tff(2334,plain,
% 11.36/11.52 (((~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)))),
% 11.36/11.52 inference(rewrite,[status(thm)],[])).
% 11.36/11.52 tff(2335,plain,
% 11.36/11.52 (((~![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_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))))),
% 11.36/11.52 inference(monotonicity,[status(thm)],[2334])).
% 11.36/11.52 tff(2336,plain,
% 11.36/11.52 (((~![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_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)))),
% 11.36/11.52 inference(transitivity,[status(thm)],[2335, 2333])).
% 11.36/11.52 tff(2337,plain,
% 11.36/11.52 ((~![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_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)))),
% 11.36/11.52 inference(quant_inst,[status(thm)],[])).
% 11.36/11.52 tff(2338,plain,
% 11.36/11.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node18(c_e_h_3, c_e, s5, s6))),
% 11.36/11.52 inference(modus_ponens,[status(thm)],[2337, 2336])).
% 11.36/11.52 tff(2339,plain,
% 11.36/11.52 ($false),
% 11.36/11.52 inference(unit_resolution,[status(thm)],[2338, 296, 2330, 2331, 2332])).
% 11.36/11.52 tff(2340,plain,((~node18(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_out(c_e_h_3, c_e, s5)), inference(lemma,lemma(discharge,[]))).
% 11.36/11.52 tff(2341,plain,
% 11.36/11.52 (~node18(c_e_h_3, c_e, s5, s6)),
% 11.36/11.52 inference(unit_resolution,[status(thm)],[2340, 2331, 2330])).
% 11.36/11.52 tff(2342,plain,
% 11.36/11.52 (succ(s5, s6) <=> succ(s5, s6)),
% 11.36/11.52 inference(rewrite,[status(thm)],[])).
% 11.36/11.52 tff(2343,axiom,(succ(s5, s6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound6')).
% 11.36/11.52 tff(2344,plain,
% 11.36/11.52 (succ(s5, s6)),
% 11.36/11.52 inference(modus_ponens,[status(thm)],[2343, 2342])).
% 11.36/11.52 tff(2345,plain,
% 11.36/11.52 (((~![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))),
% 11.36/11.52 inference(rewrite,[status(thm)],[])).
% 11.36/11.52 tff(2346,plain,
% 11.36/11.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s5, s6)) | trans(s5, s6))),
% 11.36/11.52 inference(quant_inst,[status(thm)],[])).
% 11.36/11.52 tff(2347,plain,
% 11.36/11.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s5, s6)) | trans(s5, s6)),
% 11.36/11.52 inference(modus_ponens,[status(thm)],[2346, 2345])).
% 11.36/11.52 tff(2348,plain,
% 11.36/11.52 (trans(s5, s6)),
% 11.36/11.52 inference(unit_resolution,[status(thm)],[2347, 2344, 93])).
% 11.36/11.52 tff(2349,plain,
% 11.36/11.52 (((~![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))),
% 11.36/11.52 inference(rewrite,[status(thm)],[])).
% 11.36/11.52 tff(2350,plain,
% 11.36/11.52 ((~![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))),
% 11.36/11.52 inference(quant_inst,[status(thm)],[])).
% 11.36/11.52 tff(2351,plain,
% 11.36/11.52 ((~![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)),
% 11.36/11.52 inference(modus_ponens,[status(thm)],[2350, 2349])).
% 11.36/11.52 tff(2352,plain,
% 11.36/11.52 (node19(c_e_h_3, c_e, s5, s6)),
% 11.36/11.52 inference(unit_resolution,[status(thm)],[2351, 312, 2348])).
% 11.36/11.52 tff(2353,plain,
% 11.36/11.52 (((~![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_3, c_e, s5) | (~node19(c_e_h_3, c_e, s5, s6)) | 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)))) | node17(c_e_h_3, c_e, s5) | (~node19(c_e_h_3, c_e, s5, s6)) | node18(c_e_h_3, c_e, s5, s6))),
% 11.36/11.52 inference(rewrite,[status(thm)],[])).
% 11.36/11.52 tff(2354,plain,
% 11.36/11.52 ((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))) <=> (node17(c_e_h_3, c_e, s5) | (~node19(c_e_h_3, c_e, s5, s6)) | node18(c_e_h_3, c_e, s5, s6))),
% 11.36/11.52 inference(rewrite,[status(thm)],[])).
% 11.36/11.52 tff(2355,plain,
% 11.36/11.52 (((~![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_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)))) | (node17(c_e_h_3, c_e, s5) | (~node19(c_e_h_3, c_e, s5, s6)) | node18(c_e_h_3, c_e, s5, s6)))),
% 11.36/11.52 inference(monotonicity,[status(thm)],[2354])).
% 11.36/11.52 tff(2356,plain,
% 11.36/11.52 (((~![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_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)))) | node17(c_e_h_3, c_e, s5) | (~node19(c_e_h_3, c_e, s5, s6)) | node18(c_e_h_3, c_e, s5, s6))),
% 11.36/11.52 inference(transitivity,[status(thm)],[2355, 2353])).
% 11.36/11.52 tff(2357,plain,
% 11.36/11.52 ((~![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_3, c_e, s5) | node18(c_e_h_3, c_e, s5, s6) | (~node19(c_e_h_3, c_e, s5, s6)))),
% 11.36/11.52 inference(quant_inst,[status(thm)],[])).
% 11.36/11.52 tff(2358,plain,
% 11.36/11.52 ((~![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_3, c_e, s5) | (~node19(c_e_h_3, c_e, s5, s6)) | node18(c_e_h_3, c_e, s5, s6)),
% 11.36/11.52 inference(modus_ponens,[status(thm)],[2357, 2356])).
% 11.36/11.52 tff(2359,plain,
% 11.36/11.52 (node17(c_e_h_3, c_e, s5) | node18(c_e_h_3, c_e, s5, s6)),
% 11.36/11.52 inference(unit_resolution,[status(thm)],[2358, 326, 2352])).
% 11.36/11.52 tff(2360,plain,
% 11.36/11.52 (node17(c_e_h_3, c_e, s5)),
% 11.36/11.52 inference(unit_resolution,[status(thm)],[2359, 2341])).
% 11.36/11.52 tff(2361,assumption,(node16(c_e_h_3, c_e, s5)), introduced(assumption)).
% 11.36/11.52 tff(2362,assumption,(node17(c_e_h_3, c_e, s5)), introduced(assumption)).
% 11.36/11.52 tff(2363,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_e, s5)), introduced(assumption)).
% 11.36/11.52 tff(2364,plain,
% 11.36/11.52 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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))),
% 11.36/11.52 inference(rewrite,[status(thm)],[])).
% 11.36/11.52 tff(2365,plain,
% 11.36/11.52 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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))),
% 11.36/11.52 inference(quant_inst,[status(thm)],[])).
% 11.36/11.52 tff(2366,plain,
% 11.36/11.52 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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)),
% 11.36/11.52 inference(modus_ponens,[status(thm)],[2365, 2364])).
% 11.36/11.52 tff(2367,plain,
% 11.36/11.52 (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)),
% 11.36/11.52 inference(unit_resolution,[status(thm)],[2366, 377, 2361])).
% 11.36/11.52 tff(2368,plain,
% 11.36/11.52 (m_c_h_element_v_in1(c_e_h_3, c_e, s5)),
% 11.36/11.52 inference(unit_resolution,[status(thm)],[2367, 2363])).
% 11.36/11.52 tff(2369,plain,
% 11.36/11.52 (((~![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_in2(c_e_h_3, c_e, s5) | (~m_c_h_element_v_in1(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)))) | 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)) | (~node17(c_e_h_3, c_e, s5)))),
% 11.36/11.52 inference(rewrite,[status(thm)],[])).
% 11.36/11.52 tff(2370,plain,
% 11.36/11.52 (((~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))) <=> (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)) | (~node17(c_e_h_3, c_e, s5)))),
% 11.36/11.52 inference(rewrite,[status(thm)],[])).
% 11.36/11.52 tff(2371,plain,
% 11.36/11.52 (((~![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_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)))) | (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)) | (~node17(c_e_h_3, c_e, s5))))),
% 11.36/11.52 inference(monotonicity,[status(thm)],[2370])).
% 11.36/11.52 tff(2372,plain,
% 11.36/11.52 (((~![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_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)))) | 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)) | (~node17(c_e_h_3, c_e, s5)))),
% 11.36/11.52 inference(transitivity,[status(thm)],[2371, 2369])).
% 11.36/11.52 tff(2373,plain,
% 11.36/11.52 ((~![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_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)))),
% 11.36/11.52 inference(quant_inst,[status(thm)],[])).
% 11.36/11.52 tff(2374,plain,
% 11.36/11.52 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s5)) | (~node17(c_e_h_3, c_e, s5))),
% 11.36/11.52 inference(modus_ponens,[status(thm)],[2373, 2372])).
% 11.36/11.52 tff(2375,plain,
% 11.36/11.52 (m_c_h_element_v_in2(c_e_h_3, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s5))),
% 11.36/11.52 inference(unit_resolution,[status(thm)],[2374, 359, 2362])).
% 11.36/11.52 tff(2376,plain,
% 11.36/11.52 ($false),
% 11.36/11.52 inference(unit_resolution,[status(thm)],[2375, 2368, 2363])).
% 11.36/11.52 tff(2377,plain,(m_c_h_element_v_in2(c_e_h_3, c_e, s5) | (~node17(c_e_h_3, c_e, s5)) | (~node16(c_e_h_3, c_e, s5))), inference(lemma,lemma(discharge,[]))).
% 11.36/11.52 tff(2378,plain,
% 11.36/11.52 (m_c_h_element_v_in2(c_e_h_3, c_e, s5)),
% 11.36/11.52 inference(unit_resolution,[status(thm)],[2377, 2362, 2361])).
% 11.36/11.52 tff(2379,plain,
% 11.36/11.52 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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_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] : ((~node16(I0, 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_in2(c_e_h_3, c_e, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s5)))),
% 11.36/11.52 inference(rewrite,[status(thm)],[])).
% 11.36/11.52 tff(2380,plain,
% 11.36/11.52 (((~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))) <=> ((~node16(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)))),
% 11.36/11.52 inference(rewrite,[status(thm)],[])).
% 11.36/11.52 tff(2381,plain,
% 11.36/11.52 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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_in2(c_e_h_3, c_e, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s5))))),
% 11.36/11.52 inference(monotonicity,[status(thm)],[2380])).
% 11.36/11.52 tff(2382,plain,
% 11.36/11.52 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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_in2(c_e_h_3, c_e, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s5)))),
% 11.36/11.52 inference(transitivity,[status(thm)],[2381, 2379])).
% 11.36/11.52 tff(2383,plain,
% 11.36/11.52 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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)))),
% 11.36/11.52 inference(quant_inst,[status(thm)],[])).
% 11.36/11.52 tff(2384,plain,
% 11.36/11.52 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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_in2(c_e_h_3, c_e, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s5))),
% 11.36/11.52 inference(modus_ponens,[status(thm)],[2383, 2382])).
% 11.36/11.52 tff(2385,plain,
% 11.36/11.52 ((~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))),
% 11.36/11.52 inference(unit_resolution,[status(thm)],[2384, 2142, 2361])).
% 11.36/11.52 tff(2386,plain,
% 11.36/11.52 (~m_c_h_element_v_in1(c_e_h_3, c_e, s5)),
% 11.36/11.52 inference(unit_resolution,[status(thm)],[2385, 2378])).
% 11.36/11.52 tff(2387,plain,
% 11.36/11.52 (((~![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_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)))) | 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)))),
% 11.36/11.52 inference(rewrite,[status(thm)],[])).
% 11.36/11.52 tff(2388,plain,
% 11.36/11.52 ((~![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_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)))),
% 11.36/11.52 inference(quant_inst,[status(thm)],[])).
% 11.36/11.52 tff(2389,plain,
% 11.36/11.52 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s5)) | (~node17(c_e_h_3, c_e, s5))),
% 11.36/11.52 inference(modus_ponens,[status(thm)],[2388, 2387])).
% 11.36/11.52 tff(2390,plain,
% 11.36/11.52 (m_c_h_element_v_in1(c_e_h_3, c_e, s5) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s5))),
% 11.36/11.52 inference(unit_resolution,[status(thm)],[2389, 2125, 2362])).
% 11.36/11.52 tff(2391,plain,
% 11.36/11.52 ($false),
% 11.36/11.52 inference(unit_resolution,[status(thm)],[2390, 2386, 2378])).
% 11.36/11.52 tff(2392,plain,((~node17(c_e_h_3, c_e, s5)) | (~node16(c_e_h_3, c_e, s5))), inference(lemma,lemma(discharge,[]))).
% 11.36/11.52 tff(2393,plain,
% 11.36/11.52 (~node16(c_e_h_3, c_e, s5)),
% 11.36/11.52 inference(unit_resolution,[status(thm)],[2392, 2360])).
% 11.36/11.52 tff(2394,plain,
% 11.36/11.52 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s5)) | (~node17(c_e_h_3, c_e, s5))),
% 11.36/11.52 inference(unit_resolution,[status(thm)],[2374, 359, 2363])).
% 11.36/11.52 tff(2395,plain,
% 11.36/11.52 (~m_c_h_element_v_in1(c_e_h_3, c_e, s5)),
% 11.36/11.52 inference(unit_resolution,[status(thm)],[2394, 2360])).
% 11.36/11.52 tff(2396,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s5)), introduced(assumption)).
% 11.36/11.52 tff(2397,assumption,(node14(c_e_h_3, c_e, s5, s6)), introduced(assumption)).
% 11.36/11.52 tff(2398,plain,
% 11.36/11.52 (((~![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_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~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_in1(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node14(c_e_h_3, c_e, s5, s6)))),
% 11.36/11.52 inference(rewrite,[status(thm)],[])).
% 11.36/11.52 tff(2399,plain,
% 11.36/11.52 (((~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_in1(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node14(c_e_h_3, c_e, s5, s6)))),
% 11.36/11.52 inference(rewrite,[status(thm)],[])).
% 11.36/11.52 tff(2400,plain,
% 11.36/11.52 (((~![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_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_in1(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node14(c_e_h_3, c_e, s5, s6))))),
% 11.36/11.52 inference(monotonicity,[status(thm)],[2399])).
% 11.36/11.52 tff(2401,plain,
% 11.36/11.52 (((~![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_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_in1(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node14(c_e_h_3, c_e, s5, s6)))),
% 11.36/11.52 inference(transitivity,[status(thm)],[2400, 2398])).
% 11.36/11.52 tff(2402,plain,
% 11.36/11.52 ((~![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_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)))),
% 11.36/11.52 inference(quant_inst,[status(thm)],[])).
% 11.36/11.52 tff(2403,plain,
% 11.36/11.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node14(c_e_h_3, c_e, s5, s6))),
% 11.36/11.52 inference(modus_ponens,[status(thm)],[2402, 2401])).
% 11.36/11.52 tff(2404,plain,
% 11.36/11.52 ($false),
% 11.36/11.52 inference(unit_resolution,[status(thm)],[2403, 427, 2330, 2397, 2396])).
% 11.36/11.52 tff(2405,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,[]))).
% 11.36/11.52 tff(2406,plain,
% 11.36/11.52 (~node14(c_e_h_3, c_e, s5, s6)),
% 11.36/11.52 inference(unit_resolution,[status(thm)],[2405, 2395, 2330])).
% 11.36/11.52 tff(2407,plain,
% 11.36/11.52 (((~![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)))) | (node15(c_e_h_3, c_e, s5, s6) | node16(c_e_h_3, c_e, s5) | node14(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)))) | node15(c_e_h_3, c_e, s5, s6) | node16(c_e_h_3, c_e, s5) | node14(c_e_h_3, c_e, s5, s6) | (~node19(c_e_h_3, c_e, s5, s6)))),
% 11.36/11.53 inference(rewrite,[status(thm)],[])).
% 11.36/11.53 tff(2408,plain,
% 11.36/11.53 ((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))) <=> (node15(c_e_h_3, c_e, s5, s6) | node16(c_e_h_3, c_e, s5) | node14(c_e_h_3, c_e, s5, s6) | (~node19(c_e_h_3, c_e, s5, s6)))),
% 11.36/11.53 inference(rewrite,[status(thm)],[])).
% 11.36/11.53 tff(2409,plain,
% 11.36/11.53 (((~![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_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)))) | (node15(c_e_h_3, c_e, s5, s6) | node16(c_e_h_3, c_e, s5) | node14(c_e_h_3, c_e, s5, s6) | (~node19(c_e_h_3, c_e, s5, s6))))),
% 11.36/11.53 inference(monotonicity,[status(thm)],[2408])).
% 11.36/11.53 tff(2410,plain,
% 11.36/11.53 (((~![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_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)))) | node15(c_e_h_3, c_e, s5, s6) | node16(c_e_h_3, c_e, s5) | node14(c_e_h_3, c_e, s5, s6) | (~node19(c_e_h_3, c_e, s5, s6)))),
% 11.36/11.53 inference(transitivity,[status(thm)],[2409, 2407])).
% 11.36/11.53 tff(2411,plain,
% 11.36/11.53 ((~![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_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)))),
% 11.36/11.53 inference(quant_inst,[status(thm)],[])).
% 11.36/11.53 tff(2412,plain,
% 11.36/11.53 ((~![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)))) | node15(c_e_h_3, c_e, s5, s6) | node16(c_e_h_3, c_e, s5) | node14(c_e_h_3, c_e, s5, s6) | (~node19(c_e_h_3, c_e, s5, s6))),
% 11.36/11.53 inference(modus_ponens,[status(thm)],[2411, 2410])).
% 11.36/11.53 tff(2413,plain,
% 11.36/11.53 (node15(c_e_h_3, c_e, s5, s6) | node16(c_e_h_3, c_e, s5) | node14(c_e_h_3, c_e, s5, s6)),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2412, 409, 2352])).
% 11.36/11.53 tff(2414,plain,
% 11.36/11.53 (node15(c_e_h_3, c_e, s5, s6)),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2413, 2406, 2393])).
% 11.36/11.53 tff(2415,plain,
% 11.36/11.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 11.36/11.53 inference(rewrite,[status(thm)],[])).
% 11.36/11.53 tff(2416,plain,
% 11.36/11.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 11.36/11.53 inference(quant_inst,[status(thm)],[])).
% 11.36/11.53 tff(2417,plain,
% 11.36/11.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node15(c_e_h_3, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s5)),
% 11.36/11.53 inference(modus_ponens,[status(thm)],[2416, 2415])).
% 11.36/11.53 tff(2418,plain,
% 11.36/11.53 ($false),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2417, 393, 2330, 2331, 2414])).
% 11.36/11.53 tff(2419,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,[]))).
% 11.36/11.53 tff(2420,plain,
% 11.36/11.53 ((~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)),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2419, 2329])).
% 11.36/11.53 tff(2421,plain,
% 11.36/11.53 (~m_c_h_element_v_out(c_e_h_3, c_e, s6)),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2420, 1969])).
% 11.36/11.53 tff(2422,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s8)), introduced(assumption)).
% 11.36/11.53 tff(2423,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_r, s6)), introduced(assumption)).
% 11.36/11.53 tff(2424,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s6)), introduced(assumption)).
% 11.36/11.53 tff(2425,plain,
% 11.36/11.53 (^[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)))),
% 11.36/11.53 inference(bind,[status(th)],[])).
% 11.36/11.53 tff(2426,plain,
% 11.36/11.53 (![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))),
% 11.36/11.53 inference(quant_intro,[status(thm)],[2425])).
% 11.36/11.53 tff(2427,plain,
% 11.36/11.53 (![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))),
% 11.36/11.53 inference(rewrite,[status(thm)],[])).
% 11.36/11.53 tff(2428,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')).
% 11.36/11.53 tff(2429,plain,
% 11.36/11.53 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))),
% 11.36/11.53 inference(modus_ponens,[status(thm)],[2428, 2427])).
% 11.36/11.53 tff(2430,plain,(
% 11.36/11.53 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))),
% 11.36/11.53 inference(skolemize,[status(sab)],[2429])).
% 11.36/11.53 tff(2431,plain,
% 11.36/11.53 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))),
% 11.36/11.53 inference(modus_ponens,[status(thm)],[2430, 2426])).
% 11.36/11.53 tff(2432,plain,
% 11.36/11.53 (((~![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_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))),
% 11.36/11.53 inference(rewrite,[status(thm)],[])).
% 11.36/11.53 tff(2433,plain,
% 11.36/11.53 ((~![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_3, c_r, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s6))),
% 11.36/11.53 inference(quant_inst,[status(thm)],[])).
% 11.36/11.53 tff(2434,plain,
% 11.36/11.53 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s6)),
% 11.36/11.53 inference(modus_ponens,[status(thm)],[2433, 2432])).
% 11.36/11.53 tff(2435,plain,
% 11.36/11.53 ($false),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2434, 2431, 2424, 2423])).
% 11.36/11.53 tff(2436,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,[]))).
% 11.36/11.53 tff(2437,plain,
% 11.36/11.53 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s6)),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2436, 2421])).
% 11.36/11.53 tff(2438,plain,
% 11.36/11.53 (((~![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))),
% 11.36/11.53 inference(rewrite,[status(thm)],[])).
% 11.36/11.53 tff(2439,plain,
% 11.36/11.53 ((~![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))),
% 11.36/11.53 inference(quant_inst,[status(thm)],[])).
% 11.36/11.53 tff(2440,plain,
% 11.36/11.53 ((~![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)),
% 11.36/11.53 inference(modus_ponens,[status(thm)],[2439, 2438])).
% 11.36/11.53 tff(2441,plain,
% 11.36/11.53 (~node20(c_e_h_3, c_r, s6)),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2440, 213, 2437])).
% 11.36/11.53 tff(2442,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s5)), introduced(assumption)).
% 11.36/11.53 tff(2443,assumption,(node22(c_e_h_3, c_r, s4, s5)), introduced(assumption)).
% 11.36/11.53 tff(2444,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s4)), introduced(assumption)).
% 11.36/11.53 tff(2445,plain,
% 11.36/11.53 (((~![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_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))),
% 11.36/11.53 inference(rewrite,[status(thm)],[])).
% 11.36/11.53 tff(2446,plain,
% 11.36/11.53 ((~![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_3, c_r, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s3))),
% 11.36/11.53 inference(quant_inst,[status(thm)],[])).
% 11.36/11.53 tff(2447,plain,
% 11.36/11.53 ((~![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_3, c_r, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s3)),
% 11.36/11.53 inference(modus_ponens,[status(thm)],[2446, 2445])).
% 11.36/11.53 tff(2448,plain,
% 11.36/11.53 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s3)),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2447, 2431, 2174])).
% 11.36/11.53 tff(2449,plain,
% 11.36/11.53 (((~![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))),
% 11.36/11.53 inference(rewrite,[status(thm)],[])).
% 11.36/11.53 tff(2450,plain,
% 11.36/11.53 ((~![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))),
% 11.36/11.53 inference(quant_inst,[status(thm)],[])).
% 11.36/11.53 tff(2451,plain,
% 11.36/11.53 ((~![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)),
% 11.36/11.53 inference(modus_ponens,[status(thm)],[2450, 2449])).
% 11.36/11.53 tff(2452,plain,
% 11.36/11.53 (~node20(c_e_h_3, c_r, s3)),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2451, 213, 2448])).
% 11.36/11.53 tff(2453,plain,
% 11.36/11.53 (((~![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_3, c_r, s4)) | node20(c_e_h_3, c_r, s3) | (~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)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | node20(c_e_h_3, c_r, s3) | (~node21(c_e_h_3, c_r, s3, s4)))),
% 11.36/11.53 inference(rewrite,[status(thm)],[])).
% 11.36/11.53 tff(2454,plain,
% 11.36/11.53 ((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))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | node20(c_e_h_3, c_r, s3) | (~node21(c_e_h_3, c_r, s3, s4)))),
% 11.36/11.53 inference(rewrite,[status(thm)],[])).
% 11.36/11.53 tff(2455,plain,
% 11.36/11.53 (((~![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_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)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | node20(c_e_h_3, c_r, s3) | (~node21(c_e_h_3, c_r, s3, s4))))),
% 11.36/11.53 inference(monotonicity,[status(thm)],[2454])).
% 11.36/11.53 tff(2456,plain,
% 11.36/11.53 (((~![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_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)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | node20(c_e_h_3, c_r, s3) | (~node21(c_e_h_3, c_r, s3, s4)))),
% 11.36/11.53 inference(transitivity,[status(thm)],[2455, 2453])).
% 11.36/11.53 tff(2457,plain,
% 11.36/11.53 ((~![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_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)))),
% 11.36/11.53 inference(quant_inst,[status(thm)],[])).
% 11.36/11.53 tff(2458,plain,
% 11.36/11.53 ((~![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_3, c_r, s4)) | node20(c_e_h_3, c_r, s3) | (~node21(c_e_h_3, c_r, s3, s4))),
% 11.36/11.53 inference(modus_ponens,[status(thm)],[2457, 2456])).
% 11.36/11.53 tff(2459,plain,
% 11.36/11.53 ((~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node21(c_e_h_3, c_r, s3, s4))),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2458, 228, 2452])).
% 11.36/11.53 tff(2460,plain,
% 11.36/11.53 (~node21(c_e_h_3, c_r, s3, s4)),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2459, 2444])).
% 11.36/11.53 tff(2461,plain,
% 11.36/11.53 (((~![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))),
% 11.36/11.53 inference(rewrite,[status(thm)],[])).
% 11.36/11.53 tff(2462,plain,
% 11.36/11.53 ((~![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))),
% 11.36/11.53 inference(quant_inst,[status(thm)],[])).
% 11.36/11.53 tff(2463,plain,
% 11.36/11.53 ((~![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)),
% 11.36/11.53 inference(modus_ponens,[status(thm)],[2462, 2461])).
% 11.36/11.53 tff(2464,plain,
% 11.36/11.53 (node22(c_e_h_3, c_r, s3, s4)),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2463, 247, 1092, 2460])).
% 11.36/11.53 tff(2465,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s3)), introduced(assumption)).
% 11.36/11.53 tff(2466,assumption,(node22(c_e_h_3, c_r, s2, s3)), introduced(assumption)).
% 11.36/11.53 tff(2467,plain,
% 11.36/11.53 (((~![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_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))),
% 11.36/11.53 inference(rewrite,[status(thm)],[])).
% 11.36/11.53 tff(2468,plain,
% 11.36/11.53 ((~![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_3, c_r, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s1))),
% 11.36/11.53 inference(quant_inst,[status(thm)],[])).
% 11.36/11.53 tff(2469,plain,
% 11.36/11.53 ((~![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_3, c_r, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s1)),
% 11.36/11.53 inference(modus_ponens,[status(thm)],[2468, 2467])).
% 11.36/11.53 tff(2470,plain,
% 11.36/11.53 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s1)),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2469, 2431, 2065])).
% 11.36/11.53 tff(2471,plain,
% 11.36/11.53 (((~![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))),
% 11.36/11.53 inference(rewrite,[status(thm)],[])).
% 11.36/11.53 tff(2472,plain,
% 11.36/11.53 ((~![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))),
% 11.36/11.53 inference(quant_inst,[status(thm)],[])).
% 11.36/11.53 tff(2473,plain,
% 11.36/11.53 ((~![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)),
% 11.36/11.53 inference(modus_ponens,[status(thm)],[2472, 2471])).
% 11.36/11.53 tff(2474,plain,
% 11.36/11.53 (~node20(c_e_h_3, c_r, s1)),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2473, 213, 2470])).
% 11.36/11.53 tff(2475,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s2)), introduced(assumption)).
% 11.36/11.53 tff(2476,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s1)), introduced(assumption)).
% 11.36/11.53 tff(2477,plain,
% 11.36/11.53 (((~![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_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))),
% 11.36/11.53 inference(rewrite,[status(thm)],[])).
% 11.36/11.53 tff(2478,plain,
% 11.36/11.53 ((~![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_3, c_r, s0)) | m_c_h_element_v_out(c_e_h_3, c_e, s0))),
% 11.36/11.53 inference(quant_inst,[status(thm)],[])).
% 11.36/11.53 tff(2479,plain,
% 11.36/11.53 ((~![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_3, c_r, s0)) | m_c_h_element_v_out(c_e_h_3, c_e, s0)),
% 11.36/11.53 inference(modus_ponens,[status(thm)],[2478, 2477])).
% 11.36/11.53 tff(2480,plain,
% 11.36/11.53 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s0)),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2479, 2431, 2028])).
% 11.36/11.53 tff(2481,plain,
% 11.36/11.53 (((~![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))),
% 11.36/11.53 inference(rewrite,[status(thm)],[])).
% 11.36/11.53 tff(2482,plain,
% 11.36/11.53 ((~![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))),
% 11.36/11.53 inference(quant_inst,[status(thm)],[])).
% 11.36/11.53 tff(2483,plain,
% 11.36/11.53 ((~![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)),
% 11.36/11.53 inference(modus_ponens,[status(thm)],[2482, 2481])).
% 11.36/11.53 tff(2484,plain,
% 11.36/11.53 (~node20(c_e_h_3, c_r, s0)),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2483, 213, 2480])).
% 11.36/11.53 tff(2485,plain,
% 11.36/11.53 (((~![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_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)))) | 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)))),
% 11.36/11.53 inference(rewrite,[status(thm)],[])).
% 11.36/11.53 tff(2486,plain,
% 11.36/11.53 ((~![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_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)))),
% 11.36/11.53 inference(quant_inst,[status(thm)],[])).
% 11.36/11.53 tff(2487,plain,
% 11.36/11.53 ((~![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_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))),
% 11.36/11.53 inference(modus_ponens,[status(thm)],[2486, 2485])).
% 11.36/11.53 tff(2488,plain,
% 11.36/11.53 ((~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node21(c_e_h_3, c_r, s0, s1))),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2487, 228, 2484])).
% 11.36/11.53 tff(2489,plain,
% 11.36/11.53 (~node21(c_e_h_3, c_r, s0, s1)),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2488, 2476])).
% 11.36/11.53 tff(2490,plain,
% 11.36/11.53 (((~![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))),
% 11.36/11.53 inference(rewrite,[status(thm)],[])).
% 11.36/11.53 tff(2491,plain,
% 11.36/11.53 ((~![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))),
% 11.36/11.53 inference(quant_inst,[status(thm)],[])).
% 11.36/11.53 tff(2492,plain,
% 11.36/11.53 ((~![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)),
% 11.36/11.53 inference(modus_ponens,[status(thm)],[2491, 2490])).
% 11.36/11.53 tff(2493,plain,
% 11.36/11.53 (node22(c_e_h_3, c_r, s0, s1)),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2492, 247, 100, 2489])).
% 11.36/11.53 tff(2494,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s0)), introduced(assumption)).
% 11.36/11.53 tff(2495,plain,
% 11.36/11.53 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s0))),
% 11.36/11.53 inference(quant_inst,[status(thm)],[])).
% 11.36/11.53 tff(2496,plain,
% 11.36/11.53 ($false),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2495, 260, 2494])).
% 11.36/11.53 tff(2497,plain,(~m_and_h_gate_v_out(c_e_h_3, c_r, s0)), inference(lemma,lemma(discharge,[]))).
% 11.36/11.53 tff(2498,plain,
% 11.36/11.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, 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))),
% 11.36/11.53 inference(rewrite,[status(thm)],[])).
% 11.36/11.53 tff(2499,plain,
% 11.36/11.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, 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))),
% 11.36/11.53 inference(quant_inst,[status(thm)],[])).
% 11.36/11.53 tff(2500,plain,
% 11.36/11.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node22(c_e_h_3, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s0)),
% 11.36/11.53 inference(modus_ponens,[status(thm)],[2499, 2498])).
% 11.36/11.53 tff(2501,plain,
% 11.36/11.53 ($false),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2500, 273, 2497, 2476, 2493])).
% 11.36/11.53 tff(2502,plain,(~m_and_h_gate_v_out(c_e_h_3, c_r, s1)), inference(lemma,lemma(discharge,[]))).
% 11.36/11.53 tff(2503,plain,
% 11.36/11.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, 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))),
% 11.36/11.53 inference(rewrite,[status(thm)],[])).
% 11.36/11.53 tff(2504,plain,
% 11.36/11.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, 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))),
% 11.36/11.53 inference(quant_inst,[status(thm)],[])).
% 11.36/11.53 tff(2505,plain,
% 11.36/11.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, 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)),
% 11.36/11.53 inference(modus_ponens,[status(thm)],[2504, 2503])).
% 11.36/11.53 tff(2506,plain,
% 11.36/11.53 ((~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)),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2505, 273])).
% 11.36/11.53 tff(2507,plain,
% 11.36/11.53 ((~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node22(c_e_h_3, c_r, s1, s2))),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2506, 2502])).
% 11.36/11.53 tff(2508,plain,
% 11.36/11.53 (~node22(c_e_h_3, c_r, s1, s2)),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2507, 2475])).
% 11.36/11.53 tff(2509,plain,
% 11.36/11.53 (((~![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))),
% 11.36/11.53 inference(rewrite,[status(thm)],[])).
% 11.36/11.53 tff(2510,plain,
% 11.36/11.53 ((~![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))),
% 11.36/11.53 inference(quant_inst,[status(thm)],[])).
% 11.36/11.53 tff(2511,plain,
% 11.36/11.53 ((~![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)),
% 11.36/11.53 inference(modus_ponens,[status(thm)],[2510, 2509])).
% 11.36/11.53 tff(2512,plain,
% 11.36/11.53 (node21(c_e_h_3, c_r, s1, s2) | node22(c_e_h_3, c_r, s1, s2)),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2511, 247, 470])).
% 11.36/11.53 tff(2513,plain,
% 11.36/11.53 (node21(c_e_h_3, c_r, s1, s2)),
% 11.36/11.53 inference(unit_resolution,[status(thm)],[2512, 2508])).
% 11.36/11.53 tff(2514,assumption,(~node20(c_e_h_3, c_r, s1)), introduced(assumption)).
% 11.36/11.53 tff(2515,plain,
% 11.36/11.53 (((~![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_3, c_r, s2)) | (~node21(c_e_h_3, c_r, s1, s2)) | node20(c_e_h_3, 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)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node21(c_e_h_3, c_r, s1, s2)) | node20(c_e_h_3, c_r, s1))),
% 11.36/11.53 inference(rewrite,[status(thm)],[])).
% 11.36/11.53 tff(2516,plain,
% 11.36/11.53 ((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))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node21(c_e_h_3, c_r, s1, s2)) | node20(c_e_h_3, c_r, s1))),
% 11.36/11.53 inference(rewrite,[status(thm)],[])).
% 11.36/11.53 tff(2517,plain,
% 11.36/11.53 (((~![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_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)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node21(c_e_h_3, c_r, s1, s2)) | node20(c_e_h_3, c_r, s1)))),
% 11.36/11.53 inference(monotonicity,[status(thm)],[2516])).
% 11.36/11.53 tff(2518,plain,
% 11.36/11.53 (((~![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_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)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node21(c_e_h_3, c_r, s1, s2)) | node20(c_e_h_3, c_r, s1))),
% 11.36/11.53 inference(transitivity,[status(thm)],[2517, 2515])).
% 11.36/11.53 tff(2519,plain,
% 11.36/11.53 ((~![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_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)))),
% 11.36/11.53 inference(quant_inst,[status(thm)],[])).
% 11.36/11.53 tff(2520,plain,
% 11.36/11.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node21(c_e_h_3, c_r, s1, s2)) | node20(c_e_h_3, c_r, s1)),
% 11.36/11.54 inference(modus_ponens,[status(thm)],[2519, 2518])).
% 11.36/11.54 tff(2521,plain,
% 11.36/11.54 ($false),
% 11.36/11.54 inference(unit_resolution,[status(thm)],[2520, 228, 2475, 2514, 2513])).
% 11.36/11.54 tff(2522,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,[]))).
% 11.36/11.54 tff(2523,plain,
% 11.36/11.54 (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)),
% 11.36/11.54 inference(unit_resolution,[status(thm)],[2522, 2474])).
% 11.36/11.54 tff(2524,plain,
% 11.36/11.54 (((~![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_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))),
% 11.36/11.54 inference(rewrite,[status(thm)],[])).
% 11.36/11.54 tff(2525,plain,
% 11.36/11.54 ((~![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_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))),
% 11.36/11.54 inference(quant_inst,[status(thm)],[])).
% 11.36/11.54 tff(2526,plain,
% 11.36/11.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node22(c_e_h_3, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2)),
% 11.36/11.54 inference(modus_ponens,[status(thm)],[2525, 2524])).
% 11.36/11.54 tff(2527,plain,
% 11.36/11.54 ($false),
% 11.36/11.54 inference(unit_resolution,[status(thm)],[2526, 273, 2523, 2465, 2466])).
% 11.36/11.54 tff(2528,plain,((~node22(c_e_h_3, c_r, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3))), inference(lemma,lemma(discharge,[]))).
% 11.36/11.54 tff(2529,plain,
% 11.36/11.54 (~node22(c_e_h_3, c_r, s2, s3)),
% 11.36/11.54 inference(unit_resolution,[status(thm)],[2528, 2465])).
% 11.36/11.54 tff(2530,plain,
% 11.36/11.54 (((~![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_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))),
% 11.36/11.54 inference(rewrite,[status(thm)],[])).
% 11.36/11.54 tff(2531,plain,
% 11.36/11.54 ((~![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_3, c_r, s2, s3) | node22(c_e_h_3, c_r, s2, s3))),
% 11.36/11.54 inference(quant_inst,[status(thm)],[])).
% 11.36/11.54 tff(2532,plain,
% 11.36/11.54 ((~![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_3, c_r, s2, s3) | node22(c_e_h_3, c_r, s2, s3)),
% 11.36/11.54 inference(modus_ponens,[status(thm)],[2531, 2530])).
% 11.36/11.54 tff(2533,plain,
% 11.36/11.54 (node21(c_e_h_3, c_r, s2, s3) | node22(c_e_h_3, c_r, s2, s3)),
% 11.36/11.54 inference(unit_resolution,[status(thm)],[2532, 247, 604])).
% 11.36/11.54 tff(2534,plain,
% 11.36/11.54 (node21(c_e_h_3, c_r, s2, s3)),
% 11.36/11.54 inference(unit_resolution,[status(thm)],[2533, 2529])).
% 11.36/11.54 tff(2535,plain,
% 11.36/11.54 (((~![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))),
% 11.36/11.54 inference(rewrite,[status(thm)],[])).
% 11.36/11.54 tff(2536,plain,
% 11.36/11.54 ((~![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))),
% 11.36/11.54 inference(quant_inst,[status(thm)],[])).
% 11.36/11.54 tff(2537,plain,
% 11.36/11.54 ((~![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)),
% 11.36/11.54 inference(modus_ponens,[status(thm)],[2536, 2535])).
% 11.39/11.54 tff(2538,plain,
% 11.39/11.54 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s2)),
% 11.39/11.54 inference(unit_resolution,[status(thm)],[2537, 2431, 2070])).
% 11.39/11.54 tff(2539,plain,
% 11.39/11.54 (((~![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))),
% 11.39/11.54 inference(rewrite,[status(thm)],[])).
% 11.39/11.54 tff(2540,plain,
% 11.39/11.54 ((~![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))),
% 11.39/11.54 inference(quant_inst,[status(thm)],[])).
% 11.39/11.54 tff(2541,plain,
% 11.39/11.54 ((~![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)),
% 11.39/11.54 inference(modus_ponens,[status(thm)],[2540, 2539])).
% 11.39/11.54 tff(2542,plain,
% 11.39/11.54 (~node20(c_e_h_3, c_r, s2)),
% 11.39/11.54 inference(unit_resolution,[status(thm)],[2541, 213, 2538])).
% 11.39/11.54 tff(2543,plain,
% 11.39/11.54 (((~![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_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)))),
% 11.39/11.54 inference(rewrite,[status(thm)],[])).
% 11.39/11.54 tff(2544,plain,
% 11.39/11.54 ((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)))),
% 11.39/11.54 inference(rewrite,[status(thm)],[])).
% 11.39/11.54 tff(2545,plain,
% 11.39/11.54 (((~![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_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))))),
% 11.39/11.54 inference(monotonicity,[status(thm)],[2544])).
% 11.39/11.54 tff(2546,plain,
% 11.39/11.54 (((~![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_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)))),
% 11.39/11.54 inference(transitivity,[status(thm)],[2545, 2543])).
% 11.39/11.54 tff(2547,plain,
% 11.39/11.54 ((~![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_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)))),
% 11.39/11.54 inference(quant_inst,[status(thm)],[])).
% 11.39/11.54 tff(2548,plain,
% 11.39/11.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | node20(c_e_h_3, c_r, s2) | (~node21(c_e_h_3, c_r, s2, s3))),
% 11.39/11.54 inference(modus_ponens,[status(thm)],[2547, 2546])).
% 11.39/11.54 tff(2549,plain,
% 11.39/11.54 ($false),
% 11.39/11.54 inference(unit_resolution,[status(thm)],[2548, 228, 2465, 2542, 2534])).
% 11.39/11.54 tff(2550,plain,(~m_and_h_gate_v_out(c_e_h_3, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.54 tff(2551,plain,
% 11.39/11.54 (((~![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_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))),
% 11.39/11.54 inference(rewrite,[status(thm)],[])).
% 11.39/11.54 tff(2552,plain,
% 11.39/11.54 ((~![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_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))),
% 11.39/11.54 inference(quant_inst,[status(thm)],[])).
% 11.39/11.54 tff(2553,plain,
% 11.39/11.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node22(c_e_h_3, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3)),
% 11.39/11.54 inference(modus_ponens,[status(thm)],[2552, 2551])).
% 11.39/11.54 tff(2554,plain,
% 11.39/11.54 ($false),
% 11.39/11.54 inference(unit_resolution,[status(thm)],[2553, 273, 2444, 2550, 2464])).
% 11.39/11.54 tff(2555,plain,(~m_and_h_gate_v_out(c_e_h_3, c_r, s4)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.54 tff(2556,plain,
% 11.39/11.54 (((~![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_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))),
% 11.39/11.54 inference(rewrite,[status(thm)],[])).
% 11.39/11.54 tff(2557,plain,
% 11.39/11.54 ((~![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_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))),
% 11.39/11.54 inference(quant_inst,[status(thm)],[])).
% 11.39/11.54 tff(2558,plain,
% 11.39/11.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | (~node22(c_e_h_3, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_r, s4)),
% 11.39/11.54 inference(modus_ponens,[status(thm)],[2557, 2556])).
% 11.39/11.54 tff(2559,plain,
% 11.39/11.54 ($false),
% 11.39/11.54 inference(unit_resolution,[status(thm)],[2558, 273, 2555, 2442, 2443])).
% 11.39/11.54 tff(2560,plain,((~node22(c_e_h_3, c_r, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5))), inference(lemma,lemma(discharge,[]))).
% 11.39/11.54 tff(2561,plain,
% 11.39/11.54 (~node22(c_e_h_3, c_r, s4, s5)),
% 11.39/11.54 inference(unit_resolution,[status(thm)],[2560, 2442])).
% 11.39/11.54 tff(2562,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_r, s4)), introduced(assumption)).
% 11.39/11.54 tff(2563,plain,
% 11.39/11.54 (((~![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))),
% 11.39/11.54 inference(rewrite,[status(thm)],[])).
% 11.39/11.54 tff(2564,plain,
% 11.39/11.54 ((~![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))),
% 11.39/11.54 inference(quant_inst,[status(thm)],[])).
% 11.39/11.54 tff(2565,plain,
% 11.39/11.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s4)),
% 11.39/11.54 inference(modus_ponens,[status(thm)],[2564, 2563])).
% 11.39/11.54 tff(2566,plain,
% 11.39/11.54 ($false),
% 11.39/11.54 inference(unit_resolution,[status(thm)],[2565, 2431, 2265, 2562])).
% 11.39/11.54 tff(2567,plain,(~m_and_h_gate_v_in1(c_e_h_3, c_r, s4)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.54 tff(2568,plain,
% 11.39/11.54 (((~![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))),
% 11.39/11.54 inference(rewrite,[status(thm)],[])).
% 11.39/11.54 tff(2569,plain,
% 11.39/11.54 ((~![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))),
% 11.39/11.54 inference(quant_inst,[status(thm)],[])).
% 11.39/11.54 tff(2570,plain,
% 11.39/11.54 ((~![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)),
% 11.39/11.54 inference(modus_ponens,[status(thm)],[2569, 2568])).
% 11.39/11.54 tff(2571,plain,
% 11.39/11.54 (~node20(c_e_h_3, c_r, s4)),
% 11.39/11.54 inference(unit_resolution,[status(thm)],[2570, 213, 2567])).
% 11.39/11.54 tff(2572,assumption,(node21(c_e_h_3, c_r, s4, s5)), introduced(assumption)).
% 11.39/11.54 tff(2573,assumption,(~node20(c_e_h_3, c_r, s4)), introduced(assumption)).
% 11.39/11.54 tff(2574,plain,
% 11.39/11.54 (((~![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_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)))) | 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)))),
% 11.39/11.54 inference(rewrite,[status(thm)],[])).
% 11.39/11.54 tff(2575,plain,
% 11.39/11.54 ((~![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_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)))),
% 11.39/11.54 inference(quant_inst,[status(thm)],[])).
% 11.39/11.54 tff(2576,plain,
% 11.39/11.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | (~node21(c_e_h_3, c_r, s4, s5))),
% 11.39/11.54 inference(modus_ponens,[status(thm)],[2575, 2574])).
% 11.39/11.54 tff(2577,plain,
% 11.39/11.54 ($false),
% 11.39/11.54 inference(unit_resolution,[status(thm)],[2576, 228, 2573, 2442, 2572])).
% 11.39/11.54 tff(2578,plain,((~node21(c_e_h_3, c_r, s4, s5)) | node20(c_e_h_3, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5))), inference(lemma,lemma(discharge,[]))).
% 11.39/11.54 tff(2579,plain,
% 11.39/11.54 (~node21(c_e_h_3, c_r, s4, s5)),
% 11.39/11.54 inference(unit_resolution,[status(thm)],[2578, 2442, 2571])).
% 11.39/11.54 tff(2580,plain,
% 11.39/11.54 (((~![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))),
% 11.39/11.54 inference(rewrite,[status(thm)],[])).
% 11.39/11.54 tff(2581,plain,
% 11.39/11.54 ((~![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))),
% 11.39/11.54 inference(quant_inst,[status(thm)],[])).
% 11.39/11.54 tff(2582,plain,
% 11.39/11.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_r, s4, s5) | node22(c_e_h_3, c_r, s4, s5)),
% 11.39/11.54 inference(modus_ponens,[status(thm)],[2581, 2580])).
% 11.39/11.54 tff(2583,plain,
% 11.39/11.54 (node21(c_e_h_3, c_r, s4, s5) | node22(c_e_h_3, c_r, s4, s5)),
% 11.39/11.54 inference(unit_resolution,[status(thm)],[2582, 247, 1542])).
% 11.39/11.54 tff(2584,plain,
% 11.39/11.54 ($false),
% 11.39/11.54 inference(unit_resolution,[status(thm)],[2583, 2579, 2561])).
% 11.39/11.54 tff(2585,plain,(~m_and_h_gate_v_out(c_e_h_3, c_r, s5)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.54 tff(2586,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_r, s5)), introduced(assumption)).
% 11.39/11.54 tff(2587,plain,
% 11.39/11.54 (((~![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))),
% 11.39/11.54 inference(rewrite,[status(thm)],[])).
% 11.39/11.54 tff(2588,plain,
% 11.39/11.54 ((~![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))),
% 11.39/11.54 inference(quant_inst,[status(thm)],[])).
% 11.39/11.54 tff(2589,plain,
% 11.39/11.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s5)),
% 11.39/11.54 inference(modus_ponens,[status(thm)],[2588, 2587])).
% 11.39/11.54 tff(2590,plain,
% 11.39/11.54 ($false),
% 11.39/11.54 inference(unit_resolution,[status(thm)],[2589, 2431, 2331, 2586])).
% 11.39/11.54 tff(2591,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,[]))).
% 11.39/11.54 tff(2592,plain,
% 11.39/11.54 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s5)),
% 11.39/11.54 inference(unit_resolution,[status(thm)],[2591, 2329])).
% 11.39/11.54 tff(2593,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_r, s5)), introduced(assumption)).
% 11.39/11.54 tff(2594,assumption,(node20(c_e_h_3, c_r, s5)), introduced(assumption)).
% 11.39/11.54 tff(2595,plain,
% 11.39/11.54 (((~![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))),
% 11.39/11.54 inference(rewrite,[status(thm)],[])).
% 11.39/11.54 tff(2596,plain,
% 11.39/11.54 ((~![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))),
% 11.39/11.54 inference(quant_inst,[status(thm)],[])).
% 11.39/11.54 tff(2597,plain,
% 11.39/11.54 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s5)),
% 11.39/11.54 inference(modus_ponens,[status(thm)],[2596, 2595])).
% 11.39/11.54 tff(2598,plain,
% 11.39/11.54 ($false),
% 11.39/11.54 inference(unit_resolution,[status(thm)],[2597, 213, 2594, 2593])).
% 11.39/11.54 tff(2599,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,[]))).
% 11.39/11.54 tff(2600,plain,
% 11.39/11.54 (~node20(c_e_h_3, c_r, s5)),
% 11.39/11.54 inference(unit_resolution,[status(thm)],[2599, 2592])).
% 11.39/11.54 tff(2601,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s5)), introduced(assumption)).
% 11.39/11.54 tff(2602,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s6)), introduced(assumption)).
% 11.39/11.54 tff(2603,plain,
% 11.39/11.54 (((~![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_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))),
% 11.39/11.54 inference(rewrite,[status(thm)],[])).
% 11.39/11.54 tff(2604,plain,
% 11.39/11.54 ((~![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_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))),
% 11.39/11.54 inference(quant_inst,[status(thm)],[])).
% 11.39/11.54 tff(2605,plain,
% 11.39/11.54 ((~![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_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)),
% 11.39/11.54 inference(modus_ponens,[status(thm)],[2604, 2603])).
% 11.39/11.54 tff(2606,plain,
% 11.39/11.54 ((~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)),
% 11.39/11.54 inference(unit_resolution,[status(thm)],[2605, 273])).
% 11.39/11.54 tff(2607,plain,
% 11.39/11.54 (~node22(c_e_h_3, c_r, s5, s6)),
% 11.39/11.54 inference(unit_resolution,[status(thm)],[2606, 2602, 2601])).
% 11.39/11.54 tff(2608,plain,
% 11.39/11.54 (((~![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))),
% 11.39/11.54 inference(rewrite,[status(thm)],[])).
% 11.39/11.54 tff(2609,plain,
% 11.39/11.54 ((~![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))),
% 11.39/11.54 inference(quant_inst,[status(thm)],[])).
% 11.39/11.54 tff(2610,plain,
% 11.39/11.54 ((~![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)),
% 11.39/11.54 inference(modus_ponens,[status(thm)],[2609, 2608])).
% 11.39/11.54 tff(2611,plain,
% 11.39/11.54 (node21(c_e_h_3, c_r, s5, s6)),
% 11.39/11.54 inference(unit_resolution,[status(thm)],[2610, 247, 2348, 2607])).
% 11.39/11.54 tff(2612,assumption,(~node20(c_e_h_3, c_r, s5)), introduced(assumption)).
% 11.39/11.54 tff(2613,plain,
% 11.39/11.54 (((~![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_3, c_r, s5) | (~node21(c_e_h_3, c_r, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, 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) | (~node21(c_e_h_3, c_r, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s6)))),
% 11.39/11.54 inference(rewrite,[status(thm)],[])).
% 11.39/11.54 tff(2614,plain,
% 11.39/11.54 ((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))) <=> (node20(c_e_h_3, c_r, s5) | (~node21(c_e_h_3, c_r, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s6)))),
% 11.39/11.54 inference(rewrite,[status(thm)],[])).
% 11.39/11.54 tff(2615,plain,
% 11.39/11.54 (((~![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_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) | (~node21(c_e_h_3, c_r, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s6))))),
% 11.39/11.54 inference(monotonicity,[status(thm)],[2614])).
% 11.39/11.54 tff(2616,plain,
% 11.39/11.54 (((~![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_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) | (~node21(c_e_h_3, c_r, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s6)))),
% 11.39/11.54 inference(transitivity,[status(thm)],[2615, 2613])).
% 11.39/11.54 tff(2617,plain,
% 11.39/11.54 ((~![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_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)))),
% 11.39/11.54 inference(quant_inst,[status(thm)],[])).
% 11.39/11.54 tff(2618,plain,
% 11.39/11.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s5) | (~node21(c_e_h_3, c_r, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s6))),
% 11.39/11.54 inference(modus_ponens,[status(thm)],[2617, 2616])).
% 11.39/11.54 tff(2619,plain,
% 11.39/11.54 ($false),
% 11.39/11.54 inference(unit_resolution,[status(thm)],[2618, 228, 2612, 2602, 2611])).
% 11.39/11.54 tff(2620,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | node20(c_e_h_3, c_r, s5) | m_and_h_gate_v_out(c_e_h_3, c_r, s5)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.54 tff(2621,plain,
% 11.39/11.54 ((~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)),
% 11.39/11.54 inference(unit_resolution,[status(thm)],[2620, 2600])).
% 11.39/11.54 tff(2622,plain,
% 11.39/11.54 (~m_and_h_gate_v_out(c_e_h_3, c_r, s6)),
% 11.39/11.54 inference(unit_resolution,[status(thm)],[2621, 2585])).
% 11.39/11.54 tff(2623,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s7)), introduced(assumption)).
% 11.39/11.54 tff(2624,assumption,(node22(c_e_h_3, c_r, s6, s7)), introduced(assumption)).
% 11.39/11.55 tff(2625,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s6)), introduced(assumption)).
% 11.39/11.55 tff(2626,plain,
% 11.39/11.55 (((~![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_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))),
% 11.39/11.55 inference(rewrite,[status(thm)],[])).
% 11.39/11.55 tff(2627,plain,
% 11.39/11.55 ((~![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_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))),
% 11.39/11.55 inference(quant_inst,[status(thm)],[])).
% 11.39/11.55 tff(2628,plain,
% 11.39/11.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | (~node22(c_e_h_3, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_r, s6)),
% 11.39/11.55 inference(modus_ponens,[status(thm)],[2627, 2626])).
% 11.39/11.55 tff(2629,plain,
% 11.39/11.55 ($false),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2628, 273, 2625, 2624, 2623])).
% 11.39/11.55 tff(2630,plain,((~node22(c_e_h_3, c_r, s6, s7)) | 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, s7))), inference(lemma,lemma(discharge,[]))).
% 11.39/11.55 tff(2631,plain,
% 11.39/11.55 (~node22(c_e_h_3, c_r, s6, s7)),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2630, 2623, 2622])).
% 11.39/11.55 tff(2632,assumption,(~node20(c_e_h_3, c_r, s6)), introduced(assumption)).
% 11.39/11.55 tff(2633,assumption,(node21(c_e_h_3, c_r, s6, s7)), introduced(assumption)).
% 11.39/11.55 tff(2634,plain,
% 11.39/11.55 (((~![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)))) | ((~node21(c_e_h_3, c_r, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | node20(c_e_h_3, c_r, 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)))) | (~node21(c_e_h_3, c_r, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | node20(c_e_h_3, c_r, s6))),
% 11.39/11.55 inference(rewrite,[status(thm)],[])).
% 11.39/11.55 tff(2635,plain,
% 11.39/11.55 ((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))) <=> ((~node21(c_e_h_3, c_r, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | node20(c_e_h_3, c_r, s6))),
% 11.39/11.55 inference(rewrite,[status(thm)],[])).
% 11.39/11.55 tff(2636,plain,
% 11.39/11.55 (((~![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_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)))) | ((~node21(c_e_h_3, c_r, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | node20(c_e_h_3, c_r, s6)))),
% 11.39/11.55 inference(monotonicity,[status(thm)],[2635])).
% 11.39/11.55 tff(2637,plain,
% 11.39/11.55 (((~![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_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)))) | (~node21(c_e_h_3, c_r, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | node20(c_e_h_3, c_r, s6))),
% 11.39/11.55 inference(transitivity,[status(thm)],[2636, 2634])).
% 11.39/11.55 tff(2638,plain,
% 11.39/11.55 ((~![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_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)))),
% 11.39/11.55 inference(quant_inst,[status(thm)],[])).
% 11.39/11.55 tff(2639,plain,
% 11.39/11.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_3, c_r, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | node20(c_e_h_3, c_r, s6)),
% 11.39/11.55 inference(modus_ponens,[status(thm)],[2638, 2637])).
% 11.39/11.55 tff(2640,plain,
% 11.39/11.55 ($false),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2639, 228, 2633, 2632, 2623])).
% 11.39/11.55 tff(2641,plain,((~node21(c_e_h_3, c_r, s6, s7)) | node20(c_e_h_3, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7))), inference(lemma,lemma(discharge,[]))).
% 11.39/11.55 tff(2642,plain,
% 11.39/11.55 (~node21(c_e_h_3, c_r, s6, s7)),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2641, 2623, 2632])).
% 11.39/11.55 tff(2643,plain,
% 11.39/11.55 (succ(s6, s7) <=> succ(s6, s7)),
% 11.39/11.55 inference(rewrite,[status(thm)],[])).
% 11.39/11.55 tff(2644,axiom,(succ(s6, s7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound7')).
% 11.39/11.55 tff(2645,plain,
% 11.39/11.55 (succ(s6, s7)),
% 11.39/11.55 inference(modus_ponens,[status(thm)],[2644, 2643])).
% 11.39/11.55 tff(2646,plain,
% 11.39/11.55 (((~![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))),
% 11.39/11.55 inference(rewrite,[status(thm)],[])).
% 11.39/11.55 tff(2647,plain,
% 11.39/11.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s6, s7)) | trans(s6, s7))),
% 11.39/11.55 inference(quant_inst,[status(thm)],[])).
% 11.39/11.55 tff(2648,plain,
% 11.39/11.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s6, s7)) | trans(s6, s7)),
% 11.39/11.55 inference(modus_ponens,[status(thm)],[2647, 2646])).
% 11.39/11.55 tff(2649,plain,
% 11.39/11.55 (trans(s6, s7)),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2648, 2645, 93])).
% 11.39/11.55 tff(2650,plain,
% 11.39/11.55 (((~![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))),
% 11.39/11.55 inference(rewrite,[status(thm)],[])).
% 11.39/11.55 tff(2651,plain,
% 11.39/11.55 ((~![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))),
% 11.39/11.55 inference(quant_inst,[status(thm)],[])).
% 11.39/11.55 tff(2652,plain,
% 11.39/11.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_3, c_r, s6, s7) | node22(c_e_h_3, c_r, s6, s7)),
% 11.39/11.55 inference(modus_ponens,[status(thm)],[2651, 2650])).
% 11.39/11.55 tff(2653,plain,
% 11.39/11.55 (node21(c_e_h_3, c_r, s6, s7) | node22(c_e_h_3, c_r, s6, s7)),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2652, 247, 2649])).
% 11.39/11.55 tff(2654,plain,
% 11.39/11.55 ($false),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2653, 2642, 2631])).
% 11.39/11.55 tff(2655,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | node20(c_e_h_3, c_r, s6)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.55 tff(2656,plain,
% 11.39/11.55 (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2655, 2441])).
% 11.39/11.55 tff(2657,assumption,(~node20(c_e_h_3, c_r, s7)), introduced(assumption)).
% 11.39/11.55 tff(2658,plain,
% 11.39/11.55 (((~![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_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)))),
% 11.39/11.55 inference(rewrite,[status(thm)],[])).
% 11.39/11.55 tff(2659,plain,
% 11.39/11.55 ((~![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_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)))),
% 11.39/11.55 inference(quant_inst,[status(thm)],[])).
% 11.39/11.55 tff(2660,plain,
% 11.39/11.55 ((~![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_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))),
% 11.39/11.55 inference(modus_ponens,[status(thm)],[2659, 2658])).
% 11.39/11.55 tff(2661,plain,
% 11.39/11.55 (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))),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2660, 228])).
% 11.39/11.55 tff(2662,plain,
% 11.39/11.55 (~node21(c_e_h_3, c_r, s7, s8)),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2661, 2422, 2657])).
% 11.39/11.55 tff(2663,plain,
% 11.39/11.55 (succ(s7, s8) <=> succ(s7, s8)),
% 11.39/11.55 inference(rewrite,[status(thm)],[])).
% 11.39/11.55 tff(2664,axiom,(succ(s7, s8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound8')).
% 11.39/11.55 tff(2665,plain,
% 11.39/11.55 (succ(s7, s8)),
% 11.39/11.55 inference(modus_ponens,[status(thm)],[2664, 2663])).
% 11.39/11.55 tff(2666,plain,
% 11.39/11.55 (((~![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))),
% 11.39/11.55 inference(rewrite,[status(thm)],[])).
% 11.39/11.55 tff(2667,plain,
% 11.39/11.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s7, s8)) | trans(s7, s8))),
% 11.39/11.55 inference(quant_inst,[status(thm)],[])).
% 11.39/11.55 tff(2668,plain,
% 11.39/11.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s7, s8)) | trans(s7, s8)),
% 11.39/11.55 inference(modus_ponens,[status(thm)],[2667, 2666])).
% 11.39/11.55 tff(2669,plain,
% 11.39/11.55 (trans(s7, s8)),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2668, 2665, 93])).
% 11.39/11.55 tff(2670,plain,
% 11.39/11.55 (((~![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_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))),
% 11.39/11.55 inference(rewrite,[status(thm)],[])).
% 11.39/11.55 tff(2671,plain,
% 11.39/11.55 ((~![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_3, c_r, s7, s8) | node22(c_e_h_3, c_r, s7, s8))),
% 11.39/11.55 inference(quant_inst,[status(thm)],[])).
% 11.39/11.55 tff(2672,plain,
% 11.39/11.55 ((~![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_3, c_r, s7, s8) | node22(c_e_h_3, c_r, s7, s8)),
% 11.39/11.55 inference(modus_ponens,[status(thm)],[2671, 2670])).
% 11.39/11.55 tff(2673,plain,
% 11.39/11.55 (node22(c_e_h_3, c_r, s7, s8)),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2672, 247, 2669, 2662])).
% 11.39/11.55 tff(2674,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s7)), introduced(assumption)).
% 11.39/11.55 tff(2675,plain,
% 11.39/11.55 (((~![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_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))),
% 11.39/11.55 inference(rewrite,[status(thm)],[])).
% 11.39/11.55 tff(2676,plain,
% 11.39/11.55 ((~![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_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))),
% 11.39/11.55 inference(quant_inst,[status(thm)],[])).
% 11.39/11.55 tff(2677,plain,
% 11.39/11.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | (~node22(c_e_h_3, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_r, s7)),
% 11.39/11.55 inference(modus_ponens,[status(thm)],[2676, 2675])).
% 11.39/11.55 tff(2678,plain,
% 11.39/11.55 ($false),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2677, 273, 2422, 2674, 2673])).
% 11.39/11.55 tff(2679,plain,((~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) | node20(c_e_h_3, c_r, s7)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.55 tff(2680,plain,
% 11.39/11.55 (node20(c_e_h_3, c_r, s7)),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2679, 2656, 2422])).
% 11.39/11.55 tff(2681,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_r, s7)), introduced(assumption)).
% 11.39/11.55 tff(2682,assumption,(node20(c_e_h_3, c_r, s7)), introduced(assumption)).
% 11.39/11.55 tff(2683,plain,
% 11.39/11.55 (((~![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))),
% 11.39/11.55 inference(rewrite,[status(thm)],[])).
% 11.39/11.55 tff(2684,plain,
% 11.39/11.55 ((~![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))),
% 11.39/11.55 inference(quant_inst,[status(thm)],[])).
% 11.39/11.55 tff(2685,plain,
% 11.39/11.55 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s7)),
% 11.39/11.55 inference(modus_ponens,[status(thm)],[2684, 2683])).
% 11.39/11.55 tff(2686,plain,
% 11.39/11.55 ($false),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2685, 213, 2682, 2681])).
% 11.39/11.55 tff(2687,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,[]))).
% 11.39/11.55 tff(2688,plain,
% 11.39/11.55 (m_and_h_gate_v_in1(c_e_h_3, c_r, s7)),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2687, 2680])).
% 11.39/11.55 tff(2689,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_r, s7)), introduced(assumption)).
% 11.39/11.55 tff(2690,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s7)), introduced(assumption)).
% 11.39/11.55 tff(2691,plain,
% 11.39/11.55 (((~![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))),
% 11.39/11.55 inference(rewrite,[status(thm)],[])).
% 11.39/11.55 tff(2692,plain,
% 11.39/11.55 ((~![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))),
% 11.39/11.55 inference(quant_inst,[status(thm)],[])).
% 11.39/11.55 tff(2693,plain,
% 11.39/11.55 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s7)),
% 11.39/11.55 inference(modus_ponens,[status(thm)],[2692, 2691])).
% 11.39/11.55 tff(2694,plain,
% 11.39/11.55 ($false),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2693, 2431, 2690, 2689])).
% 11.39/11.55 tff(2695,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,[]))).
% 11.39/11.55 tff(2696,plain,
% 11.39/11.55 (m_c_h_element_v_out(c_e_h_3, c_e, s7)),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2695, 2688])).
% 11.39/11.55 tff(2697,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s7)), introduced(assumption)).
% 11.39/11.55 tff(2698,assumption,(node18(c_e_h_3, c_e, s6, s7)), introduced(assumption)).
% 11.39/11.55 tff(2699,plain,
% 11.39/11.55 (((~![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_3, c_e, s6) | (~node18(c_e_h_3, c_e, s6, s7)) | (~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)) | 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) | (~node18(c_e_h_3, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)))),
% 11.39/11.55 inference(rewrite,[status(thm)],[])).
% 11.39/11.55 tff(2700,plain,
% 11.39/11.55 (((~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))) <=> (m_c_h_element_v_out(c_e_h_3, c_e, s6) | (~node18(c_e_h_3, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)))),
% 11.39/11.55 inference(rewrite,[status(thm)],[])).
% 11.39/11.55 tff(2701,plain,
% 11.39/11.55 (((~![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_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)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s6) | (~node18(c_e_h_3, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7))))),
% 11.39/11.55 inference(monotonicity,[status(thm)],[2700])).
% 11.39/11.55 tff(2702,plain,
% 11.39/11.55 (((~![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_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)))) | m_c_h_element_v_out(c_e_h_3, c_e, s6) | (~node18(c_e_h_3, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)))),
% 11.39/11.55 inference(transitivity,[status(thm)],[2701, 2699])).
% 11.39/11.55 tff(2703,plain,
% 11.39/11.55 ((~![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_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)))),
% 11.39/11.55 inference(quant_inst,[status(thm)],[])).
% 11.39/11.55 tff(2704,plain,
% 11.39/11.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s6) | (~node18(c_e_h_3, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7))),
% 11.39/11.55 inference(modus_ponens,[status(thm)],[2703, 2702])).
% 11.39/11.55 tff(2705,plain,
% 11.39/11.55 ($false),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2704, 296, 2424, 2697, 2698])).
% 11.39/11.55 tff(2706,plain,((~node18(c_e_h_3, c_e, s6, s7)) | 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, s7))), inference(lemma,lemma(discharge,[]))).
% 11.39/11.55 tff(2707,plain,
% 11.39/11.55 (~node18(c_e_h_3, c_e, s6, s7)),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2706, 2424, 2697])).
% 11.39/11.55 tff(2708,plain,
% 11.39/11.55 (((~![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))),
% 11.39/11.55 inference(rewrite,[status(thm)],[])).
% 11.39/11.55 tff(2709,plain,
% 11.39/11.55 ((~![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))),
% 11.39/11.55 inference(quant_inst,[status(thm)],[])).
% 11.39/11.55 tff(2710,plain,
% 11.39/11.55 ((~![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)),
% 11.39/11.55 inference(modus_ponens,[status(thm)],[2709, 2708])).
% 11.39/11.55 tff(2711,plain,
% 11.39/11.55 (node19(c_e_h_3, c_e, s6, s7)),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2710, 312, 2649])).
% 11.39/11.55 tff(2712,plain,
% 11.39/11.55 (((~![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_3, c_e, s6) | (~node19(c_e_h_3, c_e, s6, s7)) | 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)))) | node17(c_e_h_3, c_e, s6) | (~node19(c_e_h_3, c_e, s6, s7)) | node18(c_e_h_3, c_e, s6, s7))),
% 11.39/11.55 inference(rewrite,[status(thm)],[])).
% 11.39/11.55 tff(2713,plain,
% 11.39/11.55 ((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))) <=> (node17(c_e_h_3, c_e, s6) | (~node19(c_e_h_3, c_e, s6, s7)) | node18(c_e_h_3, c_e, s6, s7))),
% 11.39/11.55 inference(rewrite,[status(thm)],[])).
% 11.39/11.55 tff(2714,plain,
% 11.39/11.55 (((~![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_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)))) | (node17(c_e_h_3, c_e, s6) | (~node19(c_e_h_3, c_e, s6, s7)) | node18(c_e_h_3, c_e, s6, s7)))),
% 11.39/11.55 inference(monotonicity,[status(thm)],[2713])).
% 11.39/11.55 tff(2715,plain,
% 11.39/11.55 (((~![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_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)))) | node17(c_e_h_3, c_e, s6) | (~node19(c_e_h_3, c_e, s6, s7)) | node18(c_e_h_3, c_e, s6, s7))),
% 11.39/11.55 inference(transitivity,[status(thm)],[2714, 2712])).
% 11.39/11.55 tff(2716,plain,
% 11.39/11.55 ((~![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_3, c_e, s6) | node18(c_e_h_3, c_e, s6, s7) | (~node19(c_e_h_3, c_e, s6, s7)))),
% 11.39/11.55 inference(quant_inst,[status(thm)],[])).
% 11.39/11.55 tff(2717,plain,
% 11.39/11.55 ((~![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_3, c_e, s6) | (~node19(c_e_h_3, c_e, s6, s7)) | node18(c_e_h_3, c_e, s6, s7)),
% 11.39/11.55 inference(modus_ponens,[status(thm)],[2716, 2715])).
% 11.39/11.55 tff(2718,plain,
% 11.39/11.55 (node17(c_e_h_3, c_e, s6) | node18(c_e_h_3, c_e, s6, s7)),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2717, 326, 2711])).
% 11.39/11.55 tff(2719,plain,
% 11.39/11.55 (node17(c_e_h_3, c_e, s6)),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2718, 2707])).
% 11.39/11.55 tff(2720,assumption,(node15(c_e_h_3, c_e, s6, s7)), introduced(assumption)).
% 11.39/11.55 tff(2721,plain,
% 11.39/11.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 11.39/11.55 inference(rewrite,[status(thm)],[])).
% 11.39/11.55 tff(2722,plain,
% 11.39/11.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 11.39/11.55 inference(quant_inst,[status(thm)],[])).
% 11.39/11.55 tff(2723,plain,
% 11.39/11.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | (~node15(c_e_h_3, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6)),
% 11.39/11.55 inference(modus_ponens,[status(thm)],[2722, 2721])).
% 11.39/11.55 tff(2724,plain,
% 11.39/11.55 ($false),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2723, 393, 2424, 2697, 2720])).
% 11.39/11.55 tff(2725,plain,((~node15(c_e_h_3, c_e, s6, s7)) | 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, s7))), inference(lemma,lemma(discharge,[]))).
% 11.39/11.55 tff(2726,plain,
% 11.39/11.55 (~node15(c_e_h_3, c_e, s6, s7)),
% 11.39/11.55 inference(unit_resolution,[status(thm)],[2725, 2424, 2697])).
% 11.39/11.55 tff(2727,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s6)), introduced(assumption)).
% 11.39/11.55 tff(2728,assumption,(node17(c_e_h_3, c_e, s6)), introduced(assumption)).
% 11.39/11.55 tff(2729,plain,
% 11.39/11.55 (((~![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_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_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)))),
% 11.39/11.55 inference(rewrite,[status(thm)],[])).
% 11.39/11.55 tff(2730,plain,
% 11.39/11.55 ((~![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_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)))),
% 11.39/11.55 inference(quant_inst,[status(thm)],[])).
% 11.39/11.55 tff(2731,plain,
% 11.39/11.55 ((~![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_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))),
% 11.39/11.56 inference(modus_ponens,[status(thm)],[2730, 2729])).
% 11.39/11.56 tff(2732,plain,
% 11.39/11.56 (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))),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2731, 2125, 2728])).
% 11.39/11.56 tff(2733,plain,
% 11.39/11.56 (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2732, 2727])).
% 11.39/11.56 tff(2734,assumption,(~node15(c_e_h_3, c_e, s6, s7)), introduced(assumption)).
% 11.39/11.56 tff(2735,assumption,(node14(c_e_h_3, c_e, s6, s7)), introduced(assumption)).
% 11.39/11.56 tff(2736,plain,
% 11.39/11.56 (((~![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_3, c_e, s6) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | (~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_in1(c_e_h_3, c_e, s6) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | (~node14(c_e_h_3, c_e, s6, s7)))),
% 11.39/11.56 inference(rewrite,[status(thm)],[])).
% 11.39/11.56 tff(2737,plain,
% 11.39/11.56 (((~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_in1(c_e_h_3, c_e, s6) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | (~node14(c_e_h_3, c_e, s6, s7)))),
% 11.39/11.56 inference(rewrite,[status(thm)],[])).
% 11.39/11.56 tff(2738,plain,
% 11.39/11.56 (((~![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_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_in1(c_e_h_3, c_e, s6) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | (~node14(c_e_h_3, c_e, s6, s7))))),
% 11.39/11.56 inference(monotonicity,[status(thm)],[2737])).
% 11.39/11.56 tff(2739,plain,
% 11.39/11.56 (((~![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_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_in1(c_e_h_3, c_e, s6) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | (~node14(c_e_h_3, c_e, s6, s7)))),
% 11.39/11.56 inference(transitivity,[status(thm)],[2738, 2736])).
% 11.39/11.56 tff(2740,plain,
% 11.39/11.56 ((~![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_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)))),
% 11.39/11.56 inference(quant_inst,[status(thm)],[])).
% 11.39/11.56 tff(2741,plain,
% 11.39/11.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | (~node14(c_e_h_3, c_e, s6, s7))),
% 11.39/11.56 inference(modus_ponens,[status(thm)],[2740, 2739])).
% 11.39/11.56 tff(2742,plain,
% 11.39/11.56 ($false),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2741, 427, 2697, 2735, 2727])).
% 11.39/11.56 tff(2743,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,[]))).
% 11.39/11.56 tff(2744,plain,
% 11.39/11.56 (~node14(c_e_h_3, c_e, s6, s7)),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2743, 2727, 2697])).
% 11.39/11.56 tff(2745,plain,
% 11.39/11.56 (((~![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_3, c_e, s6) | (~node19(c_e_h_3, c_e, s6, s7)) | node14(c_e_h_3, c_e, s6, s7) | node15(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)))) | node16(c_e_h_3, c_e, s6) | (~node19(c_e_h_3, c_e, s6, s7)) | node14(c_e_h_3, c_e, s6, s7) | node15(c_e_h_3, c_e, s6, s7))),
% 11.39/11.56 inference(rewrite,[status(thm)],[])).
% 11.39/11.56 tff(2746,plain,
% 11.39/11.56 ((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))) <=> (node16(c_e_h_3, c_e, s6) | (~node19(c_e_h_3, c_e, s6, s7)) | node14(c_e_h_3, c_e, s6, s7) | node15(c_e_h_3, c_e, s6, s7))),
% 11.39/11.56 inference(rewrite,[status(thm)],[])).
% 11.39/11.56 tff(2747,plain,
% 11.39/11.56 (((~![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_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)))) | (node16(c_e_h_3, c_e, s6) | (~node19(c_e_h_3, c_e, s6, s7)) | node14(c_e_h_3, c_e, s6, s7) | node15(c_e_h_3, c_e, s6, s7)))),
% 11.39/11.56 inference(monotonicity,[status(thm)],[2746])).
% 11.39/11.56 tff(2748,plain,
% 11.39/11.56 (((~![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_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)))) | node16(c_e_h_3, c_e, s6) | (~node19(c_e_h_3, c_e, s6, s7)) | node14(c_e_h_3, c_e, s6, s7) | node15(c_e_h_3, c_e, s6, s7))),
% 11.39/11.56 inference(transitivity,[status(thm)],[2747, 2745])).
% 11.39/11.56 tff(2749,plain,
% 11.39/11.56 ((~![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_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)))),
% 11.39/11.56 inference(quant_inst,[status(thm)],[])).
% 11.39/11.56 tff(2750,plain,
% 11.39/11.56 ((~![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_3, c_e, s6) | (~node19(c_e_h_3, c_e, s6, s7)) | node14(c_e_h_3, c_e, s6, s7) | node15(c_e_h_3, c_e, s6, s7)),
% 11.39/11.56 inference(modus_ponens,[status(thm)],[2749, 2748])).
% 11.39/11.56 tff(2751,plain,
% 11.39/11.56 (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)),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2750, 409, 2711])).
% 11.39/11.56 tff(2752,plain,
% 11.39/11.56 (node16(c_e_h_3, c_e, s6)),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2751, 2744, 2734])).
% 11.39/11.56 tff(2753,plain,
% 11.39/11.56 (((~![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_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))),
% 11.39/11.56 inference(rewrite,[status(thm)],[])).
% 11.39/11.56 tff(2754,plain,
% 11.39/11.56 ((~![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_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))),
% 11.39/11.56 inference(quant_inst,[status(thm)],[])).
% 11.39/11.56 tff(2755,plain,
% 11.39/11.56 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | m_c_h_element_v_in2(c_e_h_3, c_e, s6)),
% 11.39/11.56 inference(modus_ponens,[status(thm)],[2754, 2753])).
% 11.39/11.56 tff(2756,plain,
% 11.39/11.56 ($false),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2755, 377, 2752, 2727, 2733])).
% 11.39/11.56 tff(2757,plain,(m_c_h_element_v_in1(c_e_h_3, c_e, s6) | node15(c_e_h_3, c_e, s6, s7) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | (~node17(c_e_h_3, c_e, s6))), inference(lemma,lemma(discharge,[]))).
% 11.39/11.56 tff(2758,plain,
% 11.39/11.56 (m_c_h_element_v_in1(c_e_h_3, c_e, s6)),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2757, 2719, 2697, 2726])).
% 11.39/11.56 tff(2759,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_e, s6)), introduced(assumption)).
% 11.39/11.56 tff(2760,plain,
% 11.39/11.56 (((~![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_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_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)))),
% 11.39/11.56 inference(rewrite,[status(thm)],[])).
% 11.39/11.56 tff(2761,plain,
% 11.39/11.56 ((~![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_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)))),
% 11.39/11.56 inference(quant_inst,[status(thm)],[])).
% 11.39/11.56 tff(2762,plain,
% 11.39/11.56 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | m_c_h_element_v_in2(c_e_h_3, c_e, s6) | (~node17(c_e_h_3, c_e, s6))),
% 11.39/11.56 inference(modus_ponens,[status(thm)],[2761, 2760])).
% 11.39/11.56 tff(2763,plain,
% 11.39/11.56 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6))),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2762, 359, 2759])).
% 11.39/11.56 tff(2764,plain,
% 11.39/11.56 ($false),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2763, 2758, 2719])).
% 11.39/11.56 tff(2765,plain,(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, s6) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7))), inference(lemma,lemma(discharge,[]))).
% 11.39/11.56 tff(2766,plain,
% 11.39/11.56 (m_c_h_element_v_in2(c_e_h_3, c_e, s6)),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2765, 2696, 2421])).
% 11.39/11.56 tff(2767,assumption,(m_c_h_element_v_in2(c_e_h_3, c_e, s6)), introduced(assumption)).
% 11.39/11.56 tff(2768,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s6)), introduced(assumption)).
% 11.39/11.56 tff(2769,plain,
% 11.39/11.56 (((~![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))),
% 11.39/11.56 inference(rewrite,[status(thm)],[])).
% 11.39/11.56 tff(2770,plain,
% 11.39/11.56 ((~![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))),
% 11.39/11.56 inference(quant_inst,[status(thm)],[])).
% 11.39/11.56 tff(2771,plain,
% 11.39/11.56 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6)),
% 11.39/11.56 inference(modus_ponens,[status(thm)],[2770, 2769])).
% 11.39/11.56 tff(2772,plain,
% 11.39/11.56 ($false),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2771, 1965, 2768, 2767])).
% 11.39/11.56 tff(2773,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.56 tff(2774,plain,
% 11.39/11.56 (m_and_h_gate_v_out(c_e_h_3, c_i, s6)),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2773, 2766])).
% 11.39/11.56 tff(2775,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s5)), introduced(assumption)).
% 11.39/11.56 tff(2776,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s6)), introduced(assumption)).
% 11.39/11.56 tff(2777,plain,
% 11.39/11.56 (((~![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_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))),
% 11.39/11.56 inference(rewrite,[status(thm)],[])).
% 11.39/11.56 tff(2778,plain,
% 11.39/11.56 ((~![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_i, s6)) | (~node22(c_e_h_3, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5))),
% 11.39/11.56 inference(quant_inst,[status(thm)],[])).
% 11.39/11.56 tff(2779,plain,
% 11.39/11.56 ((~![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_i, s6)) | (~node22(c_e_h_3, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5)),
% 11.39/11.56 inference(modus_ponens,[status(thm)],[2778, 2777])).
% 11.39/11.56 tff(2780,plain,
% 11.39/11.56 ((~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)),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2779, 273])).
% 11.39/11.56 tff(2781,plain,
% 11.39/11.56 (~node22(c_e_h_3, c_i, s5, s6)),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2780, 2776, 2775])).
% 11.39/11.56 tff(2782,assumption,(~node20(c_e_h_3, c_i, s5)), introduced(assumption)).
% 11.39/11.56 tff(2783,plain,
% 11.39/11.56 (((~![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)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | node20(c_e_h_3, c_i, s5) | (~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)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | node20(c_e_h_3, c_i, s5) | (~node21(c_e_h_3, c_i, s5, s6)))),
% 11.39/11.56 inference(rewrite,[status(thm)],[])).
% 11.39/11.56 tff(2784,plain,
% 11.39/11.56 ((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))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | node20(c_e_h_3, c_i, s5) | (~node21(c_e_h_3, c_i, s5, s6)))),
% 11.39/11.56 inference(rewrite,[status(thm)],[])).
% 11.39/11.56 tff(2785,plain,
% 11.39/11.56 (((~![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_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)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | node20(c_e_h_3, c_i, s5) | (~node21(c_e_h_3, c_i, s5, s6))))),
% 11.39/11.56 inference(monotonicity,[status(thm)],[2784])).
% 11.39/11.56 tff(2786,plain,
% 11.39/11.56 (((~![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_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)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | node20(c_e_h_3, c_i, s5) | (~node21(c_e_h_3, c_i, s5, s6)))),
% 11.39/11.56 inference(transitivity,[status(thm)],[2785, 2783])).
% 11.39/11.56 tff(2787,plain,
% 11.39/11.56 ((~![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_i, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | (~node21(c_e_h_3, c_i, s5, s6)))),
% 11.39/11.56 inference(quant_inst,[status(thm)],[])).
% 11.39/11.56 tff(2788,plain,
% 11.39/11.56 ((~![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)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | node20(c_e_h_3, c_i, s5) | (~node21(c_e_h_3, c_i, s5, s6))),
% 11.39/11.56 inference(modus_ponens,[status(thm)],[2787, 2786])).
% 11.39/11.56 tff(2789,plain,
% 11.39/11.56 ((~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | node20(c_e_h_3, c_i, s5) | (~node21(c_e_h_3, c_i, s5, s6))),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2788, 228])).
% 11.39/11.56 tff(2790,plain,
% 11.39/11.56 (~node21(c_e_h_3, c_i, s5, s6)),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2789, 2776, 2782])).
% 11.39/11.56 tff(2791,plain,
% 11.39/11.56 (((~![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))),
% 11.39/11.56 inference(rewrite,[status(thm)],[])).
% 11.39/11.56 tff(2792,plain,
% 11.39/11.56 ((~![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))),
% 11.39/11.56 inference(quant_inst,[status(thm)],[])).
% 11.39/11.56 tff(2793,plain,
% 11.39/11.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_i, s5, s6) | node22(c_e_h_3, c_i, s5, s6)),
% 11.39/11.56 inference(modus_ponens,[status(thm)],[2792, 2791])).
% 11.39/11.56 tff(2794,plain,
% 11.39/11.56 ($false),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2793, 247, 2348, 2790, 2781])).
% 11.39/11.56 tff(2795,plain,((~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | node20(c_e_h_3, c_i, s5) | m_and_h_gate_v_out(c_e_h_3, c_i, s5)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.56 tff(2796,plain,
% 11.39/11.56 (node20(c_e_h_3, c_i, s5)),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2795, 2774, 1958])).
% 11.39/11.56 tff(2797,plain,
% 11.39/11.56 (((~![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_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))),
% 11.39/11.56 inference(rewrite,[status(thm)],[])).
% 11.39/11.56 tff(2798,plain,
% 11.39/11.56 ((~![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_i, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s5))),
% 11.39/11.56 inference(quant_inst,[status(thm)],[])).
% 11.39/11.56 tff(2799,plain,
% 11.39/11.56 ((~![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_i, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s5)),
% 11.39/11.56 inference(modus_ponens,[status(thm)],[2798, 2797])).
% 11.39/11.56 tff(2800,plain,
% 11.39/11.56 (m_and_h_gate_v_in1(c_e_h_3, c_i, s5)),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2799, 213, 2796])).
% 11.39/11.56 tff(2801,plain,
% 11.39/11.56 (((~![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))),
% 11.39/11.56 inference(rewrite,[status(thm)],[])).
% 11.39/11.56 tff(2802,plain,
% 11.39/11.56 ((~![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))),
% 11.39/11.56 inference(quant_inst,[status(thm)],[])).
% 11.39/11.56 tff(2803,plain,
% 11.39/11.56 ((~![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)),
% 11.39/11.56 inference(modus_ponens,[status(thm)],[2802, 2801])).
% 11.39/11.56 tff(2804,plain,
% 11.39/11.56 (m_c_h_element_v_out(c_e_h_3, c_h, s5)),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2803, 503, 2800])).
% 11.39/11.56 tff(2805,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_h, s4)), introduced(assumption)).
% 11.39/11.56 tff(2806,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s5)), introduced(assumption)).
% 11.39/11.56 tff(2807,plain,
% 11.39/11.56 (((~![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_out(c_e_h_3, c_h, s5)) | (~node14(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_in1(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, s5)) | (~node14(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4))),
% 11.39/11.56 inference(rewrite,[status(thm)],[])).
% 11.39/11.56 tff(2808,plain,
% 11.39/11.56 (((~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)) | (~node14(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4))),
% 11.39/11.56 inference(rewrite,[status(thm)],[])).
% 11.39/11.56 tff(2809,plain,
% 11.39/11.56 (((~![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_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)) | (~node14(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4)))),
% 11.39/11.56 inference(monotonicity,[status(thm)],[2808])).
% 11.39/11.56 tff(2810,plain,
% 11.39/11.56 (((~![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_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)) | (~node14(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4))),
% 11.39/11.56 inference(transitivity,[status(thm)],[2809, 2807])).
% 11.39/11.56 tff(2811,plain,
% 11.39/11.56 ((~![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_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)))),
% 11.39/11.56 inference(quant_inst,[status(thm)],[])).
% 11.39/11.56 tff(2812,plain,
% 11.39/11.56 ((~![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_out(c_e_h_3, c_h, s5)) | (~node14(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4)),
% 11.39/11.56 inference(modus_ponens,[status(thm)],[2811, 2810])).
% 11.39/11.56 tff(2813,plain,
% 11.39/11.56 ((~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | (~node14(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4)),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2812, 427])).
% 11.39/11.56 tff(2814,plain,
% 11.39/11.56 (~node14(c_e_h_3, c_h, s4, s5)),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2813, 2806, 2805])).
% 11.39/11.56 tff(2815,assumption,(node18(c_e_h_3, c_h, s4, s5)), introduced(assumption)).
% 11.39/11.56 tff(2816,plain,
% 11.39/11.56 (((~![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)))) | ((~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)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $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_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)))),
% 11.39/11.56 inference(rewrite,[status(thm)],[])).
% 11.39/11.56 tff(2817,plain,
% 11.39/11.56 (((~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))) <=> ((~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)))),
% 11.39/11.56 inference(rewrite,[status(thm)],[])).
% 11.39/11.56 tff(2818,plain,
% 11.39/11.56 (((~![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_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)))) | ((~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))))),
% 11.39/11.56 inference(monotonicity,[status(thm)],[2817])).
% 11.39/11.56 tff(2819,plain,
% 11.39/11.56 (((~![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_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)))) | (~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)))),
% 11.39/11.56 inference(transitivity,[status(thm)],[2818, 2816])).
% 11.39/11.56 tff(2820,plain,
% 11.39/11.56 ((~![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_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)))),
% 11.39/11.56 inference(quant_inst,[status(thm)],[])).
% 11.39/11.56 tff(2821,plain,
% 11.39/11.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5))),
% 11.39/11.56 inference(modus_ponens,[status(thm)],[2820, 2819])).
% 11.39/11.56 tff(2822,plain,
% 11.39/11.56 ($false),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2821, 296, 1796, 2806, 2815])).
% 11.39/11.56 tff(2823,plain,((~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))), inference(lemma,lemma(discharge,[]))).
% 11.39/11.56 tff(2824,plain,
% 11.39/11.56 (~node18(c_e_h_3, c_h, s4, s5)),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2823, 2806, 1796])).
% 11.39/11.56 tff(2825,assumption,(~node19(c_e_h_3, c_h, s4, s5)), introduced(assumption)).
% 11.39/11.56 tff(2826,plain,
% 11.39/11.56 (((~![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))),
% 11.39/11.56 inference(rewrite,[status(thm)],[])).
% 11.39/11.56 tff(2827,plain,
% 11.39/11.56 ((~![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))),
% 11.39/11.56 inference(quant_inst,[status(thm)],[])).
% 11.39/11.56 tff(2828,plain,
% 11.39/11.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_3, c_h, s4, s5)),
% 11.39/11.56 inference(modus_ponens,[status(thm)],[2827, 2826])).
% 11.39/11.56 tff(2829,plain,
% 11.39/11.56 ($false),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2828, 312, 1542, 2825])).
% 11.39/11.56 tff(2830,plain,(node19(c_e_h_3, c_h, s4, s5)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.56 tff(2831,plain,
% 11.39/11.56 (((~![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_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)))),
% 11.39/11.56 inference(rewrite,[status(thm)],[])).
% 11.39/11.56 tff(2832,plain,
% 11.39/11.56 ((~![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_3, c_h, s4) | node18(c_e_h_3, c_h, s4, s5) | (~node19(c_e_h_3, c_h, s4, s5)))),
% 11.39/11.56 inference(quant_inst,[status(thm)],[])).
% 11.39/11.56 tff(2833,plain,
% 11.39/11.56 ((~![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_3, c_h, s4) | node18(c_e_h_3, c_h, s4, s5) | (~node19(c_e_h_3, c_h, s4, s5))),
% 11.39/11.56 inference(modus_ponens,[status(thm)],[2832, 2831])).
% 11.39/11.56 tff(2834,plain,
% 11.39/11.56 (node17(c_e_h_3, c_h, s4) | node18(c_e_h_3, c_h, s4, s5)),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2833, 326, 2830])).
% 11.39/11.56 tff(2835,plain,
% 11.39/11.56 (node17(c_e_h_3, c_h, s4)),
% 11.39/11.56 inference(unit_resolution,[status(thm)],[2834, 2824])).
% 11.39/11.56 tff(2836,plain,
% 11.39/11.56 (((~![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)))) | ((~node17(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] : (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, 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)))),
% 11.39/11.56 inference(rewrite,[status(thm)],[])).
% 11.39/11.56 tff(2837,plain,
% 11.39/11.56 ((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))) <=> ((~node17(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)))),
% 11.39/11.57 inference(rewrite,[status(thm)],[])).
% 11.39/11.57 tff(2838,plain,
% 11.39/11.57 (((~![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, 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)))) | ((~node17(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))))),
% 11.39/11.57 inference(monotonicity,[status(thm)],[2837])).
% 11.39/11.57 tff(2839,plain,
% 11.39/11.57 (((~![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, 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)))) | (~node17(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)))),
% 11.39/11.57 inference(transitivity,[status(thm)],[2838, 2836])).
% 11.39/11.57 tff(2840,plain,
% 11.39/11.57 ((~![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, s4) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4)))),
% 11.39/11.57 inference(quant_inst,[status(thm)],[])).
% 11.39/11.57 tff(2841,plain,
% 11.39/11.57 ((~![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, 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))),
% 11.39/11.57 inference(modus_ponens,[status(thm)],[2840, 2839])).
% 11.39/11.57 tff(2842,plain,
% 11.39/11.57 ((~node17(c_e_h_3, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4))),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2841, 2125, 2805])).
% 11.39/11.57 tff(2843,plain,
% 11.39/11.57 (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2842, 2835])).
% 11.39/11.57 tff(2844,plain,
% 11.39/11.57 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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))),
% 11.39/11.57 inference(rewrite,[status(thm)],[])).
% 11.39/11.57 tff(2845,plain,
% 11.39/11.57 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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))),
% 11.39/11.57 inference(quant_inst,[status(thm)],[])).
% 11.39/11.57 tff(2846,plain,
% 11.39/11.57 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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)),
% 11.39/11.57 inference(modus_ponens,[status(thm)],[2845, 2844])).
% 11.39/11.57 tff(2847,plain,
% 11.39/11.57 ((~node16(c_e_h_3, c_h, s4)) | m_c_h_element_v_in2(c_e_h_3, c_h, s4)),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2846, 377, 2805])).
% 11.39/11.57 tff(2848,plain,
% 11.39/11.57 (~node16(c_e_h_3, c_h, s4)),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2847, 2843])).
% 11.39/11.57 tff(2849,plain,
% 11.39/11.57 (((~![Y: $i, I0: $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, s4, s5) | node14(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))) <=> ((~![Y: $i, I0: $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, s4, s5) | node14(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))),
% 11.39/11.57 inference(rewrite,[status(thm)],[])).
% 11.39/11.57 tff(2850,plain,
% 11.39/11.57 ((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))) <=> (node15(c_e_h_3, c_h, s4, s5) | node14(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))),
% 11.39/11.57 inference(rewrite,[status(thm)],[])).
% 11.39/11.57 tff(2851,plain,
% 11.39/11.57 (((~![Y: $i, I0: $i, X: $i, I1: $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)))) | (node15(c_e_h_3, c_h, s4, s5) | node14(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)))),
% 11.39/11.57 inference(monotonicity,[status(thm)],[2850])).
% 11.39/11.57 tff(2852,plain,
% 11.39/11.57 (((~![Y: $i, I0: $i, X: $i, I1: $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)))) | node15(c_e_h_3, c_h, s4, s5) | node14(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))),
% 11.39/11.57 inference(transitivity,[status(thm)],[2851, 2849])).
% 11.39/11.57 tff(2853,plain,
% 11.39/11.57 ((~![Y: $i, I0: $i, X: $i, I1: $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)))),
% 11.39/11.57 inference(quant_inst,[status(thm)],[])).
% 11.39/11.57 tff(2854,plain,
% 11.39/11.57 ((~![Y: $i, I0: $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, s4, s5) | node14(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)),
% 11.39/11.57 inference(modus_ponens,[status(thm)],[2853, 2852])).
% 11.39/11.57 tff(2855,plain,
% 11.39/11.57 (node15(c_e_h_3, c_h, s4, s5) | node14(c_e_h_3, c_h, s4, s5) | node16(c_e_h_3, c_h, s4)),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2854, 409, 2830])).
% 11.39/11.57 tff(2856,plain,
% 11.39/11.57 (node15(c_e_h_3, c_h, s4, s5)),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2855, 2848, 2814])).
% 11.39/11.57 tff(2857,plain,
% 11.39/11.57 (((~![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, 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))),
% 11.39/11.57 inference(rewrite,[status(thm)],[])).
% 11.39/11.57 tff(2858,plain,
% 11.39/11.57 ((~![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, s5)) | (~node15(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s4))),
% 11.39/11.57 inference(quant_inst,[status(thm)],[])).
% 11.39/11.57 tff(2859,plain,
% 11.39/11.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | (~node15(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s4)),
% 11.39/11.57 inference(modus_ponens,[status(thm)],[2858, 2857])).
% 11.39/11.57 tff(2860,plain,
% 11.39/11.57 ($false),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2859, 393, 1796, 2806, 2856])).
% 11.39/11.57 tff(2861,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, s4) | m_c_h_element_v_in1(c_e_h_3, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.57 tff(2862,plain,
% 11.39/11.57 (m_c_h_element_v_in1(c_e_h_3, c_h, s4)),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2861, 2804, 1796])).
% 11.39/11.57 tff(2863,plain,
% 11.39/11.57 (~node18(c_e_h_3, c_h, s4, s5)),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2823, 2804, 1796])).
% 11.39/11.57 tff(2864,plain,
% 11.39/11.57 (node17(c_e_h_3, c_h, s4)),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2834, 2863])).
% 11.39/11.57 tff(2865,plain,
% 11.39/11.57 (((~![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, 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] : ((~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, 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))),
% 11.39/11.57 inference(rewrite,[status(thm)],[])).
% 11.39/11.57 tff(2866,plain,
% 11.39/11.57 (((~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))) <=> ((~node17(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))),
% 11.39/11.57 inference(rewrite,[status(thm)],[])).
% 11.39/11.57 tff(2867,plain,
% 11.39/11.57 (((~![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, 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)))) | ((~node17(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)))),
% 11.39/11.57 inference(monotonicity,[status(thm)],[2866])).
% 11.39/11.57 tff(2868,plain,
% 11.39/11.57 (((~![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, 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)))) | (~node17(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))),
% 11.39/11.57 inference(transitivity,[status(thm)],[2867, 2865])).
% 11.39/11.57 tff(2869,plain,
% 11.39/11.57 ((~![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, s4)) | m_c_h_element_v_in2(c_e_h_3, c_h, s4) | (~node17(c_e_h_3, c_h, s4)))),
% 11.39/11.57 inference(quant_inst,[status(thm)],[])).
% 11.39/11.57 tff(2870,plain,
% 11.39/11.57 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | m_c_h_element_v_in2(c_e_h_3, c_h, s4)),
% 11.39/11.57 inference(modus_ponens,[status(thm)],[2869, 2868])).
% 11.39/11.57 tff(2871,plain,
% 11.39/11.57 ((~node17(c_e_h_3, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s4))),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2870, 359, 1558])).
% 11.39/11.57 tff(2872,plain,
% 11.39/11.57 ($false),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2871, 2864, 2862])).
% 11.39/11.57 tff(2873,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, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s8))), inference(lemma,lemma(discharge,[]))).
% 11.39/11.57 tff(2874,plain,
% 11.39/11.57 (m_c_h_element_v_in2(c_e_h_3, c_h, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s8))),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2873, 1795])).
% 11.39/11.57 tff(2875,plain,
% 11.39/11.57 (~m_and_h_gate_v_out(c_e_h_3, c_r, s8)),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2874, 1558])).
% 11.39/11.57 tff(2876,plain,
% 11.39/11.57 ((~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)),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2861, 1795])).
% 11.39/11.57 tff(2877,plain,
% 11.39/11.57 (m_c_h_element_v_in1(c_e_h_3, c_h, s4)),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2876, 2806])).
% 11.39/11.57 tff(2878,plain,
% 11.39/11.57 ((~node18(c_e_h_3, c_h, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5))),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2823, 1795])).
% 11.39/11.57 tff(2879,plain,
% 11.39/11.57 (~node18(c_e_h_3, c_h, s4, s5)),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2878, 2806])).
% 11.39/11.57 tff(2880,plain,
% 11.39/11.57 (node17(c_e_h_3, c_h, s4)),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2834, 2879])).
% 11.39/11.57 tff(2881,plain,
% 11.39/11.57 ($false),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2871, 2880, 2877])).
% 11.39/11.57 tff(2882,plain,((~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,[]))).
% 11.39/11.57 tff(2883,plain,
% 11.39/11.57 (~m_c_h_element_v_out(c_e_h_3, c_h, s5)),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2882, 1558])).
% 11.39/11.57 tff(2884,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s2)), introduced(assumption)).
% 11.39/11.57 tff(2885,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s0)), introduced(assumption)).
% 11.39/11.57 tff(2886,plain,
% 11.39/11.57 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s0))),
% 11.39/11.57 inference(quant_inst,[status(thm)],[])).
% 11.39/11.57 tff(2887,plain,
% 11.39/11.57 ($false),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2886, 260, 2885])).
% 11.39/11.57 tff(2888,plain,(~m_and_h_gate_v_out(c_e_h_1, c_l, s0)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.57 tff(2889,plain,
% 11.39/11.57 (((~![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_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))),
% 11.39/11.57 inference(rewrite,[status(thm)],[])).
% 11.39/11.57 tff(2890,plain,
% 11.39/11.57 ((~![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_1, c_j, s0)) | m_and_h_gate_v_out(c_e_h_1, c_l, s0))),
% 11.39/11.57 inference(quant_inst,[status(thm)],[])).
% 11.39/11.57 tff(2891,plain,
% 11.39/11.57 ((~![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_1, c_j, s0)) | m_and_h_gate_v_out(c_e_h_1, c_l, s0)),
% 11.39/11.57 inference(modus_ponens,[status(thm)],[2890, 2889])).
% 11.39/11.57 tff(2892,plain,
% 11.39/11.57 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s0)),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2891, 920, 2888])).
% 11.39/11.57 tff(2893,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s1)), introduced(assumption)).
% 11.39/11.57 tff(2894,assumption,(node6(c_e_h_1, c_j, s0, s1)), introduced(assumption)).
% 11.39/11.57 tff(2895,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s0)), introduced(assumption)).
% 11.39/11.57 tff(2896,plain,
% 11.39/11.57 ((~![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s0))),
% 11.39/11.57 inference(quant_inst,[status(thm)],[])).
% 11.39/11.57 tff(2897,plain,
% 11.39/11.57 ($false),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2896, 660, 2895])).
% 11.39/11.57 tff(2898,plain,(~m_or_h_gate_v_out(c_e_h_1, c_j, s0)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.57 tff(2899,plain,
% 11.39/11.57 (((~![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_1, c_j, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0) | (~node6(c_e_h_1, 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_1, c_j, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0) | (~node6(c_e_h_1, c_j, s0, s1)))),
% 11.39/11.57 inference(rewrite,[status(thm)],[])).
% 11.39/11.57 tff(2900,plain,
% 11.39/11.57 (((~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)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0) | (~node6(c_e_h_1, c_j, s0, s1)))),
% 11.39/11.57 inference(rewrite,[status(thm)],[])).
% 11.39/11.57 tff(2901,plain,
% 11.39/11.57 (((~![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_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)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0) | (~node6(c_e_h_1, c_j, s0, s1))))),
% 11.39/11.57 inference(monotonicity,[status(thm)],[2900])).
% 11.39/11.57 tff(2902,plain,
% 11.39/11.57 (((~![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_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)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0) | (~node6(c_e_h_1, c_j, s0, s1)))),
% 11.39/11.57 inference(transitivity,[status(thm)],[2901, 2899])).
% 11.39/11.57 tff(2903,plain,
% 11.39/11.57 ((~![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_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))),
% 11.39/11.57 inference(quant_inst,[status(thm)],[])).
% 11.39/11.57 tff(2904,plain,
% 11.39/11.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0) | (~node6(c_e_h_1, c_j, s0, s1))),
% 11.39/11.57 inference(modus_ponens,[status(thm)],[2903, 2902])).
% 11.39/11.57 tff(2905,plain,
% 11.39/11.57 ($false),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2904, 742, 2893, 2898, 2894])).
% 11.39/11.57 tff(2906,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,[]))).
% 11.39/11.57 tff(2907,plain,
% 11.39/11.57 (~node6(c_e_h_1, c_j, s0, s1)),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2906, 2893])).
% 11.39/11.57 tff(2908,plain,
% 11.39/11.57 (((~![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))),
% 11.39/11.57 inference(rewrite,[status(thm)],[])).
% 11.39/11.57 tff(2909,plain,
% 11.39/11.57 ((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))),
% 11.39/11.57 inference(rewrite,[status(thm)],[])).
% 11.39/11.57 tff(2910,plain,
% 11.39/11.57 (((~![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_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)))),
% 11.39/11.57 inference(monotonicity,[status(thm)],[2909])).
% 11.39/11.57 tff(2911,plain,
% 11.39/11.57 (((~![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_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))),
% 11.39/11.57 inference(transitivity,[status(thm)],[2910, 2908])).
% 11.39/11.57 tff(2912,plain,
% 11.39/11.57 ((~![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_1, c_j, s0, s1) | node5(c_e_h_1, c_j, s0, s1) | (~trans(s0, s1)))),
% 11.39/11.57 inference(quant_inst,[status(thm)],[])).
% 11.39/11.57 tff(2913,plain,
% 11.39/11.57 ((~![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)),
% 11.39/11.57 inference(modus_ponens,[status(thm)],[2912, 2911])).
% 11.39/11.57 tff(2914,plain,
% 11.39/11.57 (node6(c_e_h_1, c_j, s0, s1) | node5(c_e_h_1, c_j, s0, s1)),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2913, 724, 100])).
% 11.39/11.57 tff(2915,plain,
% 11.39/11.57 (node5(c_e_h_1, c_j, s0, s1)),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2914, 2907])).
% 11.39/11.57 tff(2916,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s0)), introduced(assumption)).
% 11.39/11.57 tff(2917,plain,
% 11.39/11.57 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s0))),
% 11.39/11.57 inference(quant_inst,[status(thm)],[])).
% 11.39/11.57 tff(2918,plain,
% 11.39/11.57 ($false),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2917, 260, 2916])).
% 11.39/11.57 tff(2919,plain,(~m_and_h_gate_v_out(c_e_h_3, c_q, s0)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.57 tff(2920,assumption,(~node3(c_e_h_3, c_e_h_1, s0)), introduced(assumption)).
% 11.39/11.57 tff(2921,plain,
% 11.39/11.57 (m_cell_v_left(c_e_h_3, c_e_h_1) <=> m_cell_v_left(c_e_h_3, c_e_h_1)),
% 11.39/11.57 inference(rewrite,[status(thm)],[])).
% 11.39/11.57 tff(2922,axiom,(m_cell_v_left(c_e_h_3, c_e_h_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_7')).
% 11.39/11.57 tff(2923,plain,
% 11.39/11.57 (m_cell_v_left(c_e_h_3, c_e_h_1)),
% 11.39/11.57 inference(modus_ponens,[status(thm)],[2922, 2921])).
% 11.39/11.57 tff(2924,plain,
% 11.39/11.57 (((~![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))),
% 11.39/11.57 inference(rewrite,[status(thm)],[])).
% 11.39/11.57 tff(2925,plain,
% 11.39/11.57 ((~![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))),
% 11.39/11.57 inference(quant_inst,[status(thm)],[])).
% 11.39/11.57 tff(2926,plain,
% 11.39/11.57 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s0)),
% 11.39/11.57 inference(modus_ponens,[status(thm)],[2925, 2924])).
% 11.39/11.57 tff(2927,plain,
% 11.39/11.57 ($false),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2926, 2923, 616, 2920])).
% 11.39/11.57 tff(2928,plain,(node3(c_e_h_3, c_e_h_1, s0)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.57 tff(2929,plain,
% 11.39/11.57 (((~![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_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))),
% 11.39/11.57 inference(rewrite,[status(thm)],[])).
% 11.39/11.57 tff(2930,plain,
% 11.39/11.57 ((~![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_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))),
% 11.39/11.57 inference(quant_inst,[status(thm)],[])).
% 11.39/11.57 tff(2931,plain,
% 11.39/11.57 ((~![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_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)),
% 11.39/11.57 inference(modus_ponens,[status(thm)],[2930, 2929])).
% 11.39/11.57 tff(2932,plain,
% 11.39/11.57 ((~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)),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2931, 633])).
% 11.39/11.57 tff(2933,plain,
% 11.39/11.57 ((~m_cell_v_ack(c_e_h_1, s0)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0)),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2932, 2928])).
% 11.39/11.57 tff(2934,plain,
% 11.39/11.57 (~m_cell_v_ack(c_e_h_1, s0)),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2933, 2919])).
% 11.39/11.57 tff(2935,plain,
% 11.39/11.57 (((~![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_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))),
% 11.39/11.57 inference(rewrite,[status(thm)],[])).
% 11.39/11.57 tff(2936,plain,
% 11.39/11.57 ((~![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_1, c_j, s0)) | m_cell_v_ack(c_e_h_1, s0))),
% 11.39/11.57 inference(quant_inst,[status(thm)],[])).
% 11.39/11.57 tff(2937,plain,
% 11.39/11.57 ((~![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_1, c_j, s0)) | m_cell_v_ack(c_e_h_1, s0)),
% 11.39/11.57 inference(modus_ponens,[status(thm)],[2936, 2935])).
% 11.39/11.57 tff(2938,plain,
% 11.39/11.57 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s0)),
% 11.39/11.57 inference(unit_resolution,[status(thm)],[2937, 645, 2934])).
% 11.39/11.57 tff(2939,plain,
% 11.39/11.57 (((~![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_1, c_j, s1)) | 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_in1(c_e_h_1, 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_1, c_j, s1)) | 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_in1(c_e_h_1, c_j, s0))),
% 11.39/11.58 inference(rewrite,[status(thm)],[])).
% 11.39/11.58 tff(2940,plain,
% 11.39/11.58 ((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) | (~node5(c_e_h_1, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s0))),
% 11.39/11.58 inference(rewrite,[status(thm)],[])).
% 11.39/11.58 tff(2941,plain,
% 11.39/11.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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) | (~node5(c_e_h_1, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s0)))),
% 11.39/11.58 inference(monotonicity,[status(thm)],[2940])).
% 11.39/11.58 tff(2942,plain,
% 11.39/11.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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) | (~node5(c_e_h_1, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s0))),
% 11.39/11.58 inference(transitivity,[status(thm)],[2941, 2939])).
% 11.39/11.58 tff(2943,plain,
% 11.39/11.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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)))),
% 11.39/11.58 inference(quant_inst,[status(thm)],[])).
% 11.39/11.58 tff(2944,plain,
% 11.39/11.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s0) | (~node5(c_e_h_1, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s0)),
% 11.39/11.58 inference(modus_ponens,[status(thm)],[2943, 2942])).
% 11.39/11.58 tff(2945,plain,
% 11.39/11.58 ($false),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[2944, 705, 2893, 2938, 2915, 2892])).
% 11.39/11.58 tff(2946,plain,(~m_or_h_gate_v_out(c_e_h_1, c_j, s1)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.58 tff(2947,plain,
% 11.39/11.58 (((~![Y: $i, I0: $i, X: $i, I1: $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)))),
% 11.39/11.58 inference(rewrite,[status(thm)],[])).
% 11.39/11.58 tff(2948,plain,
% 11.39/11.58 (((~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)))),
% 11.39/11.58 inference(rewrite,[status(thm)],[])).
% 11.39/11.58 tff(2949,plain,
% 11.39/11.58 (((~![Y: $i, I0: $i, X: $i, I1: $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))))),
% 11.39/11.58 inference(monotonicity,[status(thm)],[2948])).
% 11.39/11.58 tff(2950,plain,
% 11.39/11.58 (((~![Y: $i, I0: $i, X: $i, I1: $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)))),
% 11.39/11.58 inference(transitivity,[status(thm)],[2949, 2947])).
% 11.39/11.58 tff(2951,plain,
% 11.39/11.58 ((~![Y: $i, I0: $i, X: $i, I1: $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))),
% 11.39/11.58 inference(quant_inst,[status(thm)],[])).
% 11.39/11.58 tff(2952,plain,
% 11.39/11.58 ((~![Y: $i, I0: $i, X: $i, I1: $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))),
% 11.39/11.58 inference(modus_ponens,[status(thm)],[2951, 2950])).
% 11.39/11.58 tff(2953,plain,
% 11.39/11.58 (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))),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[2952, 742])).
% 11.39/11.58 tff(2954,plain,
% 11.39/11.58 ((~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | (~node6(c_e_h_1, c_j, s1, s2))),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[2953, 2946])).
% 11.39/11.58 tff(2955,plain,
% 11.39/11.58 (~node6(c_e_h_1, c_j, s1, s2)),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[2954, 2884])).
% 11.39/11.58 tff(2956,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s1)), introduced(assumption)).
% 11.39/11.58 tff(2957,assumption,(node22(c_e_h_1, c_l, s0, s1)), introduced(assumption)).
% 11.39/11.58 tff(2958,plain,
% 11.39/11.58 (((~![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_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))),
% 11.39/11.58 inference(rewrite,[status(thm)],[])).
% 11.39/11.58 tff(2959,plain,
% 11.39/11.58 ((~![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_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))),
% 11.39/11.58 inference(quant_inst,[status(thm)],[])).
% 11.39/11.58 tff(2960,plain,
% 11.39/11.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1)) | (~node22(c_e_h_1, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_l, s0)),
% 11.39/11.58 inference(modus_ponens,[status(thm)],[2959, 2958])).
% 11.39/11.58 tff(2961,plain,
% 11.39/11.58 ($false),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[2960, 273, 2888, 2956, 2957])).
% 11.39/11.58 tff(2962,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,[]))).
% 11.39/11.58 tff(2963,plain,
% 11.39/11.58 (~node22(c_e_h_1, c_l, s0, s1)),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[2962, 2956])).
% 11.39/11.58 tff(2964,plain,
% 11.39/11.58 (((~![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))),
% 11.39/11.58 inference(rewrite,[status(thm)],[])).
% 11.39/11.58 tff(2965,plain,
% 11.39/11.58 ((~![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))),
% 11.39/11.58 inference(quant_inst,[status(thm)],[])).
% 11.39/11.58 tff(2966,plain,
% 11.39/11.58 ((~![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)),
% 11.39/11.58 inference(modus_ponens,[status(thm)],[2965, 2964])).
% 11.39/11.58 tff(2967,plain,
% 11.39/11.58 (node21(c_e_h_1, c_l, s0, s1) | node22(c_e_h_1, c_l, s0, s1)),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[2966, 247, 100])).
% 11.39/11.58 tff(2968,plain,
% 11.39/11.58 (node21(c_e_h_1, c_l, s0, s1)),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[2967, 2963])).
% 11.39/11.58 tff(2969,plain,
% 11.39/11.58 (((~![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))),
% 11.39/11.58 inference(rewrite,[status(thm)],[])).
% 11.39/11.58 tff(2970,plain,
% 11.39/11.58 ((~![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))),
% 11.39/11.58 inference(quant_inst,[status(thm)],[])).
% 11.39/11.58 tff(2971,plain,
% 11.39/11.58 ((~![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)),
% 11.39/11.58 inference(modus_ponens,[status(thm)],[2970, 2969])).
% 11.39/11.58 tff(2972,plain,
% 11.39/11.58 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s0)),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[2971, 159, 137])).
% 11.39/11.58 tff(2973,plain,
% 11.39/11.58 (((~![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))),
% 11.39/11.58 inference(rewrite,[status(thm)],[])).
% 11.39/11.58 tff(2974,plain,
% 11.39/11.58 ((~![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))),
% 11.39/11.58 inference(quant_inst,[status(thm)],[])).
% 11.39/11.58 tff(2975,plain,
% 11.39/11.58 ((~![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)),
% 11.39/11.58 inference(modus_ponens,[status(thm)],[2974, 2973])).
% 11.39/11.58 tff(2976,plain,
% 11.39/11.58 (~node20(c_e_h_1, c_l, s0)),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[2975, 173, 2972])).
% 11.39/11.58 tff(2977,plain,
% 11.39/11.58 (((~![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_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) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1)) | (~node21(c_e_h_1, c_l, s0, s1)))),
% 11.39/11.58 inference(rewrite,[status(thm)],[])).
% 11.39/11.58 tff(2978,plain,
% 11.39/11.58 ((~![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_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)))),
% 11.39/11.58 inference(quant_inst,[status(thm)],[])).
% 11.39/11.58 tff(2979,plain,
% 11.39/11.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1)) | (~node21(c_e_h_1, c_l, s0, s1))),
% 11.39/11.58 inference(modus_ponens,[status(thm)],[2978, 2977])).
% 11.39/11.58 tff(2980,plain,
% 11.39/11.58 ($false),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[2979, 228, 2976, 2956, 2968])).
% 11.39/11.58 tff(2981,plain,(~m_and_h_gate_v_out(c_e_h_1, c_l, s1)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.58 tff(2982,plain,
% 11.39/11.58 (((~![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))),
% 11.39/11.58 inference(rewrite,[status(thm)],[])).
% 11.39/11.58 tff(2983,plain,
% 11.39/11.58 ((~![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))),
% 11.39/11.58 inference(quant_inst,[status(thm)],[])).
% 11.39/11.58 tff(2984,plain,
% 11.39/11.58 ((~![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)),
% 11.39/11.58 inference(modus_ponens,[status(thm)],[2983, 2982])).
% 11.39/11.58 tff(2985,plain,
% 11.39/11.58 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s1)),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[2984, 920, 2981])).
% 11.39/11.58 tff(2986,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s1)), introduced(assumption)).
% 11.39/11.58 tff(2987,assumption,(node21(c_e_h_3, c_q, s0, s1)), introduced(assumption)).
% 11.39/11.58 tff(2988,plain,
% 11.39/11.58 (^[X: $i] : refl(m_cell_v_token(c_e_h_3, X) <=> m_cell_v_token(c_e_h_3, X))),
% 11.39/11.58 inference(bind,[status(th)],[])).
% 11.39/11.58 tff(2989,plain,
% 11.39/11.58 (![X: $i] : m_cell_v_token(c_e_h_3, X) <=> ![X: $i] : m_cell_v_token(c_e_h_3, X)),
% 11.39/11.58 inference(quant_intro,[status(thm)],[2988])).
% 11.39/11.58 tff(2990,plain,
% 11.39/11.58 (![X: $i] : m_cell_v_token(c_e_h_3, X) <=> ![X: $i] : m_cell_v_token(c_e_h_3, X)),
% 11.39/11.58 inference(rewrite,[status(thm)],[])).
% 11.39/11.58 tff(2991,axiom,(![X: $i] : m_cell_v_token(c_e_h_3, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_9')).
% 11.39/11.58 tff(2992,plain,
% 11.39/11.58 (![X: $i] : m_cell_v_token(c_e_h_3, X)),
% 11.39/11.58 inference(modus_ponens,[status(thm)],[2991, 2990])).
% 11.39/11.58 tff(2993,plain,(
% 11.39/11.58 ![X: $i] : m_cell_v_token(c_e_h_3, X)),
% 11.39/11.58 inference(skolemize,[status(sab)],[2992])).
% 11.39/11.58 tff(2994,plain,
% 11.39/11.58 (![X: $i] : m_cell_v_token(c_e_h_3, X)),
% 11.39/11.58 inference(modus_ponens,[status(thm)],[2993, 2989])).
% 11.39/11.58 tff(2995,plain,
% 11.39/11.58 ((~![X: $i] : m_cell_v_token(c_e_h_3, X)) | m_cell_v_token(c_e_h_3, s0)),
% 11.39/11.58 inference(quant_inst,[status(thm)],[])).
% 11.39/11.58 tff(2996,plain,
% 11.39/11.58 (m_cell_v_token(c_e_h_3, s0)),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[2995, 2994])).
% 11.39/11.58 tff(2997,plain,
% 11.39/11.58 (^[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))))),
% 11.39/11.58 inference(bind,[status(th)],[])).
% 11.39/11.58 tff(2998,plain,
% 11.39/11.58 (![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)))),
% 11.39/11.58 inference(quant_intro,[status(thm)],[2997])).
% 11.39/11.58 tff(2999,plain,
% 11.39/11.58 (![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)))),
% 11.39/11.58 inference(rewrite,[status(thm)],[])).
% 11.39/11.58 tff(3000,plain,
% 11.39/11.58 (^[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))))),
% 11.39/11.58 inference(bind,[status(th)],[])).
% 11.39/11.58 tff(3001,plain,
% 11.39/11.58 (![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)))),
% 11.39/11.58 inference(quant_intro,[status(thm)],[3000])).
% 11.39/11.58 tff(3002,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')).
% 11.39/11.58 tff(3003,plain,
% 11.39/11.58 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 11.39/11.58 inference(modus_ponens,[status(thm)],[3002, 3001])).
% 11.39/11.58 tff(3004,plain,
% 11.39/11.58 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 11.39/11.58 inference(modus_ponens,[status(thm)],[3003, 2999])).
% 11.39/11.58 tff(3005,plain,(
% 11.39/11.58 ![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 11.39/11.58 inference(skolemize,[status(sab)],[3004])).
% 11.39/11.58 tff(3006,plain,
% 11.39/11.58 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 11.39/11.58 inference(modus_ponens,[status(thm)],[3005, 2998])).
% 11.39/11.58 tff(3007,plain,
% 11.39/11.58 (((~![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)))),
% 11.39/11.58 inference(rewrite,[status(thm)],[])).
% 11.39/11.58 tff(3008,plain,
% 11.39/11.58 ((~![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)))),
% 11.39/11.58 inference(quant_inst,[status(thm)],[])).
% 11.39/11.58 tff(3009,plain,
% 11.39/11.58 ((~![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))),
% 11.39/11.58 inference(modus_ponens,[status(thm)],[3008, 3007])).
% 11.39/11.58 tff(3010,plain,
% 11.39/11.58 (~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0)),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[3009, 3006, 2996])).
% 11.39/11.58 tff(3011,plain,
% 11.39/11.58 (((~![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))),
% 11.39/11.58 inference(rewrite,[status(thm)],[])).
% 11.39/11.58 tff(3012,plain,
% 11.39/11.58 ((~![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))),
% 11.39/11.58 inference(quant_inst,[status(thm)],[])).
% 11.39/11.58 tff(3013,plain,
% 11.39/11.58 ((~![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)),
% 11.39/11.58 inference(modus_ponens,[status(thm)],[3012, 3011])).
% 11.39/11.58 tff(3014,plain,
% 11.39/11.58 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0)),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[3013, 133, 3010])).
% 11.39/11.58 tff(3015,plain,
% 11.39/11.58 (^[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)))),
% 11.39/11.58 inference(bind,[status(th)],[])).
% 11.39/11.58 tff(3016,plain,
% 11.39/11.58 (![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))),
% 11.39/11.58 inference(quant_intro,[status(thm)],[3015])).
% 11.39/11.58 tff(3017,plain,
% 11.39/11.58 (![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))),
% 11.39/11.58 inference(rewrite,[status(thm)],[])).
% 11.39/11.58 tff(3018,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')).
% 11.39/11.58 tff(3019,plain,
% 11.39/11.58 (![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))),
% 11.39/11.58 inference(modus_ponens,[status(thm)],[3018, 3017])).
% 11.39/11.58 tff(3020,plain,(
% 11.39/11.58 ![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))),
% 11.39/11.58 inference(skolemize,[status(sab)],[3019])).
% 11.39/11.58 tff(3021,plain,
% 11.39/11.58 (![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))),
% 11.39/11.58 inference(modus_ponens,[status(thm)],[3020, 3016])).
% 11.39/11.58 tff(3022,plain,
% 11.39/11.58 (((~![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, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0))) <=> ((~![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, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0))),
% 11.39/11.58 inference(rewrite,[status(thm)],[])).
% 11.39/11.58 tff(3023,plain,
% 11.39/11.58 ((~![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, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0))),
% 11.39/11.58 inference(quant_inst,[status(thm)],[])).
% 11.39/11.58 tff(3024,plain,
% 11.39/11.58 ((~![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, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0)),
% 11.39/11.58 inference(modus_ponens,[status(thm)],[3023, 3022])).
% 11.39/11.58 tff(3025,plain,
% 11.39/11.58 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s0)),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[3024, 3021, 3014])).
% 11.39/11.58 tff(3026,plain,
% 11.39/11.58 (((~![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, s0)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s0))) <=> ((~![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, s0)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s0))),
% 11.39/11.58 inference(rewrite,[status(thm)],[])).
% 11.39/11.58 tff(3027,plain,
% 11.39/11.58 ((~![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, s0)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s0))),
% 11.39/11.58 inference(quant_inst,[status(thm)],[])).
% 11.39/11.58 tff(3028,plain,
% 11.39/11.58 ((~![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, s0)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s0)),
% 11.39/11.58 inference(modus_ponens,[status(thm)],[3027, 3026])).
% 11.39/11.58 tff(3029,plain,
% 11.39/11.58 (~node20(c_e_h_3, c_q, s0)),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[3028, 173, 3025])).
% 11.39/11.58 tff(3030,plain,
% 11.39/11.58 (((~![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_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)))),
% 11.39/11.58 inference(rewrite,[status(thm)],[])).
% 11.39/11.58 tff(3031,plain,
% 11.39/11.58 ((~![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_q, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s1)) | (~node21(c_e_h_3, c_q, s0, s1)))),
% 11.39/11.58 inference(quant_inst,[status(thm)],[])).
% 11.39/11.58 tff(3032,plain,
% 11.39/11.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s1)) | (~node21(c_e_h_3, c_q, s0, s1))),
% 11.39/11.58 inference(modus_ponens,[status(thm)],[3031, 3030])).
% 11.39/11.58 tff(3033,plain,
% 11.39/11.58 ($false),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[3032, 228, 3029, 2986, 2987])).
% 11.39/11.58 tff(3034,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,[]))).
% 11.39/11.58 tff(3035,plain,
% 11.39/11.58 (~node21(c_e_h_3, c_q, s0, s1)),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[3034, 2986])).
% 11.39/11.58 tff(3036,plain,
% 11.39/11.58 (((~![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))),
% 11.39/11.58 inference(rewrite,[status(thm)],[])).
% 11.39/11.58 tff(3037,plain,
% 11.39/11.58 ((~![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))),
% 11.39/11.58 inference(quant_inst,[status(thm)],[])).
% 11.39/11.58 tff(3038,plain,
% 11.39/11.58 ((~![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)),
% 11.39/11.58 inference(modus_ponens,[status(thm)],[3037, 3036])).
% 11.39/11.58 tff(3039,plain,
% 11.39/11.58 (node21(c_e_h_3, c_q, s0, s1) | node22(c_e_h_3, c_q, s0, s1)),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[3038, 247, 100])).
% 11.39/11.58 tff(3040,plain,
% 11.39/11.58 (node22(c_e_h_3, c_q, s0, s1)),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[3039, 3035])).
% 11.39/11.58 tff(3041,plain,
% 11.39/11.58 (((~![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_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))),
% 11.39/11.58 inference(rewrite,[status(thm)],[])).
% 11.39/11.58 tff(3042,plain,
% 11.39/11.58 ((~![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_q, s1)) | (~node22(c_e_h_3, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0))),
% 11.39/11.58 inference(quant_inst,[status(thm)],[])).
% 11.39/11.58 tff(3043,plain,
% 11.39/11.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s1)) | (~node22(c_e_h_3, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0)),
% 11.39/11.58 inference(modus_ponens,[status(thm)],[3042, 3041])).
% 11.39/11.58 tff(3044,plain,
% 11.39/11.58 ($false),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[3043, 273, 2919, 2986, 3040])).
% 11.39/11.58 tff(3045,plain,(~m_and_h_gate_v_out(c_e_h_3, c_q, s1)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.58 tff(3046,assumption,(~node3(c_e_h_3, c_e_h_1, s1)), introduced(assumption)).
% 11.39/11.58 tff(3047,plain,
% 11.39/11.58 (((~![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))),
% 11.39/11.58 inference(rewrite,[status(thm)],[])).
% 11.39/11.58 tff(3048,plain,
% 11.39/11.58 ((~![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))),
% 11.39/11.58 inference(quant_inst,[status(thm)],[])).
% 11.39/11.58 tff(3049,plain,
% 11.39/11.58 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s1)),
% 11.39/11.58 inference(modus_ponens,[status(thm)],[3048, 3047])).
% 11.39/11.58 tff(3050,plain,
% 11.39/11.58 ($false),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[3049, 2923, 616, 3046])).
% 11.39/11.58 tff(3051,plain,(node3(c_e_h_3, c_e_h_1, s1)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.58 tff(3052,plain,
% 11.39/11.58 (((~![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))),
% 11.39/11.58 inference(rewrite,[status(thm)],[])).
% 11.39/11.58 tff(3053,plain,
% 11.39/11.58 ((~![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))),
% 11.39/11.58 inference(quant_inst,[status(thm)],[])).
% 11.39/11.58 tff(3054,plain,
% 11.39/11.58 ((~![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)),
% 11.39/11.58 inference(modus_ponens,[status(thm)],[3053, 3052])).
% 11.39/11.58 tff(3055,plain,
% 11.39/11.58 ((~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)),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[3054, 633])).
% 11.39/11.58 tff(3056,plain,
% 11.39/11.58 ((~m_cell_v_ack(c_e_h_1, s1)) | m_and_h_gate_v_out(c_e_h_3, c_q, s1)),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[3055, 3051])).
% 11.39/11.58 tff(3057,plain,
% 11.39/11.58 (~m_cell_v_ack(c_e_h_1, s1)),
% 11.39/11.58 inference(unit_resolution,[status(thm)],[3056, 3045])).
% 11.39/11.59 tff(3058,plain,
% 11.39/11.59 (((~![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))),
% 11.39/11.59 inference(rewrite,[status(thm)],[])).
% 11.39/11.59 tff(3059,plain,
% 11.39/11.59 ((~![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))),
% 11.39/11.59 inference(quant_inst,[status(thm)],[])).
% 11.39/11.59 tff(3060,plain,
% 11.39/11.59 ((~![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)),
% 11.39/11.59 inference(modus_ponens,[status(thm)],[3059, 3058])).
% 11.39/11.59 tff(3061,plain,
% 11.39/11.59 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s1)),
% 11.39/11.59 inference(unit_resolution,[status(thm)],[3060, 645, 3057])).
% 11.39/11.59 tff(3062,assumption,(node5(c_e_h_1, c_j, s1, s2)), introduced(assumption)).
% 11.39/11.59 tff(3063,plain,
% 11.39/11.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | (~node5(c_e_h_1, c_j, s1, s2)) | m_or_h_gate_v_in1(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_in2(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | (~node5(c_e_h_1, c_j, s1, s2)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s1))),
% 11.39/11.59 inference(rewrite,[status(thm)],[])).
% 11.39/11.59 tff(3064,plain,
% 11.39/11.59 ((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_in2(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | (~node5(c_e_h_1, c_j, s1, s2)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s1))),
% 11.39/11.59 inference(rewrite,[status(thm)],[])).
% 11.39/11.59 tff(3065,plain,
% 11.39/11.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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_in2(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | (~node5(c_e_h_1, c_j, s1, s2)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s1)))),
% 11.39/11.59 inference(monotonicity,[status(thm)],[3064])).
% 11.39/11.59 tff(3066,plain,
% 11.39/11.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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_in2(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | (~node5(c_e_h_1, c_j, s1, s2)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s1))),
% 11.39/11.59 inference(transitivity,[status(thm)],[3065, 3063])).
% 11.39/11.59 tff(3067,plain,
% 11.39/11.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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)))),
% 11.39/11.59 inference(quant_inst,[status(thm)],[])).
% 11.39/11.59 tff(3068,plain,
% 11.39/11.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | (~node5(c_e_h_1, c_j, s1, s2)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s1)),
% 11.39/11.59 inference(modus_ponens,[status(thm)],[3067, 3066])).
% 11.39/11.59 tff(3069,plain,
% 11.39/11.59 ($false),
% 11.39/11.59 inference(unit_resolution,[status(thm)],[3068, 705, 2884, 3062, 3061, 2985])).
% 11.39/11.59 tff(3070,plain,((~node5(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2))), inference(lemma,lemma(discharge,[]))).
% 11.39/11.59 tff(3071,plain,
% 11.39/11.59 (~node5(c_e_h_1, c_j, s1, s2)),
% 11.39/11.59 inference(unit_resolution,[status(thm)],[3070, 2884])).
% 11.39/11.59 tff(3072,plain,
% 11.39/11.59 (((~![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))),
% 11.39/11.59 inference(rewrite,[status(thm)],[])).
% 11.39/11.59 tff(3073,plain,
% 11.39/11.59 ((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))),
% 11.39/11.59 inference(rewrite,[status(thm)],[])).
% 11.39/11.59 tff(3074,plain,
% 11.39/11.59 (((~![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)))),
% 11.39/11.59 inference(monotonicity,[status(thm)],[3073])).
% 11.39/11.59 tff(3075,plain,
% 11.39/11.59 (((~![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))),
% 11.39/11.59 inference(transitivity,[status(thm)],[3074, 3072])).
% 11.39/11.59 tff(3076,plain,
% 11.39/11.59 ((~![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)))),
% 11.39/11.59 inference(quant_inst,[status(thm)],[])).
% 11.39/11.59 tff(3077,plain,
% 11.39/11.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node5(c_e_h_1, c_j, s1, s2) | node6(c_e_h_1, c_j, s1, s2)),
% 11.39/11.59 inference(modus_ponens,[status(thm)],[3076, 3075])).
% 11.39/11.59 tff(3078,plain,
% 11.39/11.59 ($false),
% 11.39/11.59 inference(unit_resolution,[status(thm)],[3077, 724, 470, 3071, 2955])).
% 11.39/11.59 tff(3079,plain,(~m_or_h_gate_v_out(c_e_h_1, c_j, s2)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.59 tff(3080,plain,
% 11.39/11.59 (((~![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))),
% 11.39/11.59 inference(rewrite,[status(thm)],[])).
% 11.39/11.59 tff(3081,plain,
% 11.39/11.59 ((~![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))),
% 11.39/11.59 inference(quant_inst,[status(thm)],[])).
% 11.39/11.59 tff(3082,plain,
% 11.39/11.59 ((~![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)),
% 11.39/11.59 inference(modus_ponens,[status(thm)],[3081, 3080])).
% 11.39/11.59 tff(3083,plain,
% 11.39/11.59 (~m_c_h_element_v_in2(c_e_h_1, c_h, s2)),
% 11.39/11.59 inference(unit_resolution,[status(thm)],[3082, 1117, 3079])).
% 11.39/11.59 tff(3084,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s2)), introduced(assumption)).
% 11.39/11.59 tff(3085,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s3)), introduced(assumption)).
% 11.39/11.59 tff(3086,assumption,(node18(c_e_h_1, c_h, s2, s3)), introduced(assumption)).
% 11.39/11.59 tff(3087,assumption,(m_and_h_gate_v_out(c_e_h_1, c_c, s0)), introduced(assumption)).
% 11.39/11.59 tff(3088,plain,
% 11.39/11.59 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s0))),
% 11.39/11.59 inference(quant_inst,[status(thm)],[])).
% 11.39/11.59 tff(3089,plain,
% 11.39/11.59 ($false),
% 11.39/11.59 inference(unit_resolution,[status(thm)],[3088, 260, 3087])).
% 11.39/11.59 tff(3090,plain,(~m_and_h_gate_v_out(c_e_h_1, c_c, s0)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.59 tff(3091,plain,
% 11.39/11.59 (((~![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_1, c_g, s0)) | m_and_h_gate_v_out(c_e_h_1, 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_1, c_g, s0)) | m_and_h_gate_v_out(c_e_h_1, c_c, s0))),
% 11.39/11.59 inference(rewrite,[status(thm)],[])).
% 11.39/11.59 tff(3092,plain,
% 11.39/11.59 ((~![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_1, c_g, s0)) | m_and_h_gate_v_out(c_e_h_1, c_c, s0))),
% 11.39/11.59 inference(quant_inst,[status(thm)],[])).
% 11.39/11.59 tff(3093,plain,
% 11.39/11.59 ((~![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_1, c_g, s0)) | m_and_h_gate_v_out(c_e_h_1, c_c, s0)),
% 11.39/11.59 inference(modus_ponens,[status(thm)],[3092, 3091])).
% 11.39/11.59 tff(3094,plain,
% 11.39/11.59 (~m_or_h_gate_v_in1(c_e_h_1, c_g, s0)),
% 11.39/11.59 inference(unit_resolution,[status(thm)],[3093, 691, 3090])).
% 11.39/11.59 tff(3095,assumption,(m_or_h_gate_v_out(c_e_h_1, c_g, s1)), introduced(assumption)).
% 11.39/11.59 tff(3096,assumption,(m_or_h_gate_v_out(c_e_h_1, c_g, s0)), introduced(assumption)).
% 11.39/11.59 tff(3097,plain,
% 11.39/11.59 ((~![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s0))),
% 11.39/11.59 inference(quant_inst,[status(thm)],[])).
% 11.39/11.59 tff(3098,plain,
% 11.39/11.59 ($false),
% 11.39/11.59 inference(unit_resolution,[status(thm)],[3097, 660, 3096])).
% 11.39/11.59 tff(3099,plain,(~m_or_h_gate_v_out(c_e_h_1, c_g, s0)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.59 tff(3100,assumption,(node6(c_e_h_1, c_g, s0, s1)), introduced(assumption)).
% 11.39/11.59 tff(3101,plain,
% 11.39/11.59 (((~![Y: $i, I0: $i, X: $i, I1: $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_g, s1)) | (~node6(c_e_h_1, c_g, s0, s1)) | m_or_h_gate_v_out(c_e_h_1, 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_1, c_g, s1)) | (~node6(c_e_h_1, c_g, s0, s1)) | m_or_h_gate_v_out(c_e_h_1, c_g, s0))),
% 11.39/11.59 inference(rewrite,[status(thm)],[])).
% 11.39/11.59 tff(3102,plain,
% 11.39/11.59 (((~node6(c_e_h_1, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)) | m_or_h_gate_v_out(c_e_h_1, c_g, s0)) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_g, s1)) | (~node6(c_e_h_1, c_g, s0, s1)) | m_or_h_gate_v_out(c_e_h_1, c_g, s0))),
% 11.39/11.59 inference(rewrite,[status(thm)],[])).
% 11.39/11.59 tff(3103,plain,
% 11.39/11.59 (((~![Y: $i, I0: $i, X: $i, I1: $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_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)) | m_or_h_gate_v_out(c_e_h_1, 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_1, c_g, s1)) | (~node6(c_e_h_1, c_g, s0, s1)) | m_or_h_gate_v_out(c_e_h_1, c_g, s0)))),
% 11.39/11.59 inference(monotonicity,[status(thm)],[3102])).
% 11.39/11.59 tff(3104,plain,
% 11.39/11.59 (((~![Y: $i, I0: $i, X: $i, I1: $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_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)) | m_or_h_gate_v_out(c_e_h_1, 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_1, c_g, s1)) | (~node6(c_e_h_1, c_g, s0, s1)) | m_or_h_gate_v_out(c_e_h_1, c_g, s0))),
% 11.39/11.59 inference(transitivity,[status(thm)],[3103, 3101])).
% 11.39/11.59 tff(3105,plain,
% 11.39/11.59 ((~![Y: $i, I0: $i, X: $i, I1: $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_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)) | m_or_h_gate_v_out(c_e_h_1, c_g, s0))),
% 11.39/11.59 inference(quant_inst,[status(thm)],[])).
% 11.39/11.59 tff(3106,plain,
% 11.39/11.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)) | (~node6(c_e_h_1, c_g, s0, s1)) | m_or_h_gate_v_out(c_e_h_1, c_g, s0)),
% 11.39/11.59 inference(modus_ponens,[status(thm)],[3105, 3104])).
% 11.39/11.59 tff(3107,plain,
% 11.39/11.59 ($false),
% 11.39/11.59 inference(unit_resolution,[status(thm)],[3106, 742, 3100, 3099, 3095])).
% 11.39/11.59 tff(3108,plain,((~node6(c_e_h_1, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1))), inference(lemma,lemma(discharge,[]))).
% 11.39/11.59 tff(3109,plain,
% 11.39/11.59 (~node6(c_e_h_1, c_g, s0, s1)),
% 11.39/11.59 inference(unit_resolution,[status(thm)],[3108, 3095])).
% 11.39/11.59 tff(3110,plain,
% 11.39/11.59 (((~![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_1, c_g, s0, s1) | node6(c_e_h_1, 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_1, c_g, s0, s1) | node6(c_e_h_1, c_g, s0, s1))),
% 11.39/11.59 inference(rewrite,[status(thm)],[])).
% 11.39/11.59 tff(3111,plain,
% 11.39/11.59 ((node6(c_e_h_1, c_g, s0, s1) | node5(c_e_h_1, c_g, s0, s1) | (~trans(s0, s1))) <=> ((~trans(s0, s1)) | node5(c_e_h_1, c_g, s0, s1) | node6(c_e_h_1, c_g, s0, s1))),
% 11.39/11.59 inference(rewrite,[status(thm)],[])).
% 11.39/11.59 tff(3112,plain,
% 11.39/11.59 (((~![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_g, s0, s1) | node5(c_e_h_1, 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_1, c_g, s0, s1) | node6(c_e_h_1, c_g, s0, s1)))),
% 11.39/11.59 inference(monotonicity,[status(thm)],[3111])).
% 11.39/11.59 tff(3113,plain,
% 11.39/11.59 (((~![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_g, s0, s1) | node5(c_e_h_1, 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_1, c_g, s0, s1) | node6(c_e_h_1, c_g, s0, s1))),
% 11.39/11.59 inference(transitivity,[status(thm)],[3112, 3110])).
% 11.39/11.59 tff(3114,plain,
% 11.39/11.59 ((~![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_g, s0, s1) | node5(c_e_h_1, c_g, s0, s1) | (~trans(s0, s1)))),
% 11.39/11.59 inference(quant_inst,[status(thm)],[])).
% 11.39/11.59 tff(3115,plain,
% 11.39/11.59 ((~![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_1, c_g, s0, s1) | node6(c_e_h_1, c_g, s0, s1)),
% 11.39/11.59 inference(modus_ponens,[status(thm)],[3114, 3113])).
% 11.39/11.59 tff(3116,plain,
% 11.39/11.59 (node5(c_e_h_1, c_g, s0, s1) | node6(c_e_h_1, c_g, s0, s1)),
% 11.39/11.59 inference(unit_resolution,[status(thm)],[3115, 724, 100])).
% 11.39/11.59 tff(3117,plain,
% 11.39/11.59 (node5(c_e_h_1, c_g, s0, s1)),
% 11.39/11.59 inference(unit_resolution,[status(thm)],[3116, 3109])).
% 11.39/11.59 tff(3118,assumption,(m_and_h_gate_v_out(c_e_h_1, c_d, s0)), introduced(assumption)).
% 11.39/11.59 tff(3119,plain,
% 11.39/11.59 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s0))),
% 11.39/11.59 inference(quant_inst,[status(thm)],[])).
% 11.39/11.59 tff(3120,plain,
% 11.39/11.59 ($false),
% 11.39/11.59 inference(unit_resolution,[status(thm)],[3119, 260, 3118])).
% 11.39/11.59 tff(3121,plain,(~m_and_h_gate_v_out(c_e_h_1, c_d, s0)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.59 tff(3122,plain,
% 11.39/11.59 (((~![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_1, c_g, s0)) | m_and_h_gate_v_out(c_e_h_1, 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_1, c_g, s0)) | m_and_h_gate_v_out(c_e_h_1, c_d, s0))),
% 11.39/11.59 inference(rewrite,[status(thm)],[])).
% 11.39/11.59 tff(3123,plain,
% 11.39/11.59 ((~![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_1, c_g, s0)) | m_and_h_gate_v_out(c_e_h_1, c_d, s0))),
% 11.39/11.59 inference(quant_inst,[status(thm)],[])).
% 11.39/11.59 tff(3124,plain,
% 11.39/11.59 ((~![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_1, c_g, s0)) | m_and_h_gate_v_out(c_e_h_1, c_d, s0)),
% 11.39/11.59 inference(modus_ponens,[status(thm)],[3123, 3122])).
% 11.39/11.59 tff(3125,plain,
% 11.39/11.59 (~m_or_h_gate_v_in2(c_e_h_1, c_g, s0)),
% 11.39/11.59 inference(unit_resolution,[status(thm)],[3124, 675, 3121])).
% 11.39/11.59 tff(3126,plain,
% 11.39/11.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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_g, s1)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s0) | m_or_h_gate_v_in2(c_e_h_1, c_g, s0) | (~node5(c_e_h_1, 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_out(c_e_h_1, c_g, s1)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s0) | m_or_h_gate_v_in2(c_e_h_1, c_g, s0) | (~node5(c_e_h_1, c_g, s0, s1)))),
% 11.39/11.59 inference(rewrite,[status(thm)],[])).
% 11.39/11.59 tff(3127,plain,
% 11.39/11.59 ((m_or_h_gate_v_in1(c_e_h_1, c_g, s0) | m_or_h_gate_v_in2(c_e_h_1, c_g, s0) | (~node5(c_e_h_1, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1))) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_g, s1)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s0) | m_or_h_gate_v_in2(c_e_h_1, c_g, s0) | (~node5(c_e_h_1, c_g, s0, s1)))),
% 11.39/11.59 inference(rewrite,[status(thm)],[])).
% 11.39/11.59 tff(3128,plain,
% 11.39/11.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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_g, s0) | m_or_h_gate_v_in2(c_e_h_1, c_g, s0) | (~node5(c_e_h_1, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, 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_out(c_e_h_1, c_g, s1)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s0) | m_or_h_gate_v_in2(c_e_h_1, c_g, s0) | (~node5(c_e_h_1, c_g, s0, s1))))),
% 11.39/11.59 inference(monotonicity,[status(thm)],[3127])).
% 11.39/11.59 tff(3129,plain,
% 11.39/11.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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_g, s0) | m_or_h_gate_v_in2(c_e_h_1, c_g, s0) | (~node5(c_e_h_1, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, 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_out(c_e_h_1, c_g, s1)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s0) | m_or_h_gate_v_in2(c_e_h_1, c_g, s0) | (~node5(c_e_h_1, c_g, s0, s1)))),
% 11.39/11.59 inference(transitivity,[status(thm)],[3128, 3126])).
% 11.39/11.59 tff(3130,plain,
% 11.39/11.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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_g, s0) | m_or_h_gate_v_in2(c_e_h_1, c_g, s0) | (~node5(c_e_h_1, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)))),
% 11.39/11.59 inference(quant_inst,[status(thm)],[])).
% 11.39/11.59 tff(3131,plain,
% 11.39/11.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s0) | m_or_h_gate_v_in2(c_e_h_1, c_g, s0) | (~node5(c_e_h_1, c_g, s0, s1))),
% 11.39/11.59 inference(modus_ponens,[status(thm)],[3130, 3129])).
% 11.39/11.59 tff(3132,plain,
% 11.39/11.59 ($false),
% 11.39/11.59 inference(unit_resolution,[status(thm)],[3131, 705, 3125, 3117, 3095, 3094])).
% 11.39/11.59 tff(3133,plain,(~m_or_h_gate_v_out(c_e_h_1, c_g, s1)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.59 tff(3134,plain,
% 11.39/11.59 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | m_or_h_gate_v_out(c_e_h_1, c_g, s1))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | m_or_h_gate_v_out(c_e_h_1, c_g, s1))),
% 11.39/11.59 inference(rewrite,[status(thm)],[])).
% 11.39/11.59 tff(3135,plain,
% 11.39/11.59 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | m_or_h_gate_v_out(c_e_h_1, c_g, s1))),
% 11.39/11.59 inference(quant_inst,[status(thm)],[])).
% 11.39/11.59 tff(3136,plain,
% 11.39/11.59 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | m_or_h_gate_v_out(c_e_h_1, c_g, s1)),
% 11.39/11.59 inference(modus_ponens,[status(thm)],[3135, 3134])).
% 11.39/11.59 tff(3137,plain,
% 11.39/11.59 (~m_c_h_element_v_in1(c_e_h_1, c_h, s1)),
% 11.39/11.59 inference(unit_resolution,[status(thm)],[3136, 1380, 3133])).
% 11.39/11.59 tff(3138,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s1)), introduced(assumption)).
% 11.39/11.59 tff(3139,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s2)), introduced(assumption)).
% 11.39/11.59 tff(3140,assumption,(node18(c_e_h_1, c_h, s1, s2)), introduced(assumption)).
% 11.39/11.59 tff(3141,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s1)), introduced(assumption)).
% 11.39/11.59 tff(3142,plain,
% 11.39/11.59 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s0)) | m_or_h_gate_v_out(c_e_h_1, c_g, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s0)) | m_or_h_gate_v_out(c_e_h_1, c_g, s0))),
% 11.39/11.59 inference(rewrite,[status(thm)],[])).
% 11.39/11.59 tff(3143,plain,
% 11.39/11.59 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s0)) | m_or_h_gate_v_out(c_e_h_1, c_g, s0))),
% 11.39/11.59 inference(quant_inst,[status(thm)],[])).
% 11.39/11.59 tff(3144,plain,
% 11.39/11.59 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s0)) | m_or_h_gate_v_out(c_e_h_1, c_g, s0)),
% 11.39/11.59 inference(modus_ponens,[status(thm)],[3143, 3142])).
% 11.39/11.59 tff(3145,plain,
% 11.39/11.59 (~m_c_h_element_v_in1(c_e_h_1, c_h, s0)),
% 11.39/11.59 inference(unit_resolution,[status(thm)],[3144, 1380, 3099])).
% 11.39/11.59 tff(3146,assumption,(node14(c_e_h_1, c_h, s0, s1)), introduced(assumption)).
% 11.39/11.59 tff(3147,plain,
% 11.39/11.59 (((~![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_out(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~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_out(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~node14(c_e_h_1, c_h, s0, s1)))),
% 11.39/11.59 inference(rewrite,[status(thm)],[])).
% 11.39/11.59 tff(3148,plain,
% 11.39/11.59 (((~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_out(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~node14(c_e_h_1, c_h, s0, s1)))),
% 11.39/11.59 inference(rewrite,[status(thm)],[])).
% 11.39/11.59 tff(3149,plain,
% 11.39/11.59 (((~![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_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_out(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~node14(c_e_h_1, c_h, s0, s1))))),
% 11.39/11.59 inference(monotonicity,[status(thm)],[3148])).
% 11.39/11.59 tff(3150,plain,
% 11.39/11.59 (((~![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_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_out(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~node14(c_e_h_1, c_h, s0, s1)))),
% 11.39/11.59 inference(transitivity,[status(thm)],[3149, 3147])).
% 11.39/11.59 tff(3151,plain,
% 11.39/11.59 ((~![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_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)))),
% 11.39/11.59 inference(quant_inst,[status(thm)],[])).
% 11.39/11.59 tff(3152,plain,
% 11.39/11.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~node14(c_e_h_1, c_h, s0, s1))),
% 11.39/11.59 inference(modus_ponens,[status(thm)],[3151, 3150])).
% 11.39/11.59 tff(3153,plain,
% 11.39/11.59 ($false),
% 11.39/11.59 inference(unit_resolution,[status(thm)],[3152, 427, 3141, 3146, 3145])).
% 11.39/11.59 tff(3154,plain,((~node14(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,[]))).
% 11.39/11.59 tff(3155,plain,
% 11.39/11.59 (~node14(c_e_h_1, c_h, s0, s1)),
% 11.39/11.59 inference(unit_resolution,[status(thm)],[3154, 3141])).
% 11.39/11.59 tff(3156,plain,
% 11.39/11.59 (((~![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))),
% 11.39/11.59 inference(rewrite,[status(thm)],[])).
% 11.39/11.59 tff(3157,plain,
% 11.39/11.59 ((~![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))),
% 11.39/11.59 inference(quant_inst,[status(thm)],[])).
% 11.39/11.59 tff(3158,plain,
% 11.39/11.59 ((~![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)),
% 11.39/11.59 inference(modus_ponens,[status(thm)],[3157, 3156])).
% 11.39/11.59 tff(3159,plain,
% 11.39/11.59 (~m_c_h_element_v_in2(c_e_h_1, c_h, s0)),
% 11.39/11.59 inference(unit_resolution,[status(thm)],[3158, 1117, 2898])).
% 11.39/11.59 tff(3160,plain,
% 11.39/11.59 (((~![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_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))),
% 11.39/11.59 inference(rewrite,[status(thm)],[])).
% 11.39/11.59 tff(3161,plain,
% 11.39/11.59 ((~![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_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))),
% 11.39/11.60 inference(quant_inst,[status(thm)],[])).
% 11.39/11.60 tff(3162,plain,
% 11.39/11.60 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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)),
% 11.39/11.60 inference(modus_ponens,[status(thm)],[3161, 3160])).
% 11.39/11.60 tff(3163,plain,
% 11.39/11.60 ((~node16(c_e_h_1, c_h, s0)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0)),
% 11.39/11.60 inference(unit_resolution,[status(thm)],[3162, 377, 3159])).
% 11.39/11.60 tff(3164,plain,
% 11.39/11.60 (~node16(c_e_h_1, c_h, s0)),
% 11.39/11.60 inference(unit_resolution,[status(thm)],[3163, 3145])).
% 11.39/11.60 tff(3165,plain,
% 11.39/11.60 (((~![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))),
% 11.39/11.60 inference(rewrite,[status(thm)],[])).
% 11.39/11.60 tff(3166,plain,
% 11.39/11.60 ((~![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))),
% 11.39/11.60 inference(quant_inst,[status(thm)],[])).
% 11.39/11.60 tff(3167,plain,
% 11.39/11.60 ((~![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)),
% 11.39/11.60 inference(modus_ponens,[status(thm)],[3166, 3165])).
% 11.39/11.60 tff(3168,plain,
% 11.39/11.60 (node19(c_e_h_1, c_h, s0, s1)),
% 11.39/11.60 inference(unit_resolution,[status(thm)],[3167, 312, 100])).
% 11.39/11.60 tff(3169,plain,
% 11.39/11.60 (((~![Y: $i, I0: $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, 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)))) <=> ((~![Y: $i, I0: $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, 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)))),
% 11.39/11.60 inference(rewrite,[status(thm)],[])).
% 11.39/11.60 tff(3170,plain,
% 11.39/11.60 ((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))) <=> (node14(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)))),
% 11.39/11.60 inference(rewrite,[status(thm)],[])).
% 11.39/11.60 tff(3171,plain,
% 11.39/11.60 (((~![Y: $i, I0: $i, X: $i, I1: $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)))) | (node14(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))))),
% 11.39/11.60 inference(monotonicity,[status(thm)],[3170])).
% 11.39/11.60 tff(3172,plain,
% 11.39/11.60 (((~![Y: $i, I0: $i, X: $i, I1: $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)))) | node14(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)))),
% 11.39/11.60 inference(transitivity,[status(thm)],[3171, 3169])).
% 11.39/11.60 tff(3173,plain,
% 11.39/11.60 ((~![Y: $i, I0: $i, X: $i, I1: $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)))),
% 11.39/11.60 inference(quant_inst,[status(thm)],[])).
% 11.39/11.60 tff(3174,plain,
% 11.39/11.60 ((~![Y: $i, I0: $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, 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))),
% 11.39/11.60 inference(modus_ponens,[status(thm)],[3173, 3172])).
% 11.39/11.60 tff(3175,plain,
% 11.39/11.60 (node14(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)),
% 11.39/11.60 inference(unit_resolution,[status(thm)],[3174, 409, 3168])).
% 11.39/11.60 tff(3176,plain,
% 11.39/11.60 (node14(c_e_h_1, c_h, s0, s1) | node15(c_e_h_1, c_h, s0, s1)),
% 11.39/11.60 inference(unit_resolution,[status(thm)],[3175, 3164])).
% 11.39/11.60 tff(3177,plain,
% 11.39/11.60 (node15(c_e_h_1, c_h, s0, s1)),
% 11.39/11.60 inference(unit_resolution,[status(thm)],[3176, 3155])).
% 11.39/11.60 tff(3178,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s0)), introduced(assumption)).
% 11.39/11.60 tff(3179,plain,
% 11.39/11.60 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s0))),
% 11.39/11.60 inference(quant_inst,[status(thm)],[])).
% 11.39/11.60 tff(3180,plain,
% 11.39/11.60 ($false),
% 11.39/11.60 inference(unit_resolution,[status(thm)],[3179, 189, 3178])).
% 11.39/11.60 tff(3181,plain,(~m_c_h_element_v_out(c_e_h_1, c_h, s0)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.60 tff(3182,plain,
% 11.39/11.60 (((~![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_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))),
% 11.39/11.60 inference(rewrite,[status(thm)],[])).
% 11.39/11.60 tff(3183,plain,
% 11.39/11.60 ((~![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_h, s1)) | (~node15(c_e_h_1, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s0))),
% 11.39/11.60 inference(quant_inst,[status(thm)],[])).
% 11.39/11.60 tff(3184,plain,
% 11.39/11.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | (~node15(c_e_h_1, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s0)),
% 11.39/11.60 inference(modus_ponens,[status(thm)],[3183, 3182])).
% 11.39/11.60 tff(3185,plain,
% 11.39/11.60 ($false),
% 11.39/11.60 inference(unit_resolution,[status(thm)],[3184, 393, 3181, 3141, 3177])).
% 11.39/11.60 tff(3186,plain,(~m_c_h_element_v_out(c_e_h_1, c_h, s1)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.60 tff(3187,plain,
% 11.39/11.60 (((~![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, s1) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | (~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)))) | 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, s2)) | (~node18(c_e_h_1, c_h, s1, s2)))),
% 11.39/11.60 inference(rewrite,[status(thm)],[])).
% 11.39/11.60 tff(3188,plain,
% 11.39/11.60 (((~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))) <=> (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, s2)) | (~node18(c_e_h_1, c_h, s1, s2)))),
% 11.39/11.60 inference(rewrite,[status(thm)],[])).
% 11.39/11.60 tff(3189,plain,
% 11.39/11.60 (((~![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, 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)))) | (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, s2)) | (~node18(c_e_h_1, c_h, s1, s2))))),
% 11.39/11.60 inference(monotonicity,[status(thm)],[3188])).
% 11.39/11.60 tff(3190,plain,
% 11.39/11.60 (((~![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, 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)))) | 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, s2)) | (~node18(c_e_h_1, c_h, s1, s2)))),
% 11.39/11.60 inference(transitivity,[status(thm)],[3189, 3187])).
% 11.39/11.60 tff(3191,plain,
% 11.39/11.60 ((~![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, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1) | (~node18(c_e_h_1, c_h, s1, s2)))),
% 11.39/11.60 inference(quant_inst,[status(thm)],[])).
% 11.39/11.60 tff(3192,plain,
% 11.39/11.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s1) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | (~node18(c_e_h_1, c_h, s1, s2))),
% 11.39/11.60 inference(modus_ponens,[status(thm)],[3191, 3190])).
% 11.39/11.60 tff(3193,plain,
% 11.39/11.60 ($false),
% 11.39/11.60 inference(unit_resolution,[status(thm)],[3192, 296, 3186, 3139, 3140])).
% 11.39/11.60 tff(3194,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,[]))).
% 11.39/11.60 tff(3195,plain,
% 11.39/11.60 (~node18(c_e_h_1, c_h, s1, s2)),
% 11.39/11.60 inference(unit_resolution,[status(thm)],[3194, 3139])).
% 11.39/11.60 tff(3196,plain,
% 11.39/11.60 (((~![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))),
% 11.39/11.60 inference(rewrite,[status(thm)],[])).
% 11.39/11.60 tff(3197,plain,
% 11.39/11.60 ((~![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))),
% 11.39/11.60 inference(quant_inst,[status(thm)],[])).
% 11.39/11.60 tff(3198,plain,
% 11.39/11.60 ((~![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)),
% 11.39/11.60 inference(modus_ponens,[status(thm)],[3197, 3196])).
% 11.39/11.60 tff(3199,plain,
% 11.39/11.60 (node19(c_e_h_1, c_h, s1, s2)),
% 11.39/11.60 inference(unit_resolution,[status(thm)],[3198, 312, 470])).
% 11.39/11.60 tff(3200,plain,
% 11.39/11.60 (((~![Y: $i, 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)))) | 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)))),
% 11.39/11.60 inference(rewrite,[status(thm)],[])).
% 11.39/11.60 tff(3201,plain,
% 11.39/11.60 ((~![Y: $i, 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)))),
% 11.39/11.60 inference(quant_inst,[status(thm)],[])).
% 11.39/11.60 tff(3202,plain,
% 11.39/11.60 ((~![Y: $i, 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))),
% 11.39/11.60 inference(modus_ponens,[status(thm)],[3201, 3200])).
% 11.39/11.60 tff(3203,plain,
% 11.39/11.60 (node17(c_e_h_1, c_h, s1) | node18(c_e_h_1, c_h, s1, s2)),
% 11.39/11.60 inference(unit_resolution,[status(thm)],[3202, 326, 3199])).
% 11.39/11.60 tff(3204,plain,
% 11.39/11.60 (node17(c_e_h_1, c_h, s1)),
% 11.39/11.60 inference(unit_resolution,[status(thm)],[3203, 3195])).
% 11.39/11.60 tff(3205,plain,
% 11.39/11.60 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, 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, s1)) | m_c_h_element_v_in1(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)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~node17(c_e_h_1, c_h, s1)))),
% 11.39/11.60 inference(rewrite,[status(thm)],[])).
% 11.39/11.60 tff(3206,plain,
% 11.39/11.60 ((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))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~node17(c_e_h_1, c_h, s1)))),
% 11.39/11.60 inference(rewrite,[status(thm)],[])).
% 11.39/11.60 tff(3207,plain,
% 11.39/11.60 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~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)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~node17(c_e_h_1, c_h, s1))))),
% 11.39/11.60 inference(monotonicity,[status(thm)],[3206])).
% 11.39/11.60 tff(3208,plain,
% 11.39/11.60 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~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)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~node17(c_e_h_1, c_h, s1)))),
% 11.39/11.60 inference(transitivity,[status(thm)],[3207, 3205])).
% 11.39/11.60 tff(3209,plain,
% 11.39/11.60 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~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)))),
% 11.39/11.60 inference(quant_inst,[status(thm)],[])).
% 11.39/11.60 tff(3210,plain,
% 11.39/11.60 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, 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, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~node17(c_e_h_1, c_h, s1))),
% 11.39/11.60 inference(modus_ponens,[status(thm)],[3209, 3208])).
% 11.39/11.60 tff(3211,plain,
% 11.39/11.60 ((~m_c_h_element_v_in2(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1)),
% 11.39/11.60 inference(unit_resolution,[status(thm)],[3210, 2125, 3204])).
% 11.39/11.60 tff(3212,plain,
% 11.39/11.60 (~m_c_h_element_v_in2(c_e_h_1, c_h, s1)),
% 11.39/11.60 inference(unit_resolution,[status(thm)],[3211, 3138])).
% 11.39/11.60 tff(3213,assumption,(~node16(c_e_h_1, c_h, s1)), introduced(assumption)).
% 11.39/11.60 tff(3214,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s1)), introduced(assumption)).
% 11.39/11.60 tff(3215,plain,
% 11.39/11.60 (((~![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_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))),
% 11.39/11.60 inference(rewrite,[status(thm)],[])).
% 11.39/11.60 tff(3216,plain,
% 11.39/11.60 ((~![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_h, s2)) | (~node15(c_e_h_1, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1))),
% 11.39/11.60 inference(quant_inst,[status(thm)],[])).
% 11.39/11.60 tff(3217,plain,
% 11.39/11.60 ((~![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_h, s2)) | (~node15(c_e_h_1, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1)),
% 11.39/11.60 inference(modus_ponens,[status(thm)],[3216, 3215])).
% 11.39/11.60 tff(3218,plain,
% 11.39/11.60 ((~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)),
% 11.39/11.60 inference(unit_resolution,[status(thm)],[3217, 393])).
% 11.39/11.60 tff(3219,plain,
% 11.39/11.60 (~node15(c_e_h_1, c_h, s1, s2)),
% 11.39/11.60 inference(unit_resolution,[status(thm)],[3218, 3139, 3214])).
% 11.39/11.60 tff(3220,plain,
% 11.39/11.60 (((~![Y: $i, I0: $i, X: $i, I1: $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) | node15(c_e_h_1, c_h, s1, s2) | 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)))) | node16(c_e_h_1, c_h, s1) | node15(c_e_h_1, c_h, s1, s2) | node14(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)))),
% 11.39/11.60 inference(rewrite,[status(thm)],[])).
% 11.39/11.60 tff(3221,plain,
% 11.39/11.60 ((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))) <=> (node16(c_e_h_1, c_h, s1) | node15(c_e_h_1, c_h, s1, s2) | node14(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)))),
% 11.39/11.60 inference(rewrite,[status(thm)],[])).
% 11.39/11.60 tff(3222,plain,
% 11.39/11.60 (((~![Y: $i, I0: $i, X: $i, I1: $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)))) | (node16(c_e_h_1, c_h, s1) | node15(c_e_h_1, c_h, s1, s2) | node14(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2))))),
% 11.39/11.60 inference(monotonicity,[status(thm)],[3221])).
% 11.39/11.60 tff(3223,plain,
% 11.39/11.60 (((~![Y: $i, I0: $i, X: $i, I1: $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)))) | node16(c_e_h_1, c_h, s1) | node15(c_e_h_1, c_h, s1, s2) | node14(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)))),
% 11.39/11.60 inference(transitivity,[status(thm)],[3222, 3220])).
% 11.39/11.60 tff(3224,plain,
% 11.39/11.60 ((~![Y: $i, I0: $i, X: $i, I1: $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)))),
% 11.39/11.60 inference(quant_inst,[status(thm)],[])).
% 11.39/11.60 tff(3225,plain,
% 11.39/11.60 ((~![Y: $i, I0: $i, X: $i, I1: $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) | node15(c_e_h_1, c_h, s1, s2) | node14(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2))),
% 11.39/11.60 inference(modus_ponens,[status(thm)],[3224, 3223])).
% 11.39/11.60 tff(3226,plain,
% 11.39/11.60 (node16(c_e_h_1, c_h, s1) | node15(c_e_h_1, c_h, s1, s2) | node14(c_e_h_1, c_h, s1, s2)),
% 11.39/11.60 inference(unit_resolution,[status(thm)],[3225, 409, 3199])).
% 11.39/11.60 tff(3227,plain,
% 11.39/11.60 (node14(c_e_h_1, c_h, s1, s2)),
% 11.39/11.60 inference(unit_resolution,[status(thm)],[3226, 3219, 3213])).
% 11.39/11.60 tff(3228,plain,
% 11.39/11.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_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, s1) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | (~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_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | (~node14(c_e_h_1, c_h, s1, s2)))),
% 11.39/11.60 inference(rewrite,[status(thm)],[])).
% 11.39/11.60 tff(3229,plain,
% 11.39/11.60 (((~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_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | (~node14(c_e_h_1, c_h, s1, s2)))),
% 11.39/11.60 inference(rewrite,[status(thm)],[])).
% 11.39/11.60 tff(3230,plain,
% 11.39/11.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | (~node14(c_e_h_1, c_h, s1, s2))))),
% 11.39/11.60 inference(monotonicity,[status(thm)],[3229])).
% 11.39/11.60 tff(3231,plain,
% 11.39/11.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | (~node14(c_e_h_1, c_h, s1, s2)))),
% 11.39/11.60 inference(transitivity,[status(thm)],[3230, 3228])).
% 11.39/11.60 tff(3232,plain,
% 11.39/11.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))),
% 11.39/11.60 inference(quant_inst,[status(thm)],[])).
% 11.39/11.60 tff(3233,plain,
% 11.39/11.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | (~node14(c_e_h_1, c_h, s1, s2))),
% 11.39/11.60 inference(modus_ponens,[status(thm)],[3232, 3231])).
% 11.39/11.60 tff(3234,plain,
% 11.39/11.60 ($false),
% 11.39/11.60 inference(unit_resolution,[status(thm)],[3233, 427, 3139, 3138, 3227])).
% 11.39/11.60 tff(3235,plain,((~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) | node16(c_e_h_1, c_h, s1) | m_c_h_element_v_out(c_e_h_1, c_h, s1)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.60 tff(3236,plain,
% 11.39/11.60 ((~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) | node16(c_e_h_1, c_h, s1)),
% 11.39/11.60 inference(unit_resolution,[status(thm)],[3235, 3186])).
% 11.39/11.60 tff(3237,plain,
% 11.39/11.60 (node16(c_e_h_1, c_h, s1)),
% 11.39/11.60 inference(unit_resolution,[status(thm)],[3236, 3138, 3139])).
% 11.39/11.60 tff(3238,plain,
% 11.39/11.60 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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))),
% 11.39/11.60 inference(rewrite,[status(thm)],[])).
% 11.39/11.60 tff(3239,plain,
% 11.39/11.60 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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))),
% 11.39/11.60 inference(quant_inst,[status(thm)],[])).
% 11.39/11.60 tff(3240,plain,
% 11.39/11.60 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | m_c_h_element_v_in2(c_e_h_1, c_h, s1)),
% 11.39/11.60 inference(modus_ponens,[status(thm)],[3239, 3238])).
% 11.39/11.60 tff(3241,plain,
% 11.39/11.60 ($false),
% 11.39/11.60 inference(unit_resolution,[status(thm)],[3240, 377, 3138, 3237, 3212])).
% 11.39/11.60 tff(3242,plain,(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))), inference(lemma,lemma(discharge,[]))).
% 11.39/11.60 tff(3243,plain,
% 11.39/11.60 (~m_c_h_element_v_out(c_e_h_1, c_h, s2)),
% 11.39/11.60 inference(unit_resolution,[status(thm)],[3242, 3137])).
% 11.39/11.60 tff(3244,plain,
% 11.39/11.60 (((~![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, 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)))),
% 11.39/11.61 inference(rewrite,[status(thm)],[])).
% 11.39/11.61 tff(3245,plain,
% 11.39/11.61 (((~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)))),
% 11.39/11.61 inference(rewrite,[status(thm)],[])).
% 11.39/11.61 tff(3246,plain,
% 11.39/11.61 (((~![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_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))))),
% 11.39/11.61 inference(monotonicity,[status(thm)],[3245])).
% 11.39/11.61 tff(3247,plain,
% 11.39/11.61 (((~![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_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)))),
% 11.39/11.61 inference(transitivity,[status(thm)],[3246, 3244])).
% 11.39/11.61 tff(3248,plain,
% 11.39/11.61 ((~![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_h, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s2) | (~node18(c_e_h_1, c_h, s2, s3)))),
% 11.39/11.61 inference(quant_inst,[status(thm)],[])).
% 11.39/11.61 tff(3249,plain,
% 11.39/11.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node18(c_e_h_1, c_h, s2, s3))),
% 11.39/11.61 inference(modus_ponens,[status(thm)],[3248, 3247])).
% 11.39/11.61 tff(3250,plain,
% 11.39/11.61 ($false),
% 11.39/11.61 inference(unit_resolution,[status(thm)],[3249, 296, 3243, 3085, 3086])).
% 11.39/11.61 tff(3251,plain,((~node18(c_e_h_1, c_h, s2, s3)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3))), inference(lemma,lemma(discharge,[]))).
% 11.39/11.61 tff(3252,plain,
% 11.39/11.61 (~node18(c_e_h_1, c_h, s2, s3)),
% 11.39/11.61 inference(unit_resolution,[status(thm)],[3251, 3085])).
% 11.39/11.61 tff(3253,plain,
% 11.39/11.61 (((~![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))),
% 11.39/11.61 inference(rewrite,[status(thm)],[])).
% 11.39/11.61 tff(3254,plain,
% 11.39/11.61 ((~![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))),
% 11.39/11.61 inference(quant_inst,[status(thm)],[])).
% 11.39/11.61 tff(3255,plain,
% 11.39/11.61 ((~![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)),
% 11.39/11.61 inference(modus_ponens,[status(thm)],[3254, 3253])).
% 11.39/11.61 tff(3256,plain,
% 11.39/11.61 (node19(c_e_h_1, c_h, s2, s3)),
% 11.39/11.61 inference(unit_resolution,[status(thm)],[3255, 312, 604])).
% 11.39/11.61 tff(3257,plain,
% 11.39/11.61 (((~![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, s2) | (~node19(c_e_h_1, c_h, s2, s3)) | node18(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) | (~node19(c_e_h_1, c_h, s2, s3)) | node18(c_e_h_1, c_h, s2, s3))),
% 11.39/11.61 inference(rewrite,[status(thm)],[])).
% 11.39/11.61 tff(3258,plain,
% 11.39/11.61 ((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))) <=> (node17(c_e_h_1, c_h, s2) | (~node19(c_e_h_1, c_h, s2, s3)) | node18(c_e_h_1, c_h, s2, s3))),
% 11.39/11.61 inference(rewrite,[status(thm)],[])).
% 11.39/11.61 tff(3259,plain,
% 11.39/11.61 (((~![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, 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) | (~node19(c_e_h_1, c_h, s2, s3)) | node18(c_e_h_1, c_h, s2, s3)))),
% 11.39/11.61 inference(monotonicity,[status(thm)],[3258])).
% 11.39/11.61 tff(3260,plain,
% 11.39/11.61 (((~![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, 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) | (~node19(c_e_h_1, c_h, s2, s3)) | node18(c_e_h_1, c_h, s2, s3))),
% 11.39/11.61 inference(transitivity,[status(thm)],[3259, 3257])).
% 11.39/11.61 tff(3261,plain,
% 11.39/11.61 ((~![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, s2) | node18(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))),
% 11.39/11.61 inference(quant_inst,[status(thm)],[])).
% 11.39/11.61 tff(3262,plain,
% 11.39/11.61 ((~![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, s2) | (~node19(c_e_h_1, c_h, s2, s3)) | node18(c_e_h_1, c_h, s2, s3)),
% 11.39/11.61 inference(modus_ponens,[status(thm)],[3261, 3260])).
% 11.39/11.61 tff(3263,plain,
% 11.39/11.61 (node17(c_e_h_1, c_h, s2) | node18(c_e_h_1, c_h, s2, s3)),
% 11.39/11.61 inference(unit_resolution,[status(thm)],[3262, 326, 3256])).
% 11.39/11.61 tff(3264,plain,
% 11.39/11.61 (node17(c_e_h_1, c_h, s2)),
% 11.39/11.61 inference(unit_resolution,[status(thm)],[3263, 3252])).
% 11.39/11.61 tff(3265,plain,
% 11.39/11.61 (((~![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)))) | ((~node17(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] : ((~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, 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))),
% 11.39/11.61 inference(rewrite,[status(thm)],[])).
% 11.39/11.61 tff(3266,plain,
% 11.39/11.61 (((~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))) <=> ((~node17(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))),
% 11.39/11.61 inference(rewrite,[status(thm)],[])).
% 11.39/11.61 tff(3267,plain,
% 11.39/11.61 (((~![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, 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)))) | ((~node17(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)))),
% 11.39/11.61 inference(monotonicity,[status(thm)],[3266])).
% 11.39/11.61 tff(3268,plain,
% 11.39/11.61 (((~![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, 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)))) | (~node17(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))),
% 11.39/11.61 inference(transitivity,[status(thm)],[3267, 3265])).
% 11.39/11.61 tff(3269,plain,
% 11.39/11.61 ((~![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, s2)) | m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~node17(c_e_h_1, c_h, s2)))),
% 11.39/11.61 inference(quant_inst,[status(thm)],[])).
% 11.39/11.61 tff(3270,plain,
% 11.39/11.61 ((~![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)))) | (~node17(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)),
% 11.39/11.61 inference(modus_ponens,[status(thm)],[3269, 3268])).
% 11.39/11.61 tff(3271,plain,
% 11.39/11.61 ((~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)),
% 11.39/11.61 inference(unit_resolution,[status(thm)],[3270, 359, 3264])).
% 11.39/11.61 tff(3272,plain,
% 11.39/11.61 (~m_c_h_element_v_in1(c_e_h_1, c_h, s2)),
% 11.39/11.61 inference(unit_resolution,[status(thm)],[3271, 3084])).
% 11.39/11.61 tff(3273,assumption,(node15(c_e_h_1, c_h, s2, s3)), introduced(assumption)).
% 11.39/11.61 tff(3274,plain,
% 11.39/11.61 (((~![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, 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))),
% 11.39/11.61 inference(rewrite,[status(thm)],[])).
% 11.39/11.61 tff(3275,plain,
% 11.39/11.61 ((~![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, s3)) | (~node15(c_e_h_1, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s2))),
% 11.39/11.61 inference(quant_inst,[status(thm)],[])).
% 11.39/11.61 tff(3276,plain,
% 11.39/11.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node15(c_e_h_1, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s2)),
% 11.39/11.61 inference(modus_ponens,[status(thm)],[3275, 3274])).
% 11.39/11.61 tff(3277,plain,
% 11.39/11.61 ($false),
% 11.39/11.61 inference(unit_resolution,[status(thm)],[3276, 393, 3243, 3085, 3273])).
% 11.39/11.61 tff(3278,plain,((~node15(c_e_h_1, c_h, s2, s3)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3))), inference(lemma,lemma(discharge,[]))).
% 11.39/11.61 tff(3279,plain,
% 11.39/11.61 (~node15(c_e_h_1, c_h, s2, s3)),
% 11.39/11.61 inference(unit_resolution,[status(thm)],[3278, 3085])).
% 11.39/11.61 tff(3280,plain,
% 11.39/11.61 (((~![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, 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))),
% 11.39/11.61 inference(rewrite,[status(thm)],[])).
% 11.39/11.61 tff(3281,plain,
% 11.39/11.61 ((~![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, 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))),
% 11.39/11.61 inference(quant_inst,[status(thm)],[])).
% 11.39/11.61 tff(3282,plain,
% 11.39/11.61 ((~![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, 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)),
% 11.39/11.61 inference(modus_ponens,[status(thm)],[3281, 3280])).
% 11.39/11.61 tff(3283,plain,
% 11.39/11.61 (~node16(c_e_h_1, c_h, s2)),
% 11.39/11.61 inference(unit_resolution,[status(thm)],[3282, 377, 3272, 3084])).
% 11.39/11.61 tff(3284,plain,
% 11.39/11.61 (((~![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, s2) | node14(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)) | node15(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) | node14(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)) | node15(c_e_h_1, c_h, s2, s3))),
% 11.39/11.61 inference(rewrite,[status(thm)],[])).
% 11.39/11.61 tff(3285,plain,
% 11.39/11.61 ((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) | node14(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)) | node15(c_e_h_1, c_h, s2, s3))),
% 11.39/11.61 inference(rewrite,[status(thm)],[])).
% 11.39/11.61 tff(3286,plain,
% 11.39/11.61 (((~![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, 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) | node14(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)) | node15(c_e_h_1, c_h, s2, s3)))),
% 11.39/11.61 inference(monotonicity,[status(thm)],[3285])).
% 11.39/11.61 tff(3287,plain,
% 11.39/11.61 (((~![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, 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) | node14(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)) | node15(c_e_h_1, c_h, s2, s3))),
% 11.39/11.61 inference(transitivity,[status(thm)],[3286, 3284])).
% 11.39/11.61 tff(3288,plain,
% 11.39/11.61 ((~![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, 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)))),
% 11.39/11.61 inference(quant_inst,[status(thm)],[])).
% 11.39/11.61 tff(3289,plain,
% 11.39/11.61 ((~![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, s2) | node14(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)) | node15(c_e_h_1, c_h, s2, s3)),
% 11.39/11.61 inference(modus_ponens,[status(thm)],[3288, 3287])).
% 11.39/11.61 tff(3290,plain,
% 11.39/11.61 (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)),
% 11.39/11.61 inference(unit_resolution,[status(thm)],[3289, 409, 3256])).
% 11.39/11.61 tff(3291,plain,
% 11.39/11.61 (node14(c_e_h_1, c_h, s2, s3)),
% 11.39/11.61 inference(unit_resolution,[status(thm)],[3290, 3283, 3279])).
% 11.39/11.61 tff(3292,plain,
% 11.39/11.61 (((~![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, 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)))),
% 11.39/11.61 inference(rewrite,[status(thm)],[])).
% 11.39/11.61 tff(3293,plain,
% 11.39/11.61 (((~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)))),
% 11.39/11.61 inference(rewrite,[status(thm)],[])).
% 11.39/11.61 tff(3294,plain,
% 11.39/11.61 (((~![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, 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))))),
% 11.39/11.61 inference(monotonicity,[status(thm)],[3293])).
% 11.39/11.61 tff(3295,plain,
% 11.39/11.61 (((~![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, 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)))),
% 11.39/11.61 inference(transitivity,[status(thm)],[3294, 3292])).
% 11.39/11.61 tff(3296,plain,
% 11.39/11.61 ((~![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, 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)))),
% 11.39/11.61 inference(quant_inst,[status(thm)],[])).
% 11.39/11.61 tff(3297,plain,
% 11.39/11.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node14(c_e_h_1, c_h, s2, s3))),
% 11.39/11.61 inference(modus_ponens,[status(thm)],[3296, 3295])).
% 11.39/11.61 tff(3298,plain,
% 11.39/11.61 ($false),
% 11.39/11.61 inference(unit_resolution,[status(thm)],[3297, 427, 3085, 3291, 3272])).
% 11.39/11.61 tff(3299,plain,(m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3))), inference(lemma,lemma(discharge,[]))).
% 11.39/11.61 tff(3300,plain,
% 11.39/11.61 (~m_c_h_element_v_out(c_e_h_1, c_h, s3)),
% 11.39/11.61 inference(unit_resolution,[status(thm)],[3299, 3083])).
% 11.39/11.61 tff(3301,plain,
% 11.39/11.61 (((~![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))),
% 11.39/11.61 inference(rewrite,[status(thm)],[])).
% 11.39/11.61 tff(3302,plain,
% 11.39/11.61 ((~![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))),
% 11.39/11.61 inference(quant_inst,[status(thm)],[])).
% 11.39/11.61 tff(3303,plain,
% 11.39/11.61 ((~![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)),
% 11.39/11.61 inference(modus_ponens,[status(thm)],[3302, 3301])).
% 11.39/11.61 tff(3304,plain,
% 11.39/11.61 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s3)),
% 11.39/11.61 inference(unit_resolution,[status(thm)],[3303, 503, 3300])).
% 11.39/11.61 tff(3305,plain,
% 11.39/11.61 (((~![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_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))),
% 11.39/11.61 inference(rewrite,[status(thm)],[])).
% 11.39/11.61 tff(3306,plain,
% 11.39/11.61 ((~![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_i, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s3))),
% 11.39/11.61 inference(quant_inst,[status(thm)],[])).
% 11.39/11.61 tff(3307,plain,
% 11.39/11.61 ((~![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_i, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s3)),
% 11.39/11.61 inference(modus_ponens,[status(thm)],[3306, 3305])).
% 11.39/11.61 tff(3308,plain,
% 11.39/11.61 (~node20(c_e_h_1, c_i, s3)),
% 11.39/11.61 inference(unit_resolution,[status(thm)],[3307, 213, 3304])).
% 11.39/11.61 tff(3309,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s4)), introduced(assumption)).
% 11.39/11.61 tff(3310,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s3)), introduced(assumption)).
% 11.39/11.61 tff(3311,assumption,(node22(c_e_h_1, c_i, s2, s3)), introduced(assumption)).
% 11.39/11.61 tff(3312,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s2)), introduced(assumption)).
% 11.39/11.61 tff(3313,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s1)), introduced(assumption)).
% 11.39/11.61 tff(3314,plain,
% 11.39/11.61 (((~![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))),
% 11.39/11.61 inference(rewrite,[status(thm)],[])).
% 11.39/11.61 tff(3315,plain,
% 11.39/11.61 ((~![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))),
% 11.39/11.61 inference(quant_inst,[status(thm)],[])).
% 11.39/11.61 tff(3316,plain,
% 11.39/11.61 ((~![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)),
% 11.39/11.61 inference(modus_ponens,[status(thm)],[3315, 3314])).
% 11.39/11.61 tff(3317,plain,
% 11.39/11.61 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s0)),
% 11.39/11.61 inference(unit_resolution,[status(thm)],[3316, 503, 3181])).
% 11.39/11.61 tff(3318,plain,
% 11.39/11.61 (((~![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_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))),
% 11.39/11.61 inference(rewrite,[status(thm)],[])).
% 11.39/11.61 tff(3319,plain,
% 11.39/11.61 ((~![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_i, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s0))),
% 11.39/11.61 inference(quant_inst,[status(thm)],[])).
% 11.39/11.61 tff(3320,plain,
% 11.39/11.61 ((~![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_i, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s0)),
% 11.39/11.61 inference(modus_ponens,[status(thm)],[3319, 3318])).
% 11.39/11.61 tff(3321,plain,
% 11.39/11.61 (~node20(c_e_h_1, c_i, s0)),
% 11.39/11.61 inference(unit_resolution,[status(thm)],[3320, 213, 3317])).
% 11.39/11.61 tff(3322,plain,
% 11.39/11.61 (((~![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_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)))) | 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)))),
% 11.39/11.61 inference(rewrite,[status(thm)],[])).
% 11.39/11.61 tff(3323,plain,
% 11.39/11.61 ((~![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_i, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | (~node21(c_e_h_1, c_i, s0, s1)))),
% 11.39/11.61 inference(quant_inst,[status(thm)],[])).
% 11.39/11.61 tff(3324,plain,
% 11.39/11.61 ((~![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_i, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | (~node21(c_e_h_1, c_i, s0, s1))),
% 11.39/11.61 inference(modus_ponens,[status(thm)],[3323, 3322])).
% 11.39/11.61 tff(3325,plain,
% 11.39/11.61 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | (~node21(c_e_h_1, c_i, s0, s1))),
% 11.39/11.61 inference(unit_resolution,[status(thm)],[3324, 228, 3321])).
% 11.39/11.61 tff(3326,plain,
% 11.39/11.61 (~node21(c_e_h_1, c_i, s0, s1)),
% 11.39/11.61 inference(unit_resolution,[status(thm)],[3325, 3313])).
% 11.39/11.61 tff(3327,plain,
% 11.39/11.61 (((~![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))),
% 11.39/11.61 inference(rewrite,[status(thm)],[])).
% 11.39/11.61 tff(3328,plain,
% 11.39/11.61 ((~![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))),
% 11.39/11.61 inference(quant_inst,[status(thm)],[])).
% 11.39/11.61 tff(3329,plain,
% 11.39/11.61 ((~![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)),
% 11.39/11.62 inference(modus_ponens,[status(thm)],[3328, 3327])).
% 11.39/11.62 tff(3330,plain,
% 11.39/11.62 (node22(c_e_h_1, c_i, s0, s1)),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3329, 247, 100, 3326])).
% 11.39/11.62 tff(3331,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s0)), introduced(assumption)).
% 11.39/11.62 tff(3332,plain,
% 11.39/11.62 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s0))),
% 11.39/11.62 inference(quant_inst,[status(thm)],[])).
% 11.39/11.62 tff(3333,plain,
% 11.39/11.62 ($false),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3332, 260, 3331])).
% 11.39/11.62 tff(3334,plain,(~m_and_h_gate_v_out(c_e_h_1, c_i, s0)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.62 tff(3335,plain,
% 11.39/11.62 (((~![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, 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))),
% 11.39/11.62 inference(rewrite,[status(thm)],[])).
% 11.39/11.62 tff(3336,plain,
% 11.39/11.62 ((~![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, s1)) | (~node22(c_e_h_1, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0))),
% 11.39/11.62 inference(quant_inst,[status(thm)],[])).
% 11.39/11.62 tff(3337,plain,
% 11.39/11.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | (~node22(c_e_h_1, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0)),
% 11.39/11.62 inference(modus_ponens,[status(thm)],[3336, 3335])).
% 11.39/11.62 tff(3338,plain,
% 11.39/11.62 ($false),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3337, 273, 3313, 3334, 3330])).
% 11.39/11.62 tff(3339,plain,(~m_and_h_gate_v_out(c_e_h_1, c_i, s1)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.62 tff(3340,plain,
% 11.39/11.62 (((~![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, 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))),
% 11.39/11.62 inference(rewrite,[status(thm)],[])).
% 11.39/11.62 tff(3341,plain,
% 11.39/11.62 ((~![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, s2)) | (~node22(c_e_h_1, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1))),
% 11.39/11.62 inference(quant_inst,[status(thm)],[])).
% 11.39/11.62 tff(3342,plain,
% 11.39/11.62 ((~![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, s2)) | (~node22(c_e_h_1, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1)),
% 11.39/11.62 inference(modus_ponens,[status(thm)],[3341, 3340])).
% 11.39/11.62 tff(3343,plain,
% 11.39/11.62 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s2)) | (~node22(c_e_h_1, c_i, s1, s2))),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3342, 273, 3339])).
% 11.39/11.62 tff(3344,plain,
% 11.39/11.62 (~node22(c_e_h_1, c_i, s1, s2)),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3343, 3312])).
% 11.39/11.62 tff(3345,plain,
% 11.39/11.62 (((~![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))),
% 11.39/11.62 inference(rewrite,[status(thm)],[])).
% 11.39/11.62 tff(3346,plain,
% 11.39/11.62 ((~![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))),
% 11.39/11.62 inference(quant_inst,[status(thm)],[])).
% 11.39/11.62 tff(3347,plain,
% 11.39/11.62 ((~![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)),
% 11.39/11.62 inference(modus_ponens,[status(thm)],[3346, 3345])).
% 11.39/11.62 tff(3348,plain,
% 11.39/11.62 (node21(c_e_h_1, c_i, s1, s2)),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3347, 247, 470, 3344])).
% 11.39/11.62 tff(3349,plain,
% 11.39/11.62 (((~![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, 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))),
% 11.39/11.62 inference(rewrite,[status(thm)],[])).
% 11.39/11.62 tff(3350,plain,
% 11.39/11.62 ((~![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, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s1))),
% 11.39/11.62 inference(quant_inst,[status(thm)],[])).
% 11.39/11.62 tff(3351,plain,
% 11.39/11.62 ((~![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, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s1)),
% 11.39/11.62 inference(modus_ponens,[status(thm)],[3350, 3349])).
% 11.39/11.62 tff(3352,plain,
% 11.39/11.62 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s1)),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3351, 503, 3186])).
% 11.39/11.62 tff(3353,plain,
% 11.39/11.62 (((~![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, 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))),
% 11.39/11.62 inference(rewrite,[status(thm)],[])).
% 11.39/11.62 tff(3354,plain,
% 11.39/11.62 ((~![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, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s1))),
% 11.39/11.62 inference(quant_inst,[status(thm)],[])).
% 11.39/11.62 tff(3355,plain,
% 11.39/11.62 ((~![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, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s1)),
% 11.39/11.62 inference(modus_ponens,[status(thm)],[3354, 3353])).
% 11.39/11.62 tff(3356,plain,
% 11.39/11.62 (~node20(c_e_h_1, c_i, s1)),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3355, 213, 3352])).
% 11.39/11.62 tff(3357,plain,
% 11.39/11.62 (((~![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, s1) | (~node21(c_e_h_1, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, 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_1, c_i, s1) | (~node21(c_e_h_1, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2)))),
% 11.39/11.62 inference(rewrite,[status(thm)],[])).
% 11.39/11.62 tff(3358,plain,
% 11.39/11.62 ((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))) <=> (node20(c_e_h_1, c_i, s1) | (~node21(c_e_h_1, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2)))),
% 11.39/11.62 inference(rewrite,[status(thm)],[])).
% 11.39/11.62 tff(3359,plain,
% 11.39/11.62 (((~![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, 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) | (~node21(c_e_h_1, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2))))),
% 11.39/11.62 inference(monotonicity,[status(thm)],[3358])).
% 11.39/11.62 tff(3360,plain,
% 11.39/11.62 (((~![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, 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) | (~node21(c_e_h_1, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2)))),
% 11.39/11.62 inference(transitivity,[status(thm)],[3359, 3357])).
% 11.39/11.62 tff(3361,plain,
% 11.39/11.62 ((~![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, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2)) | (~node21(c_e_h_1, c_i, s1, s2)))),
% 11.39/11.62 inference(quant_inst,[status(thm)],[])).
% 11.39/11.62 tff(3362,plain,
% 11.39/11.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s1) | (~node21(c_e_h_1, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2))),
% 11.39/11.62 inference(modus_ponens,[status(thm)],[3361, 3360])).
% 11.39/11.62 tff(3363,plain,
% 11.39/11.62 ($false),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3362, 228, 3312, 3356, 3348])).
% 11.39/11.62 tff(3364,plain,(~m_and_h_gate_v_out(c_e_h_1, c_i, s2)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.62 tff(3365,plain,
% 11.39/11.62 (((~![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, 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))),
% 11.39/11.62 inference(rewrite,[status(thm)],[])).
% 11.39/11.62 tff(3366,plain,
% 11.39/11.62 ((~![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, s3)) | (~node22(c_e_h_1, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2))),
% 11.39/11.62 inference(quant_inst,[status(thm)],[])).
% 11.39/11.62 tff(3367,plain,
% 11.39/11.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | (~node22(c_e_h_1, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2)),
% 11.39/11.62 inference(modus_ponens,[status(thm)],[3366, 3365])).
% 11.39/11.62 tff(3368,plain,
% 11.39/11.62 ($false),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3367, 273, 3310, 3364, 3311])).
% 11.39/11.62 tff(3369,plain,((~node22(c_e_h_1, c_i, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3))), inference(lemma,lemma(discharge,[]))).
% 11.39/11.62 tff(3370,plain,
% 11.39/11.62 (~node22(c_e_h_1, c_i, s2, s3)),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3369, 3310])).
% 11.39/11.62 tff(3371,plain,
% 11.39/11.62 (((~![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, 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))),
% 11.39/11.62 inference(rewrite,[status(thm)],[])).
% 11.39/11.62 tff(3372,plain,
% 11.39/11.62 ((~![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, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s2))),
% 11.39/11.62 inference(quant_inst,[status(thm)],[])).
% 11.39/11.62 tff(3373,plain,
% 11.39/11.62 ((~![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, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s2)),
% 11.39/11.62 inference(modus_ponens,[status(thm)],[3372, 3371])).
% 11.39/11.62 tff(3374,plain,
% 11.39/11.62 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s2)),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3373, 503, 3243])).
% 11.39/11.62 tff(3375,plain,
% 11.39/11.62 (((~![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, 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))),
% 11.39/11.62 inference(rewrite,[status(thm)],[])).
% 11.39/11.62 tff(3376,plain,
% 11.39/11.62 ((~![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, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s2))),
% 11.39/11.62 inference(quant_inst,[status(thm)],[])).
% 11.39/11.62 tff(3377,plain,
% 11.39/11.62 ((~![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, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s2)),
% 11.39/11.62 inference(modus_ponens,[status(thm)],[3376, 3375])).
% 11.39/11.62 tff(3378,plain,
% 11.39/11.62 (~node20(c_e_h_1, c_i, s2)),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3377, 213, 3374])).
% 11.39/11.62 tff(3379,assumption,(~node20(c_e_h_1, c_i, s2)), introduced(assumption)).
% 11.39/11.62 tff(3380,assumption,(node21(c_e_h_1, c_i, s2, s3)), introduced(assumption)).
% 11.39/11.62 tff(3381,plain,
% 11.39/11.62 (((~![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)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | node20(c_e_h_1, c_i, s2) | (~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)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | node20(c_e_h_1, c_i, s2) | (~node21(c_e_h_1, c_i, s2, s3)))),
% 11.39/11.62 inference(rewrite,[status(thm)],[])).
% 11.39/11.62 tff(3382,plain,
% 11.39/11.62 ((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))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | node20(c_e_h_1, c_i, s2) | (~node21(c_e_h_1, c_i, s2, s3)))),
% 11.39/11.62 inference(rewrite,[status(thm)],[])).
% 11.39/11.62 tff(3383,plain,
% 11.39/11.62 (((~![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, 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)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | node20(c_e_h_1, c_i, s2) | (~node21(c_e_h_1, c_i, s2, s3))))),
% 11.39/11.62 inference(monotonicity,[status(thm)],[3382])).
% 11.39/11.62 tff(3384,plain,
% 11.39/11.62 (((~![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, 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)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | node20(c_e_h_1, c_i, s2) | (~node21(c_e_h_1, c_i, s2, s3)))),
% 11.39/11.62 inference(transitivity,[status(thm)],[3383, 3381])).
% 11.39/11.62 tff(3385,plain,
% 11.39/11.62 ((~![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, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | (~node21(c_e_h_1, c_i, s2, s3)))),
% 11.39/11.62 inference(quant_inst,[status(thm)],[])).
% 11.39/11.62 tff(3386,plain,
% 11.39/11.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | node20(c_e_h_1, c_i, s2) | (~node21(c_e_h_1, c_i, s2, s3))),
% 11.39/11.62 inference(modus_ponens,[status(thm)],[3385, 3384])).
% 11.39/11.62 tff(3387,plain,
% 11.39/11.62 ($false),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3386, 228, 3310, 3380, 3379])).
% 11.39/11.62 tff(3388,plain,((~node21(c_e_h_1, c_i, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | node20(c_e_h_1, c_i, s2)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.62 tff(3389,plain,
% 11.39/11.62 ((~node21(c_e_h_1, c_i, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3))),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3388, 3378])).
% 11.39/11.62 tff(3390,plain,
% 11.39/11.62 (~node21(c_e_h_1, c_i, s2, s3)),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3389, 3310])).
% 11.39/11.62 tff(3391,plain,
% 11.39/11.62 (((~![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_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))),
% 11.39/11.62 inference(rewrite,[status(thm)],[])).
% 11.39/11.62 tff(3392,plain,
% 11.39/11.62 ((~![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_1, c_i, s2, s3) | node22(c_e_h_1, c_i, s2, s3))),
% 11.39/11.62 inference(quant_inst,[status(thm)],[])).
% 11.39/11.62 tff(3393,plain,
% 11.39/11.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_i, s2, s3) | node22(c_e_h_1, c_i, s2, s3)),
% 11.39/11.62 inference(modus_ponens,[status(thm)],[3392, 3391])).
% 11.39/11.62 tff(3394,plain,
% 11.39/11.62 (node21(c_e_h_1, c_i, s2, s3) | node22(c_e_h_1, c_i, s2, s3)),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3393, 247, 604])).
% 11.39/11.62 tff(3395,plain,
% 11.39/11.62 ($false),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3394, 3390, 3370])).
% 11.39/11.62 tff(3396,plain,(~m_and_h_gate_v_out(c_e_h_1, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.62 tff(3397,assumption,(node22(c_e_h_1, c_i, s3, s4)), introduced(assumption)).
% 11.39/11.62 tff(3398,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s3)), introduced(assumption)).
% 11.39/11.62 tff(3399,plain,
% 11.39/11.62 (((~![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, 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))),
% 11.39/11.62 inference(rewrite,[status(thm)],[])).
% 11.39/11.62 tff(3400,plain,
% 11.39/11.62 ((~![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, s4)) | (~node22(c_e_h_1, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3))),
% 11.39/11.62 inference(quant_inst,[status(thm)],[])).
% 11.39/11.62 tff(3401,plain,
% 11.39/11.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | (~node22(c_e_h_1, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3)),
% 11.39/11.62 inference(modus_ponens,[status(thm)],[3400, 3399])).
% 11.39/11.62 tff(3402,plain,
% 11.39/11.62 ($false),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3401, 273, 3398, 3397, 3309])).
% 11.39/11.62 tff(3403,plain,((~node22(c_e_h_1, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4))), inference(lemma,lemma(discharge,[]))).
% 11.39/11.62 tff(3404,plain,
% 11.39/11.62 ((~node22(c_e_h_1, c_i, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4))),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3403, 3396])).
% 11.39/11.62 tff(3405,plain,
% 11.39/11.62 (~node22(c_e_h_1, c_i, s3, s4)),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3404, 3309])).
% 11.39/11.62 tff(3406,assumption,(~node20(c_e_h_1, c_i, s3)), introduced(assumption)).
% 11.39/11.62 tff(3407,assumption,(node21(c_e_h_1, c_i, s3, s4)), introduced(assumption)).
% 11.39/11.62 tff(3408,plain,
% 11.39/11.62 (((~![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, 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)))),
% 11.39/11.62 inference(rewrite,[status(thm)],[])).
% 11.39/11.62 tff(3409,plain,
% 11.39/11.62 ((~![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, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | (~node21(c_e_h_1, c_i, s3, s4)))),
% 11.39/11.62 inference(quant_inst,[status(thm)],[])).
% 11.39/11.62 tff(3410,plain,
% 11.39/11.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | (~node21(c_e_h_1, c_i, s3, s4))),
% 11.39/11.62 inference(modus_ponens,[status(thm)],[3409, 3408])).
% 11.39/11.62 tff(3411,plain,
% 11.39/11.62 ($false),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3410, 228, 3407, 3309, 3406])).
% 11.39/11.62 tff(3412,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,[]))).
% 11.39/11.62 tff(3413,plain,
% 11.39/11.62 (~node21(c_e_h_1, c_i, s3, s4)),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3412, 3309, 3406])).
% 11.39/11.62 tff(3414,plain,
% 11.39/11.62 (((~![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))),
% 11.39/11.62 inference(rewrite,[status(thm)],[])).
% 11.39/11.62 tff(3415,plain,
% 11.39/11.62 ((~![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))),
% 11.39/11.62 inference(quant_inst,[status(thm)],[])).
% 11.39/11.62 tff(3416,plain,
% 11.39/11.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_i, s3, s4) | node22(c_e_h_1, c_i, s3, s4)),
% 11.39/11.62 inference(modus_ponens,[status(thm)],[3415, 3414])).
% 11.39/11.62 tff(3417,plain,
% 11.39/11.62 (node21(c_e_h_1, c_i, s3, s4) | node22(c_e_h_1, c_i, s3, s4)),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3416, 247, 1092])).
% 11.39/11.62 tff(3418,plain,
% 11.39/11.62 ($false),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3417, 3413, 3405])).
% 11.39/11.62 tff(3419,plain,((~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,[]))).
% 11.39/11.62 tff(3420,plain,
% 11.39/11.62 (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3419, 3308])).
% 11.39/11.62 tff(3421,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s4)), introduced(assumption)).
% 11.39/11.62 tff(3422,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s4)), introduced(assumption)).
% 11.39/11.62 tff(3423,plain,
% 11.39/11.62 (((~![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, 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))),
% 11.39/11.62 inference(rewrite,[status(thm)],[])).
% 11.39/11.62 tff(3424,plain,
% 11.39/11.62 ((~![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, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4))),
% 11.39/11.62 inference(quant_inst,[status(thm)],[])).
% 11.39/11.62 tff(3425,plain,
% 11.39/11.62 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4)),
% 11.39/11.62 inference(modus_ponens,[status(thm)],[3424, 3423])).
% 11.39/11.62 tff(3426,plain,
% 11.39/11.62 ($false),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3425, 1965, 3422, 3421])).
% 11.39/11.62 tff(3427,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.62 tff(3428,plain,
% 11.39/11.62 (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3427, 3420])).
% 11.39/11.62 tff(3429,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s5)), introduced(assumption)).
% 11.39/11.62 tff(3430,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s4)), introduced(assumption)).
% 11.39/11.62 tff(3431,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s3)), introduced(assumption)).
% 11.39/11.62 tff(3432,assumption,(node18(c_e_h_1, c_e, s3, s4)), introduced(assumption)).
% 11.39/11.62 tff(3433,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s3)), introduced(assumption)).
% 11.39/11.62 tff(3434,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s2)), introduced(assumption)).
% 11.39/11.62 tff(3435,assumption,(m_and_h_gate_v_out(c_e_h_1, c_c, s1)), introduced(assumption)).
% 11.39/11.62 tff(3436,assumption,(m_mutex_h_half_v_out(c_e_h_1, c_a, s0)), introduced(assumption)).
% 11.39/11.62 tff(3437,plain,
% 11.39/11.62 ((~![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s0))),
% 11.39/11.62 inference(quant_inst,[status(thm)],[])).
% 11.39/11.62 tff(3438,plain,
% 11.39/11.62 ($false),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3437, 1158, 3436])).
% 11.39/11.62 tff(3439,plain,(~m_mutex_h_half_v_out(c_e_h_1, c_a, s0)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.62 tff(3440,plain,
% 11.39/11.62 (((~![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_1, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_1, 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_1, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s0))),
% 11.39/11.62 inference(rewrite,[status(thm)],[])).
% 11.39/11.62 tff(3441,plain,
% 11.39/11.62 ((~![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_1, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s0))),
% 11.39/11.62 inference(quant_inst,[status(thm)],[])).
% 11.39/11.62 tff(3442,plain,
% 11.39/11.62 ((~![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_1, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s0)),
% 11.39/11.62 inference(modus_ponens,[status(thm)],[3441, 3440])).
% 11.39/11.62 tff(3443,plain,
% 11.39/11.62 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s0)),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3442, 1209, 3439])).
% 11.39/11.62 tff(3444,plain,
% 11.39/11.62 (((~![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_c, s0)) | m_and_h_gate_v_in1(c_e_h_1, 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_1, c_c, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s0))),
% 11.39/11.62 inference(rewrite,[status(thm)],[])).
% 11.39/11.62 tff(3445,plain,
% 11.39/11.62 ((~![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_c, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s0))),
% 11.39/11.62 inference(quant_inst,[status(thm)],[])).
% 11.39/11.62 tff(3446,plain,
% 11.39/11.62 ((~![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_c, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s0)),
% 11.39/11.62 inference(modus_ponens,[status(thm)],[3445, 3444])).
% 11.39/11.62 tff(3447,plain,
% 11.39/11.62 (~node20(c_e_h_1, c_c, s0)),
% 11.39/11.62 inference(unit_resolution,[status(thm)],[3446, 213, 3443])).
% 11.39/11.62 tff(3448,assumption,(node21(c_e_h_1, c_c, s0, s1)), introduced(assumption)).
% 11.39/11.62 tff(3449,plain,
% 11.39/11.62 (((~![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)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | node20(c_e_h_1, c_c, s0) | (~node21(c_e_h_1, 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)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | node20(c_e_h_1, c_c, s0) | (~node21(c_e_h_1, c_c, s0, s1)))),
% 11.39/11.62 inference(rewrite,[status(thm)],[])).
% 11.39/11.62 tff(3450,plain,
% 11.39/11.62 ((node20(c_e_h_1, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | (~node21(c_e_h_1, c_c, s0, s1))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | node20(c_e_h_1, c_c, s0) | (~node21(c_e_h_1, c_c, s0, s1)))),
% 11.39/11.62 inference(rewrite,[status(thm)],[])).
% 11.39/11.62 tff(3451,plain,
% 11.39/11.62 (((~![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_c, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | (~node21(c_e_h_1, 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)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | node20(c_e_h_1, c_c, s0) | (~node21(c_e_h_1, c_c, s0, s1))))),
% 11.39/11.62 inference(monotonicity,[status(thm)],[3450])).
% 11.39/11.62 tff(3452,plain,
% 11.39/11.62 (((~![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_c, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | (~node21(c_e_h_1, 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)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | node20(c_e_h_1, c_c, s0) | (~node21(c_e_h_1, c_c, s0, s1)))),
% 11.39/11.62 inference(transitivity,[status(thm)],[3451, 3449])).
% 11.39/11.62 tff(3453,plain,
% 11.39/11.63 ((~![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_1, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | (~node21(c_e_h_1, c_c, s0, s1)))),
% 11.39/11.63 inference(quant_inst,[status(thm)],[])).
% 11.39/11.63 tff(3454,plain,
% 11.39/11.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | node20(c_e_h_1, c_c, s0) | (~node21(c_e_h_1, c_c, s0, s1))),
% 11.39/11.63 inference(modus_ponens,[status(thm)],[3453, 3452])).
% 11.39/11.63 tff(3455,plain,
% 11.39/11.63 ($false),
% 11.39/11.63 inference(unit_resolution,[status(thm)],[3454, 228, 3448, 3435, 3447])).
% 11.39/11.63 tff(3456,plain,((~node21(c_e_h_1, c_c, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s1))), inference(lemma,lemma(discharge,[]))).
% 11.39/11.63 tff(3457,plain,
% 11.39/11.63 (~node21(c_e_h_1, c_c, s0, s1)),
% 11.39/11.63 inference(unit_resolution,[status(thm)],[3456, 3435])).
% 11.39/11.63 tff(3458,plain,
% 11.39/11.63 (((~![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_c, s0, s1) | node22(c_e_h_1, 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_1, c_c, s0, s1) | node22(c_e_h_1, c_c, s0, s1))),
% 11.39/11.63 inference(rewrite,[status(thm)],[])).
% 11.39/11.63 tff(3459,plain,
% 11.39/11.63 ((~![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_c, s0, s1) | node22(c_e_h_1, c_c, s0, s1))),
% 11.39/11.63 inference(quant_inst,[status(thm)],[])).
% 11.39/11.63 tff(3460,plain,
% 11.39/11.63 ((~![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_c, s0, s1) | node22(c_e_h_1, c_c, s0, s1)),
% 11.39/11.63 inference(modus_ponens,[status(thm)],[3459, 3458])).
% 11.39/11.63 tff(3461,plain,
% 11.39/11.63 (node21(c_e_h_1, c_c, s0, s1) | node22(c_e_h_1, c_c, s0, s1)),
% 11.39/11.63 inference(unit_resolution,[status(thm)],[3460, 247, 100])).
% 11.39/11.63 tff(3462,plain,
% 11.39/11.63 (node22(c_e_h_1, c_c, s0, s1)),
% 11.39/11.63 inference(unit_resolution,[status(thm)],[3461, 3457])).
% 11.39/11.63 tff(3463,plain,
% 11.39/11.63 (((~![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_1, c_c, s1)) | (~node22(c_e_h_1, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, 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_1, c_c, s1)) | (~node22(c_e_h_1, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_c, s0))),
% 11.39/11.63 inference(rewrite,[status(thm)],[])).
% 11.39/11.63 tff(3464,plain,
% 11.39/11.63 ((~![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_1, c_c, s1)) | (~node22(c_e_h_1, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_c, s0))),
% 11.39/11.63 inference(quant_inst,[status(thm)],[])).
% 11.39/11.63 tff(3465,plain,
% 11.39/11.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | (~node22(c_e_h_1, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_c, s0)),
% 11.39/11.63 inference(modus_ponens,[status(thm)],[3464, 3463])).
% 11.39/11.63 tff(3466,plain,
% 11.39/11.63 ($false),
% 11.39/11.63 inference(unit_resolution,[status(thm)],[3465, 273, 3090, 3462, 3435])).
% 11.39/11.63 tff(3467,plain,(~m_and_h_gate_v_out(c_e_h_1, c_c, s1)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.63 tff(3468,plain,
% 11.39/11.63 (((~![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, s1)) | m_and_h_gate_v_out(c_e_h_1, 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_1, c_e, s1)) | m_and_h_gate_v_out(c_e_h_1, c_c, s1))),
% 11.39/11.63 inference(rewrite,[status(thm)],[])).
% 11.39/11.63 tff(3469,plain,
% 11.39/11.63 ((~![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, s1)) | m_and_h_gate_v_out(c_e_h_1, c_c, s1))),
% 11.39/11.63 inference(quant_inst,[status(thm)],[])).
% 11.39/11.63 tff(3470,plain,
% 11.39/11.63 ((~![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, s1)) | m_and_h_gate_v_out(c_e_h_1, c_c, s1)),
% 11.39/11.63 inference(modus_ponens,[status(thm)],[3469, 3468])).
% 11.39/11.63 tff(3471,plain,
% 11.39/11.63 (~m_c_h_element_v_in1(c_e_h_1, c_e, s1)),
% 11.39/11.63 inference(unit_resolution,[status(thm)],[3470, 1984, 3467])).
% 11.39/11.63 tff(3472,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s2)), introduced(assumption)).
% 11.39/11.63 tff(3473,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s1)), introduced(assumption)).
% 11.39/11.63 tff(3474,plain,
% 11.39/11.63 (((~![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))),
% 11.39/11.63 inference(rewrite,[status(thm)],[])).
% 11.39/11.63 tff(3475,plain,
% 11.39/11.63 ((~![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))),
% 11.39/11.63 inference(quant_inst,[status(thm)],[])).
% 11.39/11.63 tff(3476,plain,
% 11.39/11.63 ((~![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)),
% 11.39/11.63 inference(modus_ponens,[status(thm)],[3475, 3474])).
% 11.39/11.63 tff(3477,plain,
% 11.39/11.63 (~m_c_h_element_v_in1(c_e_h_1, c_e, s0)),
% 11.39/11.63 inference(unit_resolution,[status(thm)],[3476, 1984, 3090])).
% 11.39/11.63 tff(3478,assumption,(node15(c_e_h_1, c_e, s0, s1)), introduced(assumption)).
% 11.39/11.63 tff(3479,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s0)), introduced(assumption)).
% 11.39/11.63 tff(3480,plain,
% 11.39/11.63 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s0))),
% 11.39/11.63 inference(quant_inst,[status(thm)],[])).
% 11.39/11.63 tff(3481,plain,
% 11.39/11.63 ($false),
% 11.39/11.63 inference(unit_resolution,[status(thm)],[3480, 189, 3479])).
% 11.39/11.63 tff(3482,plain,(~m_c_h_element_v_out(c_e_h_1, c_e, s0)), inference(lemma,lemma(discharge,[]))).
% 11.39/11.63 tff(3483,plain,
% 11.39/11.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 11.39/11.63 inference(rewrite,[status(thm)],[])).
% 11.39/11.63 tff(3484,plain,
% 11.39/11.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 11.39/11.63 inference(quant_inst,[status(thm)],[])).
% 11.39/11.63 tff(3485,plain,
% 11.39/11.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node15(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0)),
% 11.39/11.63 inference(modus_ponens,[status(thm)],[3484, 3483])).
% 11.39/11.63 tff(3486,plain,
% 11.39/11.63 ($false),
% 11.39/11.63 inference(unit_resolution,[status(thm)],[3485, 393, 3482, 3478, 3473])).
% 11.39/11.63 tff(3487,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,[]))).
% 11.39/11.63 tff(3488,plain,
% 11.39/11.63 (~node15(c_e_h_1, c_e, s0, s1)),
% 11.39/11.63 inference(unit_resolution,[status(thm)],[3487, 3473])).
% 11.39/11.63 tff(3489,plain,
% 11.39/11.63 (((~![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_1, c_e, 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_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0))),
% 11.39/11.63 inference(rewrite,[status(thm)],[])).
% 11.39/11.63 tff(3490,plain,
% 11.39/11.63 ((~![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_1, c_e, s0)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0))),
% 11.39/11.63 inference(quant_inst,[status(thm)],[])).
% 11.39/11.63 tff(3491,plain,
% 11.39/11.63 ((~![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_1, c_e, s0)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0)),
% 11.39/11.63 inference(modus_ponens,[status(thm)],[3490, 3489])).
% 11.39/11.63 tff(3492,plain,
% 11.39/11.63 (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)),
% 11.39/11.63 inference(unit_resolution,[status(thm)],[3491, 1965, 3334])).
% 11.39/11.63 tff(3493,plain,
% 11.39/11.63 (((~![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_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))),
% 11.39/11.63 inference(rewrite,[status(thm)],[])).
% 11.39/11.63 tff(3494,plain,
% 11.39/11.63 ((~![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_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))),
% 11.39/11.63 inference(quant_inst,[status(thm)],[])).
% 11.39/11.63 tff(3495,plain,
% 11.39/11.63 ((~![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_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)),
% 11.39/11.63 inference(modus_ponens,[status(thm)],[3494, 3493])).
% 11.39/11.63 tff(3496,plain,
% 11.39/11.63 ((~node16(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0)),
% 11.39/11.63 inference(unit_resolution,[status(thm)],[3495, 377, 3492])).
% 11.39/11.63 tff(3497,plain,
% 11.39/11.63 (~node16(c_e_h_1, c_e, s0)),
% 11.39/11.63 inference(unit_resolution,[status(thm)],[3496, 3477])).
% 11.39/11.63 tff(3498,plain,
% 11.39/11.63 (((~![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))),
% 11.39/11.63 inference(rewrite,[status(thm)],[])).
% 11.39/11.63 tff(3499,plain,
% 11.39/11.63 ((~![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))),
% 11.39/11.63 inference(quant_inst,[status(thm)],[])).
% 11.39/11.63 tff(3500,plain,
% 11.39/11.63 ((~![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)),
% 11.39/11.63 inference(modus_ponens,[status(thm)],[3499, 3498])).
% 11.39/11.63 tff(3501,plain,
% 11.39/11.63 (node19(c_e_h_1, c_e, s0, s1)),
% 11.39/11.63 inference(unit_resolution,[status(thm)],[3500, 312, 100])).
% 11.39/11.63 tff(3502,plain,
% 11.39/11.63 (((~![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)))) | (node14(c_e_h_1, c_e, s0, s1) | node16(c_e_h_1, c_e, s0) | 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)))) | node14(c_e_h_1, c_e, s0, s1) | node16(c_e_h_1, c_e, s0) | node15(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)))),
% 11.39/11.63 inference(rewrite,[status(thm)],[])).
% 11.39/11.63 tff(3503,plain,
% 11.39/11.63 ((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))) <=> (node14(c_e_h_1, c_e, s0, s1) | node16(c_e_h_1, c_e, s0) | node15(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)))),
% 11.39/11.63 inference(rewrite,[status(thm)],[])).
% 11.39/11.63 tff(3504,plain,
% 11.39/11.63 (((~![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_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)))) | (node14(c_e_h_1, c_e, s0, s1) | node16(c_e_h_1, c_e, s0) | node15(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1))))),
% 11.49/11.63 inference(monotonicity,[status(thm)],[3503])).
% 11.49/11.63 tff(3505,plain,
% 11.49/11.63 (((~![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_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)))) | node14(c_e_h_1, c_e, s0, s1) | node16(c_e_h_1, c_e, s0) | node15(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)))),
% 11.49/11.63 inference(transitivity,[status(thm)],[3504, 3502])).
% 11.49/11.63 tff(3506,plain,
% 11.49/11.63 ((~![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_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)))),
% 11.49/11.63 inference(quant_inst,[status(thm)],[])).
% 11.49/11.63 tff(3507,plain,
% 11.49/11.63 ((~![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)))) | node14(c_e_h_1, c_e, s0, s1) | node16(c_e_h_1, c_e, s0) | node15(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1))),
% 11.49/11.63 inference(modus_ponens,[status(thm)],[3506, 3505])).
% 11.49/11.63 tff(3508,plain,
% 11.49/11.63 (node14(c_e_h_1, c_e, s0, s1) | node16(c_e_h_1, c_e, s0) | node15(c_e_h_1, c_e, s0, s1)),
% 11.49/11.63 inference(unit_resolution,[status(thm)],[3507, 409, 3501])).
% 11.49/11.63 tff(3509,plain,
% 11.49/11.63 (node14(c_e_h_1, c_e, s0, s1) | node15(c_e_h_1, c_e, s0, s1)),
% 11.49/11.63 inference(unit_resolution,[status(thm)],[3508, 3497])).
% 11.49/11.63 tff(3510,plain,
% 11.49/11.63 (node14(c_e_h_1, c_e, s0, s1)),
% 11.49/11.63 inference(unit_resolution,[status(thm)],[3509, 3488])).
% 11.49/11.63 tff(3511,plain,
% 11.49/11.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, 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, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~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_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node14(c_e_h_1, c_e, s0, s1)))),
% 11.49/11.63 inference(rewrite,[status(thm)],[])).
% 11.49/11.63 tff(3512,plain,
% 11.49/11.63 (((~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_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node14(c_e_h_1, c_e, s0, s1)))),
% 11.49/11.63 inference(rewrite,[status(thm)],[])).
% 11.49/11.63 tff(3513,plain,
% 11.49/11.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node14(c_e_h_1, c_e, s0, s1))))),
% 11.49/11.63 inference(monotonicity,[status(thm)],[3512])).
% 11.49/11.63 tff(3514,plain,
% 11.49/11.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node14(c_e_h_1, c_e, s0, s1)))),
% 11.49/11.63 inference(transitivity,[status(thm)],[3513, 3511])).
% 11.49/11.63 tff(3515,plain,
% 11.49/11.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))),
% 11.49/11.63 inference(quant_inst,[status(thm)],[])).
% 11.49/11.63 tff(3516,plain,
% 11.49/11.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node14(c_e_h_1, c_e, s0, s1))),
% 11.49/11.63 inference(modus_ponens,[status(thm)],[3515, 3514])).
% 11.49/11.63 tff(3517,plain,
% 11.49/11.63 ($false),
% 11.49/11.63 inference(unit_resolution,[status(thm)],[3516, 427, 3510, 3477, 3473])).
% 11.49/11.63 tff(3518,plain,(~m_c_h_element_v_out(c_e_h_1, c_e, s1)), inference(lemma,lemma(discharge,[]))).
% 11.49/11.63 tff(3519,assumption,(node15(c_e_h_1, c_e, s1, s2)), introduced(assumption)).
% 11.49/11.63 tff(3520,plain,
% 11.49/11.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 11.49/11.63 inference(rewrite,[status(thm)],[])).
% 11.49/11.63 tff(3521,plain,
% 11.49/11.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 11.49/11.63 inference(quant_inst,[status(thm)],[])).
% 11.49/11.63 tff(3522,plain,
% 11.49/11.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | (~node15(c_e_h_1, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s1)),
% 11.49/11.63 inference(modus_ponens,[status(thm)],[3521, 3520])).
% 11.49/11.63 tff(3523,plain,
% 11.49/11.63 ($false),
% 11.49/11.63 inference(unit_resolution,[status(thm)],[3522, 393, 3519, 3518, 3472])).
% 11.49/11.63 tff(3524,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,[]))).
% 11.49/11.63 tff(3525,plain,
% 11.49/11.63 (~node15(c_e_h_1, c_e, s1, s2)),
% 11.49/11.63 inference(unit_resolution,[status(thm)],[3524, 3472])).
% 11.49/11.63 tff(3526,plain,
% 11.49/11.63 (((~![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_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))),
% 11.49/11.63 inference(rewrite,[status(thm)],[])).
% 11.49/11.63 tff(3527,plain,
% 11.49/11.63 ((~![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_1, c_e, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1))),
% 11.49/11.63 inference(quant_inst,[status(thm)],[])).
% 11.49/11.63 tff(3528,plain,
% 11.49/11.63 ((~![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_1, c_e, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1)),
% 11.49/11.63 inference(modus_ponens,[status(thm)],[3527, 3526])).
% 11.49/11.63 tff(3529,plain,
% 11.49/11.63 ((~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)),
% 11.49/11.63 inference(unit_resolution,[status(thm)],[3528, 1965])).
% 11.49/11.63 tff(3530,plain,
% 11.49/11.63 (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)),
% 11.49/11.63 inference(unit_resolution,[status(thm)],[3529, 3339])).
% 11.49/11.63 tff(3531,plain,
% 11.49/11.63 (((~![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_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))),
% 11.49/11.63 inference(rewrite,[status(thm)],[])).
% 11.49/11.63 tff(3532,plain,
% 11.49/11.63 ((~![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_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))),
% 11.49/11.63 inference(quant_inst,[status(thm)],[])).
% 11.49/11.63 tff(3533,plain,
% 11.49/11.63 ((~![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_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)),
% 11.49/11.63 inference(modus_ponens,[status(thm)],[3532, 3531])).
% 11.49/11.63 tff(3534,plain,
% 11.49/11.63 ((~node16(c_e_h_1, c_e, s1)) | m_c_h_element_v_in2(c_e_h_1, c_e, s1)),
% 11.49/11.63 inference(unit_resolution,[status(thm)],[3533, 377, 3471])).
% 11.49/11.63 tff(3535,plain,
% 11.49/11.63 (~node16(c_e_h_1, c_e, s1)),
% 11.49/11.63 inference(unit_resolution,[status(thm)],[3534, 3530])).
% 11.49/11.63 tff(3536,plain,
% 11.49/11.63 (((~![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))),
% 11.49/11.63 inference(rewrite,[status(thm)],[])).
% 11.49/11.63 tff(3537,plain,
% 11.49/11.63 ((~![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))),
% 11.49/11.63 inference(quant_inst,[status(thm)],[])).
% 11.49/11.63 tff(3538,plain,
% 11.49/11.63 ((~![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)),
% 11.49/11.63 inference(modus_ponens,[status(thm)],[3537, 3536])).
% 11.49/11.63 tff(3539,plain,
% 11.49/11.63 (node19(c_e_h_1, c_e, s1, s2)),
% 11.49/11.63 inference(unit_resolution,[status(thm)],[3538, 312, 470])).
% 11.49/11.63 tff(3540,plain,
% 11.49/11.63 (((~![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_1, c_e, s1) | (~node19(c_e_h_1, c_e, s1, s2)) | node15(c_e_h_1, c_e, s1, s2) | node14(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)))) | node16(c_e_h_1, c_e, s1) | (~node19(c_e_h_1, c_e, s1, s2)) | node15(c_e_h_1, c_e, s1, s2) | node14(c_e_h_1, c_e, s1, s2))),
% 11.49/11.63 inference(rewrite,[status(thm)],[])).
% 11.49/11.63 tff(3541,plain,
% 11.49/11.63 ((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))) <=> (node16(c_e_h_1, c_e, s1) | (~node19(c_e_h_1, c_e, s1, s2)) | node15(c_e_h_1, c_e, s1, s2) | node14(c_e_h_1, c_e, s1, s2))),
% 11.49/11.63 inference(rewrite,[status(thm)],[])).
% 11.49/11.63 tff(3542,plain,
% 11.49/11.63 (((~![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_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)))) | (node16(c_e_h_1, c_e, s1) | (~node19(c_e_h_1, c_e, s1, s2)) | node15(c_e_h_1, c_e, s1, s2) | node14(c_e_h_1, c_e, s1, s2)))),
% 11.49/11.63 inference(monotonicity,[status(thm)],[3541])).
% 11.49/11.63 tff(3543,plain,
% 11.49/11.63 (((~![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_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)))) | node16(c_e_h_1, c_e, s1) | (~node19(c_e_h_1, c_e, s1, s2)) | node15(c_e_h_1, c_e, s1, s2) | node14(c_e_h_1, c_e, s1, s2))),
% 11.49/11.63 inference(transitivity,[status(thm)],[3542, 3540])).
% 11.49/11.63 tff(3544,plain,
% 11.49/11.63 ((~![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_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)))),
% 11.49/11.64 inference(quant_inst,[status(thm)],[])).
% 11.49/11.64 tff(3545,plain,
% 11.49/11.64 ((~![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_1, c_e, s1) | (~node19(c_e_h_1, c_e, s1, s2)) | node15(c_e_h_1, c_e, s1, s2) | node14(c_e_h_1, c_e, s1, s2)),
% 11.49/11.64 inference(modus_ponens,[status(thm)],[3544, 3543])).
% 11.49/11.64 tff(3546,plain,
% 11.49/11.64 (node16(c_e_h_1, c_e, s1) | node15(c_e_h_1, c_e, s1, s2) | node14(c_e_h_1, c_e, s1, s2)),
% 11.49/11.64 inference(unit_resolution,[status(thm)],[3545, 409, 3539])).
% 11.49/11.64 tff(3547,plain,
% 11.49/11.64 (node15(c_e_h_1, c_e, s1, s2) | node14(c_e_h_1, c_e, s1, s2)),
% 11.49/11.64 inference(unit_resolution,[status(thm)],[3546, 3535])).
% 11.49/11.64 tff(3548,plain,
% 11.49/11.64 (node14(c_e_h_1, c_e, s1, s2)),
% 11.49/11.64 inference(unit_resolution,[status(thm)],[3547, 3525])).
% 11.49/11.64 tff(3549,plain,
% 11.49/11.64 (((~![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)))) | (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)))),
% 11.49/11.64 inference(rewrite,[status(thm)],[])).
% 11.49/11.64 tff(3550,plain,
% 11.49/11.64 (((~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)))),
% 11.49/11.64 inference(rewrite,[status(thm)],[])).
% 11.49/11.64 tff(3551,plain,
% 11.49/11.64 (((~![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_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))))),
% 11.49/11.64 inference(monotonicity,[status(thm)],[3550])).
% 11.49/11.64 tff(3552,plain,
% 11.49/11.64 (((~![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_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)))),
% 11.49/11.64 inference(transitivity,[status(thm)],[3551, 3549])).
% 11.49/11.64 tff(3553,plain,
% 11.49/11.64 ((~![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_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)))),
% 11.49/11.64 inference(quant_inst,[status(thm)],[])).
% 11.49/11.64 tff(3554,plain,
% 11.49/11.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | (~node14(c_e_h_1, c_e, s1, s2))),
% 11.49/11.64 inference(modus_ponens,[status(thm)],[3553, 3552])).
% 11.49/11.64 tff(3555,plain,
% 11.49/11.64 ($false),
% 11.49/11.64 inference(unit_resolution,[status(thm)],[3554, 427, 3548, 3472, 3471])).
% 11.49/11.64 tff(3556,plain,(~m_c_h_element_v_out(c_e_h_1, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 11.49/11.64 tff(3557,plain,
% 11.49/11.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_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)))),
% 11.49/11.64 inference(rewrite,[status(thm)],[])).
% 11.49/11.64 tff(3558,plain,
% 11.49/11.64 (((~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)))),
% 11.49/11.64 inference(rewrite,[status(thm)],[])).
% 11.49/11.64 tff(3559,plain,
% 11.49/11.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_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))))),
% 11.49/11.64 inference(monotonicity,[status(thm)],[3558])).
% 11.49/11.64 tff(3560,plain,
% 11.49/11.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_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)))),
% 11.49/11.64 inference(transitivity,[status(thm)],[3559, 3557])).
% 11.49/11.64 tff(3561,plain,
% 11.49/11.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_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)))),
% 11.49/11.64 inference(quant_inst,[status(thm)],[])).
% 11.49/11.64 tff(3562,plain,
% 11.49/11.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_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))),
% 11.49/11.64 inference(modus_ponens,[status(thm)],[3561, 3560])).
% 11.49/11.64 tff(3563,plain,
% 11.49/11.64 ((~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~node18(c_e_h_1, c_e, s2, s3))),
% 11.49/11.64 inference(unit_resolution,[status(thm)],[3562, 296, 3556])).
% 11.49/11.64 tff(3564,plain,
% 11.49/11.64 (~node18(c_e_h_1, c_e, s2, s3)),
% 11.49/11.64 inference(unit_resolution,[status(thm)],[3563, 3433])).
% 11.49/11.64 tff(3565,assumption,(~node19(c_e_h_1, c_e, s2, s3)), introduced(assumption)).
% 11.49/11.64 tff(3566,plain,
% 11.49/11.64 (((~![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))),
% 11.49/11.64 inference(rewrite,[status(thm)],[])).
% 11.49/11.64 tff(3567,plain,
% 11.49/11.64 ((~![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))),
% 11.49/11.64 inference(quant_inst,[status(thm)],[])).
% 11.49/11.64 tff(3568,plain,
% 11.49/11.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_1, c_e, s2, s3)),
% 11.49/11.64 inference(modus_ponens,[status(thm)],[3567, 3566])).
% 11.49/11.64 tff(3569,plain,
% 11.49/11.64 ($false),
% 11.49/11.64 inference(unit_resolution,[status(thm)],[3568, 312, 604, 3565])).
% 11.49/11.64 tff(3570,plain,(node19(c_e_h_1, c_e, s2, s3)), inference(lemma,lemma(discharge,[]))).
% 11.49/11.64 tff(3571,plain,
% 11.49/11.64 (((~![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_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) | node18(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3)))),
% 11.49/11.64 inference(rewrite,[status(thm)],[])).
% 11.49/11.64 tff(3572,plain,
% 11.49/11.64 ((~![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_1, c_e, s2) | node18(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3)))),
% 11.49/11.64 inference(quant_inst,[status(thm)],[])).
% 11.49/11.64 tff(3573,plain,
% 11.49/11.64 ((~![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_1, c_e, s2) | node18(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3))),
% 11.49/11.64 inference(modus_ponens,[status(thm)],[3572, 3571])).
% 11.49/11.64 tff(3574,plain,
% 11.49/11.64 (node17(c_e_h_1, c_e, s2) | node18(c_e_h_1, c_e, s2, s3)),
% 11.49/11.64 inference(unit_resolution,[status(thm)],[3573, 326, 3570])).
% 11.49/11.64 tff(3575,plain,
% 11.49/11.64 (node17(c_e_h_1, c_e, s2)),
% 11.49/11.64 inference(unit_resolution,[status(thm)],[3574, 3564])).
% 11.49/11.64 tff(3576,plain,
% 11.49/11.64 (((~![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_1, c_e, s2)) | m_c_h_element_v_in1(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)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~node17(c_e_h_1, c_e, s2)))),
% 11.49/11.64 inference(rewrite,[status(thm)],[])).
% 11.49/11.64 tff(3577,plain,
% 11.49/11.64 ((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)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~node17(c_e_h_1, c_e, s2)))),
% 11.49/11.64 inference(rewrite,[status(thm)],[])).
% 11.49/11.64 tff(3578,plain,
% 11.49/11.64 (((~![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_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)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~node17(c_e_h_1, c_e, s2))))),
% 11.49/11.64 inference(monotonicity,[status(thm)],[3577])).
% 11.49/11.64 tff(3579,plain,
% 11.49/11.64 (((~![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_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)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~node17(c_e_h_1, c_e, s2)))),
% 11.49/11.64 inference(transitivity,[status(thm)],[3578, 3576])).
% 11.49/11.64 tff(3580,plain,
% 11.49/11.64 ((~![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_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)))),
% 11.49/11.64 inference(quant_inst,[status(thm)],[])).
% 11.49/11.64 tff(3581,plain,
% 11.49/11.64 ((~![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_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~node17(c_e_h_1, c_e, s2))),
% 11.49/11.64 inference(modus_ponens,[status(thm)],[3580, 3579])).
% 11.49/11.64 tff(3582,plain,
% 11.49/11.64 ((~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)),
% 11.49/11.64 inference(unit_resolution,[status(thm)],[3581, 2125, 3575])).
% 11.49/11.64 tff(3583,plain,
% 11.49/11.64 (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)),
% 11.49/11.64 inference(unit_resolution,[status(thm)],[3582, 3434])).
% 11.49/11.64 tff(3584,plain,
% 11.49/11.64 (((~![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_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))),
% 11.49/11.64 inference(rewrite,[status(thm)],[])).
% 11.49/11.64 tff(3585,plain,
% 11.49/11.64 ((~![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_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))),
% 11.49/11.64 inference(quant_inst,[status(thm)],[])).
% 11.49/11.64 tff(3586,plain,
% 11.49/11.64 ((~![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_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)),
% 11.49/11.64 inference(modus_ponens,[status(thm)],[3585, 3584])).
% 11.49/11.64 tff(3587,plain,
% 11.49/11.64 ((~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~node15(c_e_h_1, c_e, s2, s3))),
% 11.49/11.64 inference(unit_resolution,[status(thm)],[3586, 393, 3556])).
% 11.49/11.64 tff(3588,plain,
% 11.49/11.64 (~node15(c_e_h_1, c_e, s2, s3)),
% 11.49/11.64 inference(unit_resolution,[status(thm)],[3587, 3433])).
% 11.49/11.64 tff(3589,plain,
% 11.49/11.64 (((~![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)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~node14(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_in1(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_out(c_e_h_1, c_e, s3)) | (~node14(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2))),
% 11.49/11.64 inference(rewrite,[status(thm)],[])).
% 11.49/11.64 tff(3590,plain,
% 11.49/11.64 (((~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)) | (~node14(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2))),
% 11.49/11.64 inference(rewrite,[status(thm)],[])).
% 11.49/11.64 tff(3591,plain,
% 11.49/11.64 (((~![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_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)) | (~node14(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2)))),
% 11.49/11.64 inference(monotonicity,[status(thm)],[3590])).
% 11.49/11.64 tff(3592,plain,
% 11.49/11.64 (((~![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_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)) | (~node14(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2))),
% 11.49/11.64 inference(transitivity,[status(thm)],[3591, 3589])).
% 11.49/11.64 tff(3593,plain,
% 11.49/11.64 ((~![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_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)))),
% 11.49/11.64 inference(quant_inst,[status(thm)],[])).
% 11.49/11.64 tff(3594,plain,
% 11.49/11.64 ((~![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)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~node14(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2)),
% 11.49/11.64 inference(modus_ponens,[status(thm)],[3593, 3592])).
% 11.49/11.64 tff(3595,plain,
% 11.49/11.64 ((~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~node14(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2)),
% 11.49/11.64 inference(unit_resolution,[status(thm)],[3594, 427])).
% 11.49/11.64 tff(3596,plain,
% 11.49/11.64 (~node14(c_e_h_1, c_e, s2, s3)),
% 11.49/11.64 inference(unit_resolution,[status(thm)],[3595, 3434, 3433])).
% 11.49/11.64 tff(3597,plain,
% 11.49/11.64 (((~![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)))) | (node15(c_e_h_1, c_e, s2, s3) | node16(c_e_h_1, c_e, s2) | (~node19(c_e_h_1, c_e, s2, s3)) | node14(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)))) | node15(c_e_h_1, c_e, s2, s3) | node16(c_e_h_1, c_e, s2) | (~node19(c_e_h_1, c_e, s2, s3)) | node14(c_e_h_1, c_e, s2, s3))),
% 11.49/11.64 inference(rewrite,[status(thm)],[])).
% 11.49/11.64 tff(3598,plain,
% 11.49/11.64 ((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))) <=> (node15(c_e_h_1, c_e, s2, s3) | node16(c_e_h_1, c_e, s2) | (~node19(c_e_h_1, c_e, s2, s3)) | node14(c_e_h_1, c_e, s2, s3))),
% 11.49/11.64 inference(rewrite,[status(thm)],[])).
% 11.49/11.64 tff(3599,plain,
% 11.49/11.64 (((~![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_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)))) | (node15(c_e_h_1, c_e, s2, s3) | node16(c_e_h_1, c_e, s2) | (~node19(c_e_h_1, c_e, s2, s3)) | node14(c_e_h_1, c_e, s2, s3)))),
% 11.49/11.64 inference(monotonicity,[status(thm)],[3598])).
% 11.49/11.64 tff(3600,plain,
% 11.49/11.64 (((~![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_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)))) | node15(c_e_h_1, c_e, s2, s3) | node16(c_e_h_1, c_e, s2) | (~node19(c_e_h_1, c_e, s2, s3)) | node14(c_e_h_1, c_e, s2, s3))),
% 11.49/11.64 inference(transitivity,[status(thm)],[3599, 3597])).
% 11.49/11.64 tff(3601,plain,
% 11.49/11.64 ((~![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_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)))),
% 11.49/11.64 inference(quant_inst,[status(thm)],[])).
% 11.49/11.64 tff(3602,plain,
% 11.49/11.64 ((~![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)))) | node15(c_e_h_1, c_e, s2, s3) | node16(c_e_h_1, c_e, s2) | (~node19(c_e_h_1, c_e, s2, s3)) | node14(c_e_h_1, c_e, s2, s3)),
% 11.49/11.64 inference(modus_ponens,[status(thm)],[3601, 3600])).
% 11.49/11.64 tff(3603,plain,
% 11.49/11.64 (node15(c_e_h_1, c_e, s2, s3) | node16(c_e_h_1, c_e, s2) | node14(c_e_h_1, c_e, s2, s3)),
% 11.49/11.64 inference(unit_resolution,[status(thm)],[3602, 409, 3570])).
% 11.49/11.64 tff(3604,plain,
% 11.49/11.64 (node16(c_e_h_1, c_e, s2)),
% 11.49/11.64 inference(unit_resolution,[status(thm)],[3603, 3596, 3588])).
% 11.49/11.64 tff(3605,plain,
% 11.49/11.64 (((~![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_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))),
% 11.49/11.64 inference(rewrite,[status(thm)],[])).
% 11.49/11.64 tff(3606,plain,
% 11.49/11.64 ((~![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_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))),
% 11.49/11.64 inference(quant_inst,[status(thm)],[])).
% 11.49/11.64 tff(3607,plain,
% 11.49/11.64 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | m_c_h_element_v_in2(c_e_h_1, c_e, s2)),
% 11.49/11.64 inference(modus_ponens,[status(thm)],[3606, 3605])).
% 11.49/11.64 tff(3608,plain,
% 11.49/11.64 ($false),
% 11.49/11.64 inference(unit_resolution,[status(thm)],[3607, 377, 3434, 3604, 3583])).
% 11.49/11.64 tff(3609,plain,(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))), inference(lemma,lemma(discharge,[]))).
% 11.49/11.64 tff(3610,plain,
% 11.49/11.64 (m_c_h_element_v_in1(c_e_h_1, c_e, s2)),
% 11.49/11.64 inference(unit_resolution,[status(thm)],[3609, 3433])).
% 11.49/11.64 tff(3611,plain,
% 11.49/11.64 (((~![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))),
% 11.49/11.64 inference(rewrite,[status(thm)],[])).
% 11.49/11.64 tff(3612,plain,
% 11.49/11.64 ((~![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))),
% 11.49/11.64 inference(quant_inst,[status(thm)],[])).
% 11.49/11.64 tff(3613,plain,
% 11.49/11.64 ((~![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)),
% 11.49/11.64 inference(modus_ponens,[status(thm)],[3612, 3611])).
% 11.49/11.64 tff(3614,plain,
% 11.49/11.64 (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)),
% 11.49/11.64 inference(unit_resolution,[status(thm)],[3613, 1965, 3364])).
% 11.49/11.64 tff(3615,plain,
% 11.49/11.64 (((~![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_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))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | 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)) | (~node17(c_e_h_1, c_e, s2)) | m_c_h_element_v_in2(c_e_h_1, c_e, s2))),
% 11.49/11.64 inference(rewrite,[status(thm)],[])).
% 11.49/11.64 tff(3616,plain,
% 11.49/11.64 (((~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_in1(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))),
% 11.49/11.64 inference(rewrite,[status(thm)],[])).
% 11.49/11.64 tff(3617,plain,
% 11.49/11.64 (((~![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_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_in1(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)))),
% 11.49/11.64 inference(monotonicity,[status(thm)],[3616])).
% 11.49/11.64 tff(3618,plain,
% 11.49/11.64 (((~![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_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_in1(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))),
% 11.49/11.64 inference(transitivity,[status(thm)],[3617, 3615])).
% 11.49/11.64 tff(3619,plain,
% 11.49/11.64 ((~![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_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)))),
% 11.49/11.64 inference(quant_inst,[status(thm)],[])).
% 11.49/11.64 tff(3620,plain,
% 11.49/11.64 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s2)) | (~node17(c_e_h_1, c_e, s2)) | m_c_h_element_v_in2(c_e_h_1, c_e, s2)),
% 11.49/11.65 inference(modus_ponens,[status(thm)],[3619, 3618])).
% 11.49/11.65 tff(3621,plain,
% 11.49/11.65 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s2)) | (~node17(c_e_h_1, c_e, s2))),
% 11.49/11.65 inference(unit_resolution,[status(thm)],[3620, 359, 3614])).
% 11.49/11.65 tff(3622,plain,
% 11.49/11.65 ($false),
% 11.49/11.65 inference(unit_resolution,[status(thm)],[3621, 3575, 3610])).
% 11.49/11.65 tff(3623,plain,(~m_c_h_element_v_out(c_e_h_1, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 11.49/11.65 tff(3624,plain,
% 11.49/11.65 (((~![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_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)))),
% 11.49/11.65 inference(rewrite,[status(thm)],[])).
% 11.49/11.65 tff(3625,plain,
% 11.49/11.65 (((~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)))),
% 11.49/11.65 inference(rewrite,[status(thm)],[])).
% 11.49/11.65 tff(3626,plain,
% 11.49/11.65 (((~![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_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))))),
% 11.49/11.65 inference(monotonicity,[status(thm)],[3625])).
% 11.49/11.65 tff(3627,plain,
% 11.49/11.65 (((~![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_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)))),
% 11.49/11.65 inference(transitivity,[status(thm)],[3626, 3624])).
% 11.49/11.65 tff(3628,plain,
% 11.49/11.65 ((~![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_e, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3) | (~node18(c_e_h_1, c_e, s3, s4)))),
% 11.49/11.65 inference(quant_inst,[status(thm)],[])).
% 11.49/11.65 tff(3629,plain,
% 11.49/11.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s3) | (~node18(c_e_h_1, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4))),
% 11.49/11.65 inference(modus_ponens,[status(thm)],[3628, 3627])).
% 11.49/11.65 tff(3630,plain,
% 11.49/11.65 ($false),
% 11.49/11.65 inference(unit_resolution,[status(thm)],[3629, 296, 3623, 3430, 3432])).
% 11.49/11.65 tff(3631,plain,((~node18(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,[]))).
% 11.49/11.65 tff(3632,plain,
% 11.49/11.65 (~node18(c_e_h_1, c_e, s3, s4)),
% 11.49/11.65 inference(unit_resolution,[status(thm)],[3631, 3430])).
% 11.49/11.65 tff(3633,assumption,(~node19(c_e_h_1, c_e, s3, s4)), introduced(assumption)).
% 11.49/11.65 tff(3634,plain,
% 11.49/11.65 (((~![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))),
% 11.49/11.65 inference(rewrite,[status(thm)],[])).
% 11.49/11.65 tff(3635,plain,
% 11.49/11.65 ((~![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))),
% 11.49/11.65 inference(quant_inst,[status(thm)],[])).
% 11.49/11.65 tff(3636,plain,
% 11.49/11.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_1, c_e, s3, s4)),
% 11.49/11.65 inference(modus_ponens,[status(thm)],[3635, 3634])).
% 11.49/11.65 tff(3637,plain,
% 11.49/11.65 ($false),
% 11.49/11.65 inference(unit_resolution,[status(thm)],[3636, 312, 1092, 3633])).
% 11.49/11.65 tff(3638,plain,(node19(c_e_h_1, c_e, s3, s4)), inference(lemma,lemma(discharge,[]))).
% 11.49/11.65 tff(3639,plain,
% 11.49/11.65 (((~![Y: $i, 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)))) | 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)))),
% 11.49/11.65 inference(rewrite,[status(thm)],[])).
% 11.49/11.65 tff(3640,plain,
% 11.49/11.65 ((~![Y: $i, 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)))),
% 11.49/11.65 inference(quant_inst,[status(thm)],[])).
% 11.49/11.65 tff(3641,plain,
% 11.49/11.65 ((~![Y: $i, 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))),
% 11.49/11.65 inference(modus_ponens,[status(thm)],[3640, 3639])).
% 11.49/11.65 tff(3642,plain,
% 11.49/11.65 (node17(c_e_h_1, c_e, s3) | node18(c_e_h_1, c_e, s3, s4)),
% 11.49/11.65 inference(unit_resolution,[status(thm)],[3641, 326, 3638])).
% 11.49/11.65 tff(3643,plain,
% 11.49/11.65 (node17(c_e_h_1, c_e, s3)),
% 11.49/11.65 inference(unit_resolution,[status(thm)],[3642, 3632])).
% 11.49/11.65 tff(3644,plain,
% 11.49/11.65 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, 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)))),
% 11.49/11.65 inference(rewrite,[status(thm)],[])).
% 11.49/11.65 tff(3645,plain,
% 11.49/11.65 ((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)))),
% 11.49/11.65 inference(rewrite,[status(thm)],[])).
% 11.49/11.65 tff(3646,plain,
% 11.49/11.65 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~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))))),
% 11.49/11.65 inference(monotonicity,[status(thm)],[3645])).
% 11.49/11.65 tff(3647,plain,
% 11.49/11.65 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~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)))),
% 11.49/11.65 inference(transitivity,[status(thm)],[3646, 3644])).
% 11.49/11.65 tff(3648,plain,
% 11.49/11.65 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~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)))),
% 11.49/11.65 inference(quant_inst,[status(thm)],[])).
% 11.49/11.65 tff(3649,plain,
% 11.49/11.65 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, 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))),
% 11.49/11.65 inference(modus_ponens,[status(thm)],[3648, 3647])).
% 11.49/11.65 tff(3650,plain,
% 11.49/11.65 ((~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)),
% 11.49/11.65 inference(unit_resolution,[status(thm)],[3649, 2125, 3643])).
% 11.49/11.65 tff(3651,plain,
% 11.49/11.65 (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)),
% 11.49/11.65 inference(unit_resolution,[status(thm)],[3650, 3431])).
% 11.49/11.65 tff(3652,assumption,(node15(c_e_h_1, c_e, s3, s4)), introduced(assumption)).
% 11.49/11.65 tff(3653,plain,
% 11.49/11.65 (((~![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_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))),
% 11.49/11.65 inference(rewrite,[status(thm)],[])).
% 11.49/11.65 tff(3654,plain,
% 11.49/11.65 ((~![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_e, s4)) | (~node15(c_e_h_1, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3))),
% 11.49/11.65 inference(quant_inst,[status(thm)],[])).
% 11.49/11.65 tff(3655,plain,
% 11.49/11.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | (~node15(c_e_h_1, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3)),
% 11.49/11.65 inference(modus_ponens,[status(thm)],[3654, 3653])).
% 11.49/11.65 tff(3656,plain,
% 11.49/11.65 ($false),
% 11.49/11.65 inference(unit_resolution,[status(thm)],[3655, 393, 3623, 3430, 3652])).
% 11.49/11.65 tff(3657,plain,((~node15(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,[]))).
% 11.49/11.65 tff(3658,plain,
% 11.49/11.65 (~node15(c_e_h_1, c_e, s3, s4)),
% 11.49/11.65 inference(unit_resolution,[status(thm)],[3657, 3430])).
% 11.49/11.65 tff(3659,assumption,(node14(c_e_h_1, c_e, s3, s4)), introduced(assumption)).
% 11.49/11.65 tff(3660,plain,
% 11.49/11.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_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, s3) | (~node14(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] : ((~node14(I0, I1, X, Y)) | m_c_h_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, s3) | (~node14(c_e_h_1, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)))),
% 11.49/11.65 inference(rewrite,[status(thm)],[])).
% 11.49/11.65 tff(3661,plain,
% 11.49/11.65 (((~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))) <=> (m_c_h_element_v_in1(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)))),
% 11.49/11.65 inference(rewrite,[status(thm)],[])).
% 11.49/11.65 tff(3662,plain,
% 11.49/11.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))) | (m_c_h_element_v_in1(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))))),
% 11.49/11.65 inference(monotonicity,[status(thm)],[3661])).
% 11.49/11.65 tff(3663,plain,
% 11.49/11.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))) | m_c_h_element_v_in1(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)))),
% 11.49/11.65 inference(transitivity,[status(thm)],[3662, 3660])).
% 11.49/11.65 tff(3664,plain,
% 11.49/11.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))),
% 11.49/11.65 inference(quant_inst,[status(thm)],[])).
% 11.49/11.65 tff(3665,plain,
% 11.49/11.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | (~node14(c_e_h_1, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4))),
% 11.49/11.65 inference(modus_ponens,[status(thm)],[3664, 3663])).
% 11.49/11.65 tff(3666,plain,
% 11.49/11.65 ($false),
% 11.49/11.65 inference(unit_resolution,[status(thm)],[3665, 427, 3430, 3659, 3431])).
% 11.49/11.65 tff(3667,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,[]))).
% 11.49/11.65 tff(3668,plain,
% 11.49/11.65 (~node14(c_e_h_1, c_e, s3, s4)),
% 11.49/11.65 inference(unit_resolution,[status(thm)],[3667, 3431, 3430])).
% 11.49/11.65 tff(3669,plain,
% 11.49/11.65 (((~![Y: $i, I0: $i, X: $i, I1: $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) | node15(c_e_h_1, c_e, s3, s4) | node14(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)))) | node16(c_e_h_1, c_e, s3) | node15(c_e_h_1, c_e, s3, s4) | node14(c_e_h_1, c_e, s3, s4) | (~node19(c_e_h_1, c_e, s3, s4)))),
% 11.49/11.65 inference(rewrite,[status(thm)],[])).
% 11.49/11.65 tff(3670,plain,
% 11.49/11.65 ((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))) <=> (node16(c_e_h_1, c_e, s3) | node15(c_e_h_1, c_e, s3, s4) | node14(c_e_h_1, c_e, s3, s4) | (~node19(c_e_h_1, c_e, s3, s4)))),
% 11.49/11.65 inference(rewrite,[status(thm)],[])).
% 11.49/11.65 tff(3671,plain,
% 11.49/11.65 (((~![Y: $i, I0: $i, X: $i, I1: $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)))) | (node16(c_e_h_1, c_e, s3) | node15(c_e_h_1, c_e, s3, s4) | node14(c_e_h_1, c_e, s3, s4) | (~node19(c_e_h_1, c_e, s3, s4))))),
% 11.49/11.65 inference(monotonicity,[status(thm)],[3670])).
% 11.49/11.65 tff(3672,plain,
% 11.49/11.65 (((~![Y: $i, I0: $i, X: $i, I1: $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)))) | node16(c_e_h_1, c_e, s3) | node15(c_e_h_1, c_e, s3, s4) | node14(c_e_h_1, c_e, s3, s4) | (~node19(c_e_h_1, c_e, s3, s4)))),
% 11.49/11.65 inference(transitivity,[status(thm)],[3671, 3669])).
% 11.49/11.65 tff(3673,plain,
% 11.49/11.65 ((~![Y: $i, I0: $i, X: $i, I1: $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)))),
% 11.49/11.65 inference(quant_inst,[status(thm)],[])).
% 11.49/11.65 tff(3674,plain,
% 11.49/11.65 ((~![Y: $i, I0: $i, X: $i, I1: $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) | node15(c_e_h_1, c_e, s3, s4) | node14(c_e_h_1, c_e, s3, s4) | (~node19(c_e_h_1, c_e, s3, s4))),
% 11.49/11.65 inference(modus_ponens,[status(thm)],[3673, 3672])).
% 11.49/11.65 tff(3675,plain,
% 11.49/11.65 (node16(c_e_h_1, c_e, s3) | node15(c_e_h_1, c_e, s3, s4) | node14(c_e_h_1, c_e, s3, s4)),
% 11.49/11.65 inference(unit_resolution,[status(thm)],[3674, 409, 3638])).
% 11.49/11.65 tff(3676,plain,
% 11.49/11.65 (node16(c_e_h_1, c_e, s3)),
% 11.49/11.65 inference(unit_resolution,[status(thm)],[3675, 3668, 3658])).
% 11.49/11.65 tff(3677,plain,
% 11.49/11.65 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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))),
% 11.49/11.65 inference(rewrite,[status(thm)],[])).
% 11.49/11.65 tff(3678,plain,
% 11.49/11.65 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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))),
% 11.49/11.65 inference(quant_inst,[status(thm)],[])).
% 11.49/11.65 tff(3679,plain,
% 11.49/11.65 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | m_c_h_element_v_in2(c_e_h_1, c_e, s3)),
% 11.49/11.65 inference(modus_ponens,[status(thm)],[3678, 3677])).
% 11.49/11.65 tff(3680,plain,
% 11.49/11.65 ($false),
% 11.49/11.65 inference(unit_resolution,[status(thm)],[3679, 377, 3676, 3651, 3431])).
% 11.49/11.65 tff(3681,plain,(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))), inference(lemma,lemma(discharge,[]))).
% 11.49/11.65 tff(3682,plain,
% 11.49/11.65 (m_c_h_element_v_in1(c_e_h_1, c_e, s3)),
% 11.49/11.65 inference(unit_resolution,[status(thm)],[3681, 3430])).
% 11.49/11.65 tff(3683,plain,
% 11.49/11.65 (((~![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))),
% 11.49/11.65 inference(rewrite,[status(thm)],[])).
% 11.49/11.65 tff(3684,plain,
% 11.49/11.65 ((~![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))),
% 11.49/11.65 inference(quant_inst,[status(thm)],[])).
% 11.49/11.65 tff(3685,plain,
% 11.49/11.65 ((~![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)),
% 11.49/11.65 inference(modus_ponens,[status(thm)],[3684, 3683])).
% 11.49/11.65 tff(3686,plain,
% 11.49/11.65 (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)),
% 11.49/11.65 inference(unit_resolution,[status(thm)],[3685, 1965, 3396])).
% 11.49/11.65 tff(3687,plain,
% 11.49/11.65 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, 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)))),
% 11.49/11.65 inference(rewrite,[status(thm)],[])).
% 11.49/11.65 tff(3688,plain,
% 11.49/11.65 (((~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)))),
% 11.49/11.65 inference(rewrite,[status(thm)],[])).
% 11.49/11.65 tff(3689,plain,
% 11.49/11.65 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | 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))))),
% 11.49/11.65 inference(monotonicity,[status(thm)],[3688])).
% 11.49/11.65 tff(3690,plain,
% 11.49/11.65 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | 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)))),
% 11.49/11.65 inference(transitivity,[status(thm)],[3689, 3687])).
% 11.49/11.65 tff(3691,plain,
% 11.49/11.65 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | 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)))),
% 11.49/11.65 inference(quant_inst,[status(thm)],[])).
% 11.49/11.65 tff(3692,plain,
% 11.49/11.65 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~node17(c_e_h_1, c_e, s3))),
% 11.49/11.65 inference(modus_ponens,[status(thm)],[3691, 3690])).
% 11.49/11.65 tff(3693,plain,
% 11.49/11.65 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~node17(c_e_h_1, c_e, s3))),
% 11.49/11.65 inference(unit_resolution,[status(thm)],[3692, 359, 3686])).
% 11.49/11.65 tff(3694,plain,
% 11.49/11.65 ($false),
% 11.49/11.65 inference(unit_resolution,[status(thm)],[3693, 3643, 3682])).
% 11.49/11.65 tff(3695,plain,(~m_c_h_element_v_out(c_e_h_1, c_e, s4)), inference(lemma,lemma(discharge,[]))).
% 11.49/11.65 tff(3696,assumption,(node18(c_e_h_1, c_e, s4, s5)), introduced(assumption)).
% 11.49/11.65 tff(3697,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s4)), introduced(assumption)).
% 11.49/11.65 tff(3698,plain,
% 11.49/11.65 (((~![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_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, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4) | (~node18(c_e_h_1, c_e, s4, s5)))),
% 11.49/11.65 inference(rewrite,[status(thm)],[])).
% 11.49/11.65 tff(3699,plain,
% 11.49/11.65 ((~![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_e, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4) | (~node18(c_e_h_1, c_e, s4, s5)))),
% 11.49/11.65 inference(quant_inst,[status(thm)],[])).
% 11.49/11.65 tff(3700,plain,
% 11.49/11.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4) | (~node18(c_e_h_1, c_e, s4, s5))),
% 11.49/11.65 inference(modus_ponens,[status(thm)],[3699, 3698])).
% 11.49/11.65 tff(3701,plain,
% 11.49/11.65 ($false),
% 11.49/11.65 inference(unit_resolution,[status(thm)],[3700, 296, 3697, 3429, 3696])).
% 11.49/11.65 tff(3702,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,[]))).
% 11.49/11.65 tff(3703,plain,
% 11.49/11.65 ((~node18(c_e_h_1, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5))),
% 11.49/11.65 inference(unit_resolution,[status(thm)],[3702, 3695])).
% 11.49/11.65 tff(3704,plain,
% 11.49/11.65 (~node18(c_e_h_1, c_e, s4, s5)),
% 11.49/11.65 inference(unit_resolution,[status(thm)],[3703, 3429])).
% 11.49/11.65 tff(3705,assumption,(node15(c_e_h_1, c_e, s4, s5)), introduced(assumption)).
% 11.49/11.65 tff(3706,plain,
% 11.49/11.65 (((~![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_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))),
% 11.49/11.65 inference(rewrite,[status(thm)],[])).
% 11.49/11.65 tff(3707,plain,
% 11.49/11.65 ((~![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_e, s5)) | (~node15(c_e_h_1, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4))),
% 11.49/11.66 inference(quant_inst,[status(thm)],[])).
% 11.49/11.66 tff(3708,plain,
% 11.49/11.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | (~node15(c_e_h_1, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4)),
% 11.49/11.66 inference(modus_ponens,[status(thm)],[3707, 3706])).
% 11.49/11.66 tff(3709,plain,
% 11.49/11.66 ($false),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3708, 393, 3697, 3429, 3705])).
% 11.49/11.66 tff(3710,plain,((~node15(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,[]))).
% 11.49/11.66 tff(3711,plain,
% 11.49/11.66 ((~node15(c_e_h_1, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5))),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3710, 3695])).
% 11.49/11.66 tff(3712,plain,
% 11.49/11.66 (~node15(c_e_h_1, c_e, s4, s5)),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3711, 3429])).
% 11.49/11.66 tff(3713,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s4)), introduced(assumption)).
% 11.49/11.66 tff(3714,assumption,(node17(c_e_h_1, c_e, s4)), introduced(assumption)).
% 11.49/11.66 tff(3715,plain,
% 11.49/11.66 (((~![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)))) | ((~node17(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] : ((~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, 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))),
% 11.49/11.66 inference(rewrite,[status(thm)],[])).
% 11.49/11.66 tff(3716,plain,
% 11.49/11.66 (((~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))) <=> ((~node17(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))),
% 11.49/11.66 inference(rewrite,[status(thm)],[])).
% 11.49/11.66 tff(3717,plain,
% 11.49/11.66 (((~![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_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)))) | ((~node17(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)))),
% 11.49/11.66 inference(monotonicity,[status(thm)],[3716])).
% 11.49/11.66 tff(3718,plain,
% 11.49/11.66 (((~![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_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)))) | (~node17(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))),
% 11.49/11.66 inference(transitivity,[status(thm)],[3717, 3715])).
% 11.49/11.66 tff(3719,plain,
% 11.49/11.66 ((~![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_e, s4)) | m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~node17(c_e_h_1, c_e, s4)))),
% 11.49/11.66 inference(quant_inst,[status(thm)],[])).
% 11.49/11.66 tff(3720,plain,
% 11.49/11.66 ((~![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)))) | (~node17(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)),
% 11.49/11.66 inference(modus_ponens,[status(thm)],[3719, 3718])).
% 11.49/11.66 tff(3721,plain,
% 11.49/11.66 ((~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)),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3720, 359, 3714])).
% 11.49/11.66 tff(3722,plain,
% 11.49/11.66 (~m_c_h_element_v_in1(c_e_h_1, c_e, s4)),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3721, 3713])).
% 11.49/11.66 tff(3723,assumption,(~node15(c_e_h_1, c_e, s4, s5)), introduced(assumption)).
% 11.49/11.66 tff(3724,plain,
% 11.49/11.66 (((~![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_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))),
% 11.49/11.66 inference(rewrite,[status(thm)],[])).
% 11.49/11.66 tff(3725,plain,
% 11.49/11.66 ((~![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_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))),
% 11.49/11.66 inference(quant_inst,[status(thm)],[])).
% 11.49/11.66 tff(3726,plain,
% 11.49/11.66 ((~![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_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)),
% 11.49/11.66 inference(modus_ponens,[status(thm)],[3725, 3724])).
% 11.49/11.66 tff(3727,plain,
% 11.49/11.66 (~node16(c_e_h_1, c_e, s4)),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3726, 377, 3722, 3713])).
% 11.49/11.66 tff(3728,plain,
% 11.49/11.66 (((~![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))),
% 11.49/11.66 inference(rewrite,[status(thm)],[])).
% 11.49/11.66 tff(3729,plain,
% 11.49/11.66 ((~![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))),
% 11.49/11.66 inference(quant_inst,[status(thm)],[])).
% 11.49/11.66 tff(3730,plain,
% 11.49/11.66 ((~![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)),
% 11.49/11.66 inference(modus_ponens,[status(thm)],[3729, 3728])).
% 11.49/11.66 tff(3731,plain,
% 11.49/11.66 (node19(c_e_h_1, c_e, s4, s5)),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3730, 312, 1542])).
% 11.49/11.66 tff(3732,plain,
% 11.49/11.66 (((~![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_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))),
% 11.49/11.66 inference(rewrite,[status(thm)],[])).
% 11.49/11.66 tff(3733,plain,
% 11.49/11.66 ((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))),
% 11.49/11.66 inference(rewrite,[status(thm)],[])).
% 11.49/11.66 tff(3734,plain,
% 11.49/11.66 (((~![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_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)))),
% 11.49/11.66 inference(monotonicity,[status(thm)],[3733])).
% 11.49/11.66 tff(3735,plain,
% 11.49/11.66 (((~![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_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))),
% 11.49/11.66 inference(transitivity,[status(thm)],[3734, 3732])).
% 11.49/11.66 tff(3736,plain,
% 11.49/11.66 ((~![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_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)))),
% 11.49/11.66 inference(quant_inst,[status(thm)],[])).
% 11.49/11.66 tff(3737,plain,
% 11.49/11.66 ((~![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_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)),
% 11.49/11.66 inference(modus_ponens,[status(thm)],[3736, 3735])).
% 11.49/11.66 tff(3738,plain,
% 11.49/11.66 (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)),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3737, 409, 3731])).
% 11.49/11.66 tff(3739,plain,
% 11.49/11.66 (node14(c_e_h_1, c_e, s4, s5)),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3738, 3727, 3723])).
% 11.49/11.66 tff(3740,plain,
% 11.49/11.66 (((~![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_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)))),
% 11.49/11.66 inference(rewrite,[status(thm)],[])).
% 11.49/11.66 tff(3741,plain,
% 11.49/11.66 (((~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)))),
% 11.49/11.66 inference(rewrite,[status(thm)],[])).
% 11.49/11.66 tff(3742,plain,
% 11.49/11.66 (((~![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_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))))),
% 11.49/11.66 inference(monotonicity,[status(thm)],[3741])).
% 11.49/11.66 tff(3743,plain,
% 11.49/11.66 (((~![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_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)))),
% 11.49/11.66 inference(transitivity,[status(thm)],[3742, 3740])).
% 11.49/11.66 tff(3744,plain,
% 11.49/11.66 ((~![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_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)))),
% 11.49/11.66 inference(quant_inst,[status(thm)],[])).
% 11.49/11.66 tff(3745,plain,
% 11.49/11.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~node14(c_e_h_1, c_e, s4, s5))),
% 11.49/11.66 inference(modus_ponens,[status(thm)],[3744, 3743])).
% 11.49/11.66 tff(3746,plain,
% 11.49/11.66 ($false),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3745, 427, 3429, 3739, 3722])).
% 11.49/11.66 tff(3747,plain,(m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | node15(c_e_h_1, c_e, s4, s5) | (~node17(c_e_h_1, c_e, s4))), inference(lemma,lemma(discharge,[]))).
% 11.49/11.66 tff(3748,plain,
% 11.49/11.66 (~node17(c_e_h_1, c_e, s4)),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3747, 3429, 3713, 3712])).
% 11.49/11.66 tff(3749,plain,
% 11.49/11.66 (((~![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_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) | node18(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5)))),
% 11.49/11.66 inference(rewrite,[status(thm)],[])).
% 11.49/11.66 tff(3750,plain,
% 11.49/11.66 ((~![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_e, s4) | node18(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5)))),
% 11.49/11.66 inference(quant_inst,[status(thm)],[])).
% 11.49/11.66 tff(3751,plain,
% 11.49/11.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s4) | node18(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5))),
% 11.49/11.66 inference(modus_ponens,[status(thm)],[3750, 3749])).
% 11.49/11.66 tff(3752,plain,
% 11.49/11.66 (node17(c_e_h_1, c_e, s4) | node18(c_e_h_1, c_e, s4, s5)),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3751, 326, 3731])).
% 11.49/11.66 tff(3753,plain,
% 11.49/11.66 ($false),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3752, 3748, 3704])).
% 11.49/11.66 tff(3754,plain,((~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,[]))).
% 11.49/11.66 tff(3755,plain,
% 11.49/11.66 (~m_c_h_element_v_out(c_e_h_1, c_e, s5)),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3754, 3428])).
% 11.49/11.66 tff(3756,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)), introduced(assumption)).
% 11.49/11.66 tff(3757,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s5)), introduced(assumption)).
% 11.49/11.66 tff(3758,plain,
% 11.49/11.66 (^[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)))),
% 11.49/11.66 inference(bind,[status(th)],[])).
% 11.49/11.66 tff(3759,plain,
% 11.49/11.66 (![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))),
% 11.49/11.66 inference(quant_intro,[status(thm)],[3758])).
% 11.49/11.66 tff(3760,plain,
% 11.49/11.66 (![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))),
% 11.49/11.66 inference(rewrite,[status(thm)],[])).
% 11.49/11.66 tff(3761,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')).
% 11.49/11.66 tff(3762,plain,
% 11.49/11.66 (![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))),
% 11.49/11.66 inference(modus_ponens,[status(thm)],[3761, 3760])).
% 11.49/11.66 tff(3763,plain,(
% 11.49/11.66 ![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))),
% 11.49/11.66 inference(skolemize,[status(sab)],[3762])).
% 11.49/11.66 tff(3764,plain,
% 11.49/11.66 (![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))),
% 11.49/11.66 inference(modus_ponens,[status(thm)],[3763, 3759])).
% 11.49/11.66 tff(3765,plain,
% 11.49/11.66 (((~![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))),
% 11.49/11.66 inference(rewrite,[status(thm)],[])).
% 11.49/11.66 tff(3766,plain,
% 11.49/11.66 ((~![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))),
% 11.49/11.66 inference(quant_inst,[status(thm)],[])).
% 11.49/11.66 tff(3767,plain,
% 11.49/11.66 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5) | m_c_h_element_v_out(c_e_h_1, c_e, s5)),
% 11.49/11.66 inference(modus_ponens,[status(thm)],[3766, 3765])).
% 11.49/11.66 tff(3768,plain,
% 11.49/11.66 ($false),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3767, 3764, 3757, 3756])).
% 11.49/11.66 tff(3769,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s5) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)), inference(lemma,lemma(discharge,[]))).
% 11.49/11.66 tff(3770,plain,
% 11.49/11.66 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3769, 3755])).
% 11.49/11.66 tff(3771,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)), introduced(assumption)).
% 11.49/11.66 tff(3772,plain,
% 11.49/11.66 (((~![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))),
% 11.49/11.66 inference(rewrite,[status(thm)],[])).
% 11.49/11.66 tff(3773,plain,
% 11.49/11.66 ((~![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))),
% 11.49/11.66 inference(quant_inst,[status(thm)],[])).
% 11.49/11.66 tff(3774,plain,
% 11.49/11.66 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4) | m_c_h_element_v_out(c_e_h_1, c_e, s4)),
% 11.49/11.66 inference(modus_ponens,[status(thm)],[3773, 3772])).
% 11.49/11.66 tff(3775,plain,
% 11.49/11.66 ($false),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3774, 3764, 3697, 3771])).
% 11.49/11.66 tff(3776,plain,(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)), inference(lemma,lemma(discharge,[]))).
% 11.49/11.66 tff(3777,plain,
% 11.49/11.66 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3776, 3695])).
% 11.49/11.66 tff(3778,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)), introduced(assumption)).
% 11.49/11.66 tff(3779,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s3)), introduced(assumption)).
% 11.49/11.66 tff(3780,plain,
% 11.49/11.66 (((~![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))),
% 11.49/11.66 inference(rewrite,[status(thm)],[])).
% 11.49/11.66 tff(3781,plain,
% 11.49/11.66 ((~![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))),
% 11.49/11.66 inference(quant_inst,[status(thm)],[])).
% 11.49/11.66 tff(3782,plain,
% 11.49/11.66 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3) | m_c_h_element_v_out(c_e_h_1, c_e, s3)),
% 11.49/11.66 inference(modus_ponens,[status(thm)],[3781, 3780])).
% 11.49/11.66 tff(3783,plain,
% 11.49/11.66 ($false),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3782, 3764, 3779, 3778])).
% 11.49/11.66 tff(3784,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s3) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)), inference(lemma,lemma(discharge,[]))).
% 11.49/11.66 tff(3785,plain,
% 11.49/11.66 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3784, 3623])).
% 11.49/11.66 tff(3786,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)), introduced(assumption)).
% 11.49/11.66 tff(3787,assumption,(node11(c_e_h_1, c_n, s1, s2)), introduced(assumption)).
% 11.49/11.66 tff(3788,plain,
% 11.49/11.66 (^[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)))),
% 11.49/11.66 inference(bind,[status(th)],[])).
% 11.49/11.66 tff(3789,plain,
% 11.49/11.66 (![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))),
% 11.49/11.66 inference(quant_intro,[status(thm)],[3788])).
% 11.49/11.66 tff(3790,plain,
% 11.49/11.66 (![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))),
% 11.49/11.66 inference(rewrite,[status(thm)],[])).
% 11.49/11.66 tff(3791,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')).
% 11.49/11.66 tff(3792,plain,
% 11.49/11.66 (![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))),
% 11.49/11.66 inference(modus_ponens,[status(thm)],[3791, 3790])).
% 11.49/11.66 tff(3793,plain,(
% 11.49/11.66 ![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))),
% 11.49/11.66 inference(skolemize,[status(sab)],[3792])).
% 11.49/11.66 tff(3794,plain,
% 11.49/11.66 (![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))),
% 11.49/11.66 inference(modus_ponens,[status(thm)],[3793, 3789])).
% 11.49/11.66 tff(3795,plain,
% 11.49/11.66 (((~![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))),
% 11.49/11.66 inference(rewrite,[status(thm)],[])).
% 11.49/11.66 tff(3796,plain,
% 11.49/11.66 ((~![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))),
% 11.49/11.66 inference(quant_inst,[status(thm)],[])).
% 11.49/11.66 tff(3797,plain,
% 11.49/11.66 ((~![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)),
% 11.49/11.66 inference(modus_ponens,[status(thm)],[3796, 3795])).
% 11.49/11.66 tff(3798,plain,
% 11.49/11.66 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3797, 3794, 137])).
% 11.49/11.66 tff(3799,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)), introduced(assumption)).
% 11.49/11.66 tff(3800,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)), introduced(assumption)).
% 11.49/11.66 tff(3801,plain,
% 11.49/11.66 (^[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))))),
% 11.49/11.66 inference(bind,[status(th)],[])).
% 11.49/11.66 tff(3802,plain,
% 11.49/11.66 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_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)))),
% 11.49/11.66 inference(quant_intro,[status(thm)],[3801])).
% 11.49/11.66 tff(3803,plain,
% 11.49/11.66 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_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)))),
% 11.49/11.66 inference(rewrite,[status(thm)],[])).
% 11.49/11.66 tff(3804,plain,
% 11.49/11.66 (^[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)))))),
% 11.49/11.66 inference(bind,[status(th)],[])).
% 11.49/11.66 tff(3805,plain,
% 11.49/11.66 (![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)))),
% 11.49/11.66 inference(quant_intro,[status(thm)],[3804])).
% 11.49/11.66 tff(3806,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')).
% 11.49/11.66 tff(3807,plain,
% 11.49/11.66 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 11.49/11.66 inference(modus_ponens,[status(thm)],[3806, 3805])).
% 11.49/11.66 tff(3808,plain,
% 11.49/11.66 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 11.49/11.66 inference(modus_ponens,[status(thm)],[3807, 3803])).
% 11.49/11.66 tff(3809,plain,(
% 11.49/11.66 ![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 11.49/11.66 inference(skolemize,[status(sab)],[3808])).
% 11.49/11.66 tff(3810,plain,
% 11.49/11.66 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 11.49/11.66 inference(modus_ponens,[status(thm)],[3809, 3802])).
% 11.49/11.66 tff(3811,plain,
% 11.49/11.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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, 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)))),
% 11.49/11.66 inference(rewrite,[status(thm)],[])).
% 11.49/11.66 tff(3812,plain,
% 11.49/11.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)))),
% 11.49/11.66 inference(quant_inst,[status(thm)],[])).
% 11.49/11.66 tff(3813,plain,
% 11.49/11.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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))),
% 11.49/11.66 inference(modus_ponens,[status(thm)],[3812, 3811])).
% 11.49/11.66 tff(3814,plain,
% 11.49/11.66 (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))),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3813, 3810])).
% 11.49/11.66 tff(3815,plain,
% 11.49/11.66 (~node11(c_e_h_1, c_n, s0, s1)),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3814, 3800, 3799])).
% 11.49/11.66 tff(3816,plain,
% 11.49/11.66 (((~![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))),
% 11.49/11.66 inference(rewrite,[status(thm)],[])).
% 11.49/11.66 tff(3817,plain,
% 11.49/11.66 ((~![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))),
% 11.49/11.66 inference(quant_inst,[status(thm)],[])).
% 11.49/11.66 tff(3818,plain,
% 11.49/11.66 ((~![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)),
% 11.49/11.66 inference(modus_ponens,[status(thm)],[3817, 3816])).
% 11.49/11.66 tff(3819,plain,
% 11.49/11.66 (node10(c_e_h_1, c_n, s0, s1)),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3818, 110, 100, 3815])).
% 11.49/11.66 tff(3820,plain,
% 11.49/11.66 (((~![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))),
% 11.49/11.66 inference(rewrite,[status(thm)],[])).
% 11.49/11.66 tff(3821,plain,
% 11.49/11.66 ((~![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))),
% 11.49/11.66 inference(quant_inst,[status(thm)],[])).
% 11.49/11.66 tff(3822,plain,
% 11.49/11.66 ((~![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)),
% 11.49/11.66 inference(modus_ponens,[status(thm)],[3821, 3820])).
% 11.49/11.66 tff(3823,plain,
% 11.49/11.66 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)),
% 11.49/11.66 inference(unit_resolution,[status(thm)],[3822, 3764, 3482])).
% 11.49/11.66 tff(3824,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)), introduced(assumption)).
% 11.49/11.66 tff(3825,plain,
% 11.49/11.66 (^[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)))),
% 11.49/11.66 inference(bind,[status(th)],[])).
% 11.49/11.66 tff(3826,plain,
% 11.49/11.66 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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))),
% 11.49/11.66 inference(quant_intro,[status(thm)],[3825])).
% 11.49/11.66 tff(3827,plain,
% 11.49/11.66 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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))),
% 11.49/11.66 inference(rewrite,[status(thm)],[])).
% 11.49/11.66 tff(3828,plain,
% 11.49/11.66 (^[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))))),
% 11.49/11.67 inference(bind,[status(th)],[])).
% 11.49/11.67 tff(3829,plain,
% 11.49/11.67 (![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))),
% 11.49/11.67 inference(quant_intro,[status(thm)],[3828])).
% 11.49/11.67 tff(3830,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')).
% 11.49/11.67 tff(3831,plain,
% 11.49/11.67 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 11.49/11.67 inference(modus_ponens,[status(thm)],[3830, 3829])).
% 11.49/11.67 tff(3832,plain,
% 11.49/11.67 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 11.49/11.67 inference(modus_ponens,[status(thm)],[3831, 3827])).
% 11.49/11.67 tff(3833,plain,(
% 11.49/11.67 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 11.49/11.67 inference(skolemize,[status(sab)],[3832])).
% 11.49/11.67 tff(3834,plain,
% 11.49/11.67 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 11.49/11.67 inference(modus_ponens,[status(thm)],[3833, 3826])).
% 11.49/11.67 tff(3835,plain,
% 11.49/11.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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, 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)) | (~node10(c_e_h_1, 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_1, c_n, 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)) | (~node10(c_e_h_1, c_n, s0, s1)))),
% 11.49/11.67 inference(rewrite,[status(thm)],[])).
% 11.49/11.67 tff(3836,plain,
% 11.49/11.67 (((~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_out(c_e_h_1, c_n, 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)) | (~node10(c_e_h_1, c_n, s0, s1)))),
% 11.49/11.67 inference(rewrite,[status(thm)],[])).
% 11.49/11.67 tff(3837,plain,
% 11.49/11.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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_out(c_e_h_1, c_n, 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)) | (~node10(c_e_h_1, c_n, s0, s1))))),
% 11.49/11.67 inference(monotonicity,[status(thm)],[3836])).
% 11.49/11.67 tff(3838,plain,
% 11.49/11.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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_out(c_e_h_1, c_n, 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)) | (~node10(c_e_h_1, c_n, s0, s1)))),
% 11.49/11.67 inference(transitivity,[status(thm)],[3837, 3835])).
% 11.49/11.67 tff(3839,plain,
% 11.49/11.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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))),
% 11.49/11.67 inference(quant_inst,[status(thm)],[])).
% 11.49/11.67 tff(3840,plain,
% 11.49/11.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)) | (~node10(c_e_h_1, c_n, s0, s1))),
% 11.49/11.67 inference(modus_ponens,[status(thm)],[3839, 3838])).
% 11.49/11.67 tff(3841,plain,
% 11.49/11.67 ($false),
% 11.49/11.67 inference(unit_resolution,[status(thm)],[3840, 3834, 3800, 3824, 3823, 3819])).
% 11.49/11.67 tff(3842,plain,(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)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0))), inference(lemma,lemma(discharge,[]))).
% 11.49/11.67 tff(3843,plain,
% 11.49/11.67 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)),
% 11.49/11.67 inference(unit_resolution,[status(thm)],[3842, 3798, 42])).
% 11.49/11.67 tff(3844,plain,
% 11.49/11.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~node11(c_e_h_1, 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_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~node11(c_e_h_1, c_n, s1, s2)))),
% 11.49/11.67 inference(rewrite,[status(thm)],[])).
% 11.49/11.67 tff(3845,plain,
% 11.49/11.67 ((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))) <=> ((~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) | (~node11(c_e_h_1, c_n, s1, s2)))),
% 11.49/11.67 inference(rewrite,[status(thm)],[])).
% 11.49/11.67 tff(3846,plain,
% 11.49/11.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)))) | ((~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) | (~node11(c_e_h_1, c_n, s1, s2))))),
% 11.49/11.67 inference(monotonicity,[status(thm)],[3845])).
% 11.49/11.67 tff(3847,plain,
% 11.49/11.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)))) | (~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) | (~node11(c_e_h_1, c_n, s1, s2)))),
% 11.49/11.67 inference(transitivity,[status(thm)],[3846, 3844])).
% 11.49/11.67 tff(3848,plain,
% 11.49/11.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)))),
% 11.49/11.67 inference(quant_inst,[status(thm)],[])).
% 11.49/11.67 tff(3849,plain,
% 11.49/11.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~node11(c_e_h_1, c_n, s1, s2))),
% 11.49/11.67 inference(modus_ponens,[status(thm)],[3848, 3847])).
% 11.49/11.67 tff(3850,plain,
% 11.49/11.67 ($false),
% 11.49/11.67 inference(unit_resolution,[status(thm)],[3849, 3810, 3843, 3786, 3787])).
% 11.49/11.67 tff(3851,plain,((~node11(c_e_h_1, c_n, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)), inference(lemma,lemma(discharge,[]))).
% 11.49/11.67 tff(3852,plain,
% 11.49/11.67 (~node11(c_e_h_1, c_n, s1, s2)),
% 11.49/11.67 inference(unit_resolution,[status(thm)],[3851, 3786])).
% 11.49/11.67 tff(3853,plain,
% 11.49/11.67 (((~![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))),
% 11.49/11.67 inference(rewrite,[status(thm)],[])).
% 11.49/11.67 tff(3854,plain,
% 11.49/11.67 ((~![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))),
% 11.49/11.67 inference(quant_inst,[status(thm)],[])).
% 11.49/11.67 tff(3855,plain,
% 11.49/11.67 ((~![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)),
% 11.49/11.67 inference(modus_ponens,[status(thm)],[3854, 3853])).
% 11.49/11.67 tff(3856,plain,
% 11.49/11.67 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)),
% 11.49/11.67 inference(unit_resolution,[status(thm)],[3855, 3794, 152])).
% 11.49/11.67 tff(3857,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)), introduced(assumption)).
% 11.49/11.67 tff(3858,plain,
% 11.49/11.67 (((~![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))),
% 11.49/11.67 inference(rewrite,[status(thm)],[])).
% 11.49/11.67 tff(3859,plain,
% 11.49/11.67 ((~![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))),
% 11.49/11.67 inference(quant_inst,[status(thm)],[])).
% 11.49/11.67 tff(3860,plain,
% 11.49/11.67 ((~![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)),
% 11.49/11.67 inference(modus_ponens,[status(thm)],[3859, 3858])).
% 11.49/11.67 tff(3861,plain,
% 11.49/11.67 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)),
% 11.49/11.67 inference(unit_resolution,[status(thm)],[3860, 3764, 3518])).
% 11.49/11.67 tff(3862,assumption,(node10(c_e_h_1, c_n, s1, s2)), introduced(assumption)).
% 11.49/11.67 tff(3863,plain,
% 11.49/11.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~m_and_h_gate_h_init_v_in2(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) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)))),
% 11.49/11.67 inference(rewrite,[status(thm)],[])).
% 11.49/11.67 tff(3864,plain,
% 11.49/11.67 (((~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) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)))),
% 11.49/11.67 inference(rewrite,[status(thm)],[])).
% 11.49/11.67 tff(3865,plain,
% 11.49/11.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1))))),
% 11.49/11.67 inference(monotonicity,[status(thm)],[3864])).
% 11.49/11.67 tff(3866,plain,
% 11.49/11.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)))),
% 11.49/11.67 inference(transitivity,[status(thm)],[3865, 3863])).
% 11.49/11.67 tff(3867,plain,
% 11.49/11.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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))),
% 11.49/11.67 inference(quant_inst,[status(thm)],[])).
% 11.49/11.67 tff(3868,plain,
% 11.49/11.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1))),
% 11.49/11.67 inference(modus_ponens,[status(thm)],[3867, 3866])).
% 11.49/11.67 tff(3869,plain,
% 11.49/11.67 ($false),
% 11.49/11.67 inference(unit_resolution,[status(thm)],[3868, 3834, 3786, 3862, 3861, 3857])).
% 11.49/11.67 tff(3870,plain,((~node10(c_e_h_1, c_n, s1, 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))), inference(lemma,lemma(discharge,[]))).
% 11.49/11.67 tff(3871,plain,
% 11.49/11.67 (~node10(c_e_h_1, c_n, s1, s2)),
% 11.49/11.67 inference(unit_resolution,[status(thm)],[3870, 3786, 3856])).
% 11.49/11.67 tff(3872,plain,
% 11.49/11.67 (((~![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))),
% 11.49/11.67 inference(rewrite,[status(thm)],[])).
% 11.49/11.67 tff(3873,plain,
% 11.49/11.67 ((~![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))),
% 11.49/11.67 inference(quant_inst,[status(thm)],[])).
% 11.49/11.67 tff(3874,plain,
% 11.49/11.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_1, c_n, s1, s2) | node11(c_e_h_1, c_n, s1, s2)),
% 11.49/11.67 inference(modus_ponens,[status(thm)],[3873, 3872])).
% 11.49/11.67 tff(3875,plain,
% 11.49/11.67 (node10(c_e_h_1, c_n, s1, s2) | node11(c_e_h_1, c_n, s1, s2)),
% 11.49/11.67 inference(unit_resolution,[status(thm)],[3874, 110, 470])).
% 11.49/11.67 tff(3876,plain,
% 11.49/11.67 ($false),
% 11.49/11.67 inference(unit_resolution,[status(thm)],[3875, 3871, 3852])).
% 11.49/11.67 tff(3877,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)), inference(lemma,lemma(discharge,[]))).
% 11.49/11.67 tff(3878,plain,
% 11.49/11.67 (((~![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)))),
% 11.49/11.67 inference(rewrite,[status(thm)],[])).
% 11.49/11.67 tff(3879,plain,
% 11.49/11.67 ((~![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)))),
% 11.49/11.67 inference(quant_inst,[status(thm)],[])).
% 11.49/11.67 tff(3880,plain,
% 11.49/11.67 ((~![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))),
% 11.49/11.67 inference(modus_ponens,[status(thm)],[3879, 3878])).
% 11.49/11.67 tff(3881,plain,
% 11.49/11.67 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2)),
% 11.49/11.67 inference(unit_resolution,[status(thm)],[3880, 49, 3877])).
% 11.49/11.67 tff(3882,plain,
% 11.49/11.67 (((~![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))),
% 11.49/11.67 inference(rewrite,[status(thm)],[])).
% 11.49/11.67 tff(3883,plain,
% 11.49/11.67 ((~![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))),
% 11.49/11.67 inference(quant_inst,[status(thm)],[])).
% 11.49/11.67 tff(3884,plain,
% 11.49/11.67 ((~![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)),
% 11.49/11.67 inference(modus_ponens,[status(thm)],[3883, 3882])).
% 11.49/11.67 tff(3885,plain,
% 11.49/11.67 (~node9(c_e_h_1, c_m, s2)),
% 11.49/11.67 inference(unit_resolution,[status(thm)],[3884, 63, 3881])).
% 11.49/11.67 tff(3886,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)), introduced(assumption)).
% 11.49/11.67 tff(3887,assumption,(node11(c_e_h_1, c_m, s2, s3)), introduced(assumption)).
% 11.49/11.67 tff(3888,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)), introduced(assumption)).
% 11.49/11.67 tff(3889,assumption,(node10(c_e_h_1, c_m, s1, s2)), introduced(assumption)).
% 11.49/11.67 tff(3890,plain,
% 11.49/11.67 (((~![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)))),
% 11.49/11.67 inference(rewrite,[status(thm)],[])).
% 11.49/11.67 tff(3891,plain,
% 11.49/11.67 ((~![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)))),
% 11.49/11.67 inference(quant_inst,[status(thm)],[])).
% 11.49/11.67 tff(3892,plain,
% 11.49/11.67 ((~![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))),
% 11.49/11.67 inference(modus_ponens,[status(thm)],[3891, 3890])).
% 11.49/11.67 tff(3893,plain,
% 11.49/11.67 ((~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))),
% 11.49/11.67 inference(unit_resolution,[status(thm)],[3892, 49])).
% 11.49/11.67 tff(3894,plain,
% 11.49/11.67 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1)),
% 11.49/11.67 inference(unit_resolution,[status(thm)],[3893, 3843])).
% 11.49/11.67 tff(3895,plain,
% 11.49/11.67 (((~![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))),
% 11.49/11.67 inference(rewrite,[status(thm)],[])).
% 11.49/11.67 tff(3896,plain,
% 11.49/11.67 ((~![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))),
% 11.49/11.67 inference(quant_inst,[status(thm)],[])).
% 11.49/11.67 tff(3897,plain,
% 11.49/11.67 ((~![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)),
% 11.49/11.67 inference(modus_ponens,[status(thm)],[3896, 3895])).
% 11.49/11.67 tff(3898,plain,
% 11.49/11.67 (~node9(c_e_h_1, c_m, s1)),
% 11.49/11.67 inference(unit_resolution,[status(thm)],[3897, 63, 3894])).
% 11.49/11.67 tff(3899,plain,
% 11.49/11.67 (((~![Y: $i, I0: $i, 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)))),
% 11.49/11.67 inference(rewrite,[status(thm)],[])).
% 11.49/11.67 tff(3900,plain,
% 11.49/11.67 ((~![Y: $i, I0: $i, 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)))),
% 11.49/11.67 inference(quant_inst,[status(thm)],[])).
% 11.49/11.67 tff(3901,plain,
% 11.49/11.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | (~node10(c_e_h_1, c_m, s1, s2))),
% 11.49/11.67 inference(modus_ponens,[status(thm)],[3900, 3899])).
% 11.49/11.67 tff(3902,plain,
% 11.49/11.67 ($false),
% 11.49/11.67 inference(unit_resolution,[status(thm)],[3901, 77, 3898, 3888, 3889])).
% 11.49/11.67 tff(3903,plain,((~node10(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,[]))).
% 11.49/11.67 tff(3904,plain,
% 11.49/11.67 (~node10(c_e_h_1, c_m, s1, s2)),
% 11.49/11.67 inference(unit_resolution,[status(thm)],[3903, 3888])).
% 11.49/11.67 tff(3905,plain,
% 11.49/11.67 (((~![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))),
% 11.49/11.67 inference(rewrite,[status(thm)],[])).
% 11.49/11.67 tff(3906,plain,
% 11.49/11.67 ((~![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))),
% 11.49/11.67 inference(quant_inst,[status(thm)],[])).
% 11.49/11.67 tff(3907,plain,
% 11.49/11.67 ((~![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)),
% 11.49/11.67 inference(modus_ponens,[status(thm)],[3906, 3905])).
% 11.49/11.67 tff(3908,plain,
% 11.49/11.67 (node10(c_e_h_1, c_m, s1, s2) | node11(c_e_h_1, c_m, s1, s2)),
% 11.49/11.67 inference(unit_resolution,[status(thm)],[3907, 110, 470])).
% 11.49/11.67 tff(3909,plain,
% 11.49/11.67 (node11(c_e_h_1, c_m, s1, s2)),
% 11.49/11.67 inference(unit_resolution,[status(thm)],[3908, 3904])).
% 11.49/11.67 tff(3910,plain,
% 11.49/11.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, 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))),
% 11.49/11.67 inference(rewrite,[status(thm)],[])).
% 11.49/11.67 tff(3911,plain,
% 11.49/11.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, 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))),
% 11.49/11.67 inference(quant_inst,[status(thm)],[])).
% 11.49/11.67 tff(3912,plain,
% 11.49/11.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | (~node11(c_e_h_1, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)),
% 11.49/11.67 inference(modus_ponens,[status(thm)],[3911, 3910])).
% 11.49/11.67 tff(3913,plain,
% 11.49/11.67 ($false),
% 11.49/11.67 inference(unit_resolution,[status(thm)],[3912, 147, 152, 3888, 3909])).
% 11.49/11.67 tff(3914,plain,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)), inference(lemma,lemma(discharge,[]))).
% 11.49/11.67 tff(3915,plain,
% 11.49/11.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, 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))),
% 11.49/11.67 inference(rewrite,[status(thm)],[])).
% 11.49/11.67 tff(3916,plain,
% 11.49/11.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, 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))),
% 11.49/11.67 inference(quant_inst,[status(thm)],[])).
% 11.49/11.67 tff(3917,plain,
% 11.49/11.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node11(c_e_h_1, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)),
% 11.49/11.67 inference(modus_ponens,[status(thm)],[3916, 3915])).
% 11.49/11.67 tff(3918,plain,
% 11.49/11.67 ($false),
% 11.49/11.67 inference(unit_resolution,[status(thm)],[3917, 147, 3914, 3886, 3887])).
% 11.49/11.67 tff(3919,plain,((~node11(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,[]))).
% 11.49/11.67 tff(3920,plain,
% 11.49/11.67 (~node11(c_e_h_1, c_m, s2, s3)),
% 11.49/11.67 inference(unit_resolution,[status(thm)],[3919, 3886])).
% 11.49/11.67 tff(3921,plain,
% 11.49/11.67 (((~![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))),
% 11.49/11.68 inference(rewrite,[status(thm)],[])).
% 11.49/11.68 tff(3922,plain,
% 11.49/11.68 ((~![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))),
% 11.49/11.68 inference(quant_inst,[status(thm)],[])).
% 11.49/11.68 tff(3923,plain,
% 11.49/11.68 ((~![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)),
% 11.49/11.68 inference(modus_ponens,[status(thm)],[3922, 3921])).
% 11.49/11.68 tff(3924,plain,
% 11.49/11.68 (node10(c_e_h_1, c_m, s2, s3) | node11(c_e_h_1, c_m, s2, s3)),
% 11.49/11.68 inference(unit_resolution,[status(thm)],[3923, 110, 604])).
% 11.49/11.68 tff(3925,plain,
% 11.49/11.68 (node10(c_e_h_1, c_m, s2, s3)),
% 11.49/11.68 inference(unit_resolution,[status(thm)],[3924, 3920])).
% 11.49/11.68 tff(3926,plain,
% 11.49/11.68 (((~![Y: $i, I0: $i, 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, s3)) | (~node10(c_e_h_1, c_m, s2, s3)) | node9(c_e_h_1, c_m, 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)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node10(c_e_h_1, c_m, s2, s3)) | node9(c_e_h_1, c_m, s2))),
% 11.49/11.68 inference(rewrite,[status(thm)],[])).
% 11.49/11.68 tff(3927,plain,
% 11.49/11.68 ((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))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node10(c_e_h_1, c_m, s2, s3)) | node9(c_e_h_1, c_m, s2))),
% 11.49/11.68 inference(rewrite,[status(thm)],[])).
% 11.49/11.68 tff(3928,plain,
% 11.49/11.68 (((~![Y: $i, I0: $i, 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)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node10(c_e_h_1, c_m, s2, s3)) | node9(c_e_h_1, c_m, s2)))),
% 11.49/11.68 inference(monotonicity,[status(thm)],[3927])).
% 11.49/11.68 tff(3929,plain,
% 11.49/11.68 (((~![Y: $i, I0: $i, 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)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node10(c_e_h_1, c_m, s2, s3)) | node9(c_e_h_1, c_m, s2))),
% 11.49/11.68 inference(transitivity,[status(thm)],[3928, 3926])).
% 11.49/11.68 tff(3930,plain,
% 11.49/11.68 ((~![Y: $i, I0: $i, 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)))),
% 11.49/11.68 inference(quant_inst,[status(thm)],[])).
% 11.49/11.68 tff(3931,plain,
% 11.49/11.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node10(c_e_h_1, c_m, s2, s3)) | node9(c_e_h_1, c_m, s2)),
% 11.49/11.68 inference(modus_ponens,[status(thm)],[3930, 3929])).
% 11.49/11.68 tff(3932,plain,
% 11.49/11.68 ($false),
% 11.49/11.68 inference(unit_resolution,[status(thm)],[3931, 77, 3886, 3925, 3885])).
% 11.49/11.68 tff(3933,plain,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)), inference(lemma,lemma(discharge,[]))).
% 11.49/11.68 tff(3934,plain,
% 11.49/11.68 (((~![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))),
% 11.49/11.68 inference(rewrite,[status(thm)],[])).
% 11.49/11.68 tff(3935,plain,
% 11.49/11.68 ((~![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))),
% 11.49/11.68 inference(quant_inst,[status(thm)],[])).
% 11.49/11.68 tff(3936,plain,
% 11.49/11.68 ((~![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)),
% 11.49/11.68 inference(modus_ponens,[status(thm)],[3935, 3934])).
% 11.49/11.68 tff(3937,plain,
% 11.49/11.68 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)),
% 11.49/11.68 inference(unit_resolution,[status(thm)],[3936, 3794, 3933])).
% 11.49/11.68 tff(3938,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)), introduced(assumption)).
% 11.49/11.68 tff(3939,plain,
% 11.49/11.68 (((~![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))),
% 11.49/11.68 inference(rewrite,[status(thm)],[])).
% 11.49/11.68 tff(3940,plain,
% 11.49/11.68 ((~![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))),
% 11.49/11.68 inference(quant_inst,[status(thm)],[])).
% 11.49/11.68 tff(3941,plain,
% 11.49/11.68 ((~![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)),
% 11.49/11.68 inference(modus_ponens,[status(thm)],[3940, 3939])).
% 11.49/11.68 tff(3942,plain,
% 11.49/11.68 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)),
% 11.49/11.68 inference(unit_resolution,[status(thm)],[3941, 3764, 3556])).
% 11.49/11.68 tff(3943,plain,
% 11.49/11.68 (((~![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))),
% 11.49/11.68 inference(rewrite,[status(thm)],[])).
% 11.49/11.68 tff(3944,plain,
% 11.49/11.68 ((~![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))),
% 11.49/11.68 inference(quant_inst,[status(thm)],[])).
% 11.49/11.68 tff(3945,plain,
% 11.49/11.68 ((~![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)),
% 11.49/11.68 inference(modus_ponens,[status(thm)],[3944, 3943])).
% 11.49/11.68 tff(3946,plain,
% 11.49/11.68 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)),
% 11.49/11.68 inference(unit_resolution,[status(thm)],[3945, 3794, 3914])).
% 11.49/11.68 tff(3947,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)), introduced(assumption)).
% 11.49/11.68 tff(3948,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)), introduced(assumption)).
% 11.49/11.68 tff(3949,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)), introduced(assumption)).
% 11.49/11.68 tff(3950,assumption,(node10(c_e_h_1, c_n, s2, s3)), introduced(assumption)).
% 11.49/11.68 tff(3951,plain,
% 11.49/11.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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)))),
% 11.49/11.68 inference(rewrite,[status(thm)],[])).
% 11.49/11.68 tff(3952,plain,
% 11.49/11.68 (((~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)))),
% 11.49/11.68 inference(rewrite,[status(thm)],[])).
% 11.49/11.68 tff(3953,plain,
% 11.49/11.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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))))),
% 11.49/11.68 inference(monotonicity,[status(thm)],[3952])).
% 11.49/11.68 tff(3954,plain,
% 11.49/11.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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)))),
% 11.49/11.68 inference(transitivity,[status(thm)],[3953, 3951])).
% 11.49/11.68 tff(3955,plain,
% 11.49/11.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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))),
% 11.49/11.68 inference(quant_inst,[status(thm)],[])).
% 11.49/11.68 tff(3956,plain,
% 11.49/11.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)) | (~node10(c_e_h_1, c_n, s2, s3))),
% 11.49/11.68 inference(modus_ponens,[status(thm)],[3955, 3954])).
% 11.49/11.68 tff(3957,plain,
% 11.49/11.68 ($false),
% 11.49/11.68 inference(unit_resolution,[status(thm)],[3956, 3834, 3949, 3950, 3948, 3947])).
% 11.49/11.68 tff(3958,plain,((~node10(c_e_h_1, c_n, s2, 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))), inference(lemma,lemma(discharge,[]))).
% 11.49/11.68 tff(3959,plain,
% 11.49/11.68 (~node10(c_e_h_1, c_n, s2, s3)),
% 11.49/11.68 inference(unit_resolution,[status(thm)],[3958, 3949, 3948, 3947])).
% 11.49/11.68 tff(3960,plain,
% 11.49/11.68 (((~![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))),
% 11.49/11.68 inference(rewrite,[status(thm)],[])).
% 11.49/11.68 tff(3961,plain,
% 11.49/11.68 ((~![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))),
% 11.49/11.68 inference(quant_inst,[status(thm)],[])).
% 11.49/11.68 tff(3962,plain,
% 11.49/11.68 ((~![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)),
% 11.49/11.68 inference(modus_ponens,[status(thm)],[3961, 3960])).
% 11.49/11.68 tff(3963,plain,
% 11.49/11.68 (node10(c_e_h_1, c_n, s2, s3) | node11(c_e_h_1, c_n, s2, s3)),
% 11.49/11.68 inference(unit_resolution,[status(thm)],[3962, 110, 604])).
% 11.49/11.68 tff(3964,plain,
% 11.49/11.68 (node11(c_e_h_1, c_n, s2, s3)),
% 11.49/11.68 inference(unit_resolution,[status(thm)],[3963, 3959])).
% 11.49/11.68 tff(3965,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)), introduced(assumption)).
% 11.49/11.68 tff(3966,plain,
% 11.49/11.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)))),
% 11.49/11.68 inference(rewrite,[status(thm)],[])).
% 11.49/11.68 tff(3967,plain,
% 11.49/11.68 ((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)))),
% 11.49/11.68 inference(rewrite,[status(thm)],[])).
% 11.49/11.68 tff(3968,plain,
% 11.49/11.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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))))),
% 11.49/11.68 inference(monotonicity,[status(thm)],[3967])).
% 11.49/11.68 tff(3969,plain,
% 11.49/11.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)))),
% 11.49/11.68 inference(transitivity,[status(thm)],[3968, 3966])).
% 11.49/11.68 tff(3970,plain,
% 11.49/11.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)))),
% 11.49/11.68 inference(quant_inst,[status(thm)],[])).
% 11.49/11.68 tff(3971,plain,
% 11.49/11.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)) | (~node11(c_e_h_1, c_n, s2, s3))),
% 11.49/11.68 inference(modus_ponens,[status(thm)],[3970, 3969])).
% 11.49/11.68 tff(3972,plain,
% 11.49/11.68 ($false),
% 11.49/11.68 inference(unit_resolution,[status(thm)],[3971, 3810, 3949, 3965, 3964])).
% 11.49/11.68 tff(3973,plain,(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)) | (~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))), inference(lemma,lemma(discharge,[]))).
% 11.49/11.68 tff(3974,plain,
% 11.49/11.68 (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))),
% 11.49/11.68 inference(unit_resolution,[status(thm)],[3973, 3877])).
% 11.49/11.68 tff(3975,plain,
% 11.49/11.68 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)),
% 11.49/11.68 inference(unit_resolution,[status(thm)],[3974, 3946, 3942])).
% 11.49/11.68 tff(3976,assumption,(node11(c_e_h_1, c_n, s3, s4)), introduced(assumption)).
% 11.49/11.68 tff(3977,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)), introduced(assumption)).
% 11.49/11.68 tff(3978,plain,
% 11.49/11.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)))),
% 11.49/11.68 inference(rewrite,[status(thm)],[])).
% 11.49/11.68 tff(3979,plain,
% 11.49/11.68 ((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)))),
% 11.49/11.68 inference(rewrite,[status(thm)],[])).
% 11.49/11.68 tff(3980,plain,
% 11.49/11.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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))))),
% 11.49/11.68 inference(monotonicity,[status(thm)],[3979])).
% 11.49/11.68 tff(3981,plain,
% 11.49/11.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)))),
% 11.49/11.68 inference(transitivity,[status(thm)],[3980, 3978])).
% 11.49/11.68 tff(3982,plain,
% 11.49/11.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)))),
% 11.49/11.68 inference(quant_inst,[status(thm)],[])).
% 11.49/11.68 tff(3983,plain,
% 11.49/11.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)) | (~node11(c_e_h_1, c_n, s3, s4))),
% 11.49/11.68 inference(modus_ponens,[status(thm)],[3982, 3981])).
% 11.49/11.68 tff(3984,plain,
% 11.49/11.68 ($false),
% 11.49/11.68 inference(unit_resolution,[status(thm)],[3983, 3810, 3938, 3977, 3976])).
% 11.49/11.68 tff(3985,plain,((~node11(c_e_h_1, c_n, s3, s4)) | 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))), inference(lemma,lemma(discharge,[]))).
% 11.49/11.68 tff(3986,plain,
% 11.49/11.68 ((~node11(c_e_h_1, c_n, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)),
% 11.49/11.68 inference(unit_resolution,[status(thm)],[3985, 3975])).
% 11.49/11.68 tff(3987,plain,
% 11.49/11.68 (~node11(c_e_h_1, c_n, s3, s4)),
% 11.49/11.68 inference(unit_resolution,[status(thm)],[3986, 3938])).
% 11.49/11.68 tff(3988,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)), introduced(assumption)).
% 11.49/11.68 tff(3989,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)), introduced(assumption)).
% 11.49/11.68 tff(3990,assumption,(node10(c_e_h_1, c_n, s3, s4)), introduced(assumption)).
% 11.49/11.68 tff(3991,plain,
% 11.49/11.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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) | (~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)) | (~node10(c_e_h_1, 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_1, c_n, 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)) | (~node10(c_e_h_1, c_n, s3, s4)))),
% 11.49/11.68 inference(rewrite,[status(thm)],[])).
% 11.49/11.68 tff(3992,plain,
% 11.49/11.68 (((~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) | (~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)) | (~node10(c_e_h_1, c_n, s3, s4)))),
% 11.49/11.68 inference(rewrite,[status(thm)],[])).
% 11.49/11.68 tff(3993,plain,
% 11.49/11.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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) | (~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)) | (~node10(c_e_h_1, c_n, s3, s4))))),
% 11.49/11.68 inference(monotonicity,[status(thm)],[3992])).
% 11.49/11.68 tff(3994,plain,
% 11.49/11.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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) | (~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)) | (~node10(c_e_h_1, c_n, s3, s4)))),
% 11.49/11.68 inference(transitivity,[status(thm)],[3993, 3991])).
% 11.49/11.68 tff(3995,plain,
% 11.49/11.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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))),
% 11.49/11.68 inference(quant_inst,[status(thm)],[])).
% 11.49/11.68 tff(3996,plain,
% 11.49/11.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)) | (~node10(c_e_h_1, c_n, s3, s4))),
% 11.49/11.68 inference(modus_ponens,[status(thm)],[3995, 3994])).
% 11.49/11.68 tff(3997,plain,
% 11.49/11.68 ($false),
% 11.49/11.68 inference(unit_resolution,[status(thm)],[3996, 3834, 3938, 3990, 3989, 3988])).
% 11.49/11.68 tff(3998,plain,((~node10(c_e_h_1, c_n, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, 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))), inference(lemma,lemma(discharge,[]))).
% 11.49/11.68 tff(3999,plain,
% 11.49/11.68 (~node10(c_e_h_1, c_n, s3, s4)),
% 11.49/11.68 inference(unit_resolution,[status(thm)],[3998, 3938, 3989, 3988])).
% 11.49/11.68 tff(4000,plain,
% 11.49/11.68 (((~![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))),
% 11.49/11.68 inference(rewrite,[status(thm)],[])).
% 11.49/11.68 tff(4001,plain,
% 11.49/11.68 ((~![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))),
% 11.49/11.68 inference(quant_inst,[status(thm)],[])).
% 11.49/11.68 tff(4002,plain,
% 11.49/11.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_1, c_n, s3, s4) | node11(c_e_h_1, c_n, s3, s4)),
% 11.49/11.68 inference(modus_ponens,[status(thm)],[4001, 4000])).
% 11.49/11.68 tff(4003,plain,
% 11.49/11.68 (node10(c_e_h_1, c_n, s3, s4) | node11(c_e_h_1, c_n, s3, s4)),
% 11.49/11.68 inference(unit_resolution,[status(thm)],[4002, 110, 1092])).
% 11.49/11.68 tff(4004,plain,
% 11.49/11.68 ($false),
% 11.49/11.68 inference(unit_resolution,[status(thm)],[4003, 3999, 3987])).
% 11.49/11.68 tff(4005,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, 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))), inference(lemma,lemma(discharge,[]))).
% 11.49/11.68 tff(4006,plain,
% 11.49/11.68 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3))),
% 11.49/11.68 inference(unit_resolution,[status(thm)],[4005, 3937])).
% 11.49/11.68 tff(4007,plain,
% 11.49/11.68 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)),
% 11.49/11.68 inference(unit_resolution,[status(thm)],[4006, 3785])).
% 11.49/11.68 tff(4008,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)), introduced(assumption)).
% 11.49/11.68 tff(4009,assumption,(node11(c_e_h_1, c_n, s4, s5)), introduced(assumption)).
% 11.49/11.68 tff(4010,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)), introduced(assumption)).
% 11.49/11.68 tff(4011,plain,
% 11.49/11.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)))),
% 11.49/11.68 inference(rewrite,[status(thm)],[])).
% 11.49/11.68 tff(4012,plain,
% 11.49/11.68 ((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)))),
% 11.49/11.68 inference(rewrite,[status(thm)],[])).
% 11.49/11.68 tff(4013,plain,
% 11.49/11.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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))))),
% 11.49/11.68 inference(monotonicity,[status(thm)],[4012])).
% 11.49/11.68 tff(4014,plain,
% 11.49/11.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)))),
% 11.49/11.69 inference(transitivity,[status(thm)],[4013, 4011])).
% 11.49/11.69 tff(4015,plain,
% 11.49/11.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)))),
% 11.49/11.69 inference(quant_inst,[status(thm)],[])).
% 11.49/11.69 tff(4016,plain,
% 11.49/11.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)) | (~node11(c_e_h_1, c_n, s4, s5))),
% 11.49/11.69 inference(modus_ponens,[status(thm)],[4015, 4014])).
% 11.49/11.69 tff(4017,plain,
% 11.49/11.69 ($false),
% 11.49/11.69 inference(unit_resolution,[status(thm)],[4016, 3810, 4010, 4008, 4009])).
% 11.49/11.69 tff(4018,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 11.49/11.69 tff(4019,plain,
% 11.49/11.69 (~node11(c_e_h_1, c_n, s4, s5)),
% 11.49/11.69 inference(unit_resolution,[status(thm)],[4018, 4008, 4007])).
% 11.49/11.69 tff(4020,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)), introduced(assumption)).
% 11.49/11.69 tff(4021,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)), introduced(assumption)).
% 11.49/11.69 tff(4022,plain,
% 11.49/11.69 (((~![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)))),
% 11.49/11.69 inference(rewrite,[status(thm)],[])).
% 11.49/11.69 tff(4023,plain,
% 11.49/11.69 ((~![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)))),
% 11.49/11.69 inference(quant_inst,[status(thm)],[])).
% 11.49/11.69 tff(4024,plain,
% 11.49/11.69 ((~![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))),
% 11.49/11.69 inference(modus_ponens,[status(thm)],[4023, 4022])).
% 11.49/11.69 tff(4025,plain,
% 11.49/11.69 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s3)),
% 11.49/11.69 inference(unit_resolution,[status(thm)],[4024, 49, 3975])).
% 11.49/11.69 tff(4026,plain,
% 11.49/11.69 (((~![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))),
% 11.49/11.69 inference(rewrite,[status(thm)],[])).
% 11.49/11.69 tff(4027,plain,
% 11.49/11.69 ((~![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))),
% 11.49/11.69 inference(quant_inst,[status(thm)],[])).
% 11.49/11.69 tff(4028,plain,
% 11.49/11.69 ((~![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)),
% 11.49/11.69 inference(modus_ponens,[status(thm)],[4027, 4026])).
% 11.49/11.69 tff(4029,plain,
% 11.49/11.69 (~node9(c_e_h_1, c_m, s3)),
% 11.49/11.69 inference(unit_resolution,[status(thm)],[4028, 63, 4025])).
% 11.49/11.69 tff(4030,assumption,(node10(c_e_h_1, c_m, s3, s4)), introduced(assumption)).
% 11.49/11.69 tff(4031,plain,
% 11.49/11.69 (((~![Y: $i, I0: $i, 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, s4)) | (~node10(c_e_h_1, c_m, s3, s4)) | node9(c_e_h_1, c_m, 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_1, c_m, s4)) | (~node10(c_e_h_1, c_m, s3, s4)) | node9(c_e_h_1, c_m, s3))),
% 11.49/11.69 inference(rewrite,[status(thm)],[])).
% 11.49/11.69 tff(4032,plain,
% 11.49/11.69 ((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))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node10(c_e_h_1, c_m, s3, s4)) | node9(c_e_h_1, c_m, s3))),
% 11.49/11.69 inference(rewrite,[status(thm)],[])).
% 11.49/11.69 tff(4033,plain,
% 11.49/11.69 (((~![Y: $i, I0: $i, 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)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node10(c_e_h_1, c_m, s3, s4)) | node9(c_e_h_1, c_m, s3)))),
% 11.49/11.69 inference(monotonicity,[status(thm)],[4032])).
% 11.49/11.69 tff(4034,plain,
% 11.49/11.69 (((~![Y: $i, I0: $i, 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)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node10(c_e_h_1, c_m, s3, s4)) | node9(c_e_h_1, c_m, s3))),
% 11.49/11.69 inference(transitivity,[status(thm)],[4033, 4031])).
% 11.49/11.69 tff(4035,plain,
% 11.49/11.69 ((~![Y: $i, I0: $i, 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)))),
% 11.49/11.69 inference(quant_inst,[status(thm)],[])).
% 11.49/11.69 tff(4036,plain,
% 11.49/11.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node10(c_e_h_1, c_m, s3, s4)) | node9(c_e_h_1, c_m, s3)),
% 11.49/11.69 inference(modus_ponens,[status(thm)],[4035, 4034])).
% 11.49/11.69 tff(4037,plain,
% 11.49/11.69 ($false),
% 11.49/11.69 inference(unit_resolution,[status(thm)],[4036, 77, 4021, 4030, 4029])).
% 11.49/11.69 tff(4038,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))), inference(lemma,lemma(discharge,[]))).
% 11.49/11.69 tff(4039,plain,
% 11.49/11.69 (~node10(c_e_h_1, c_m, s3, s4)),
% 11.49/11.69 inference(unit_resolution,[status(thm)],[4038, 4021])).
% 11.49/11.69 tff(4040,plain,
% 11.49/11.69 (((~![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))),
% 11.49/11.69 inference(rewrite,[status(thm)],[])).
% 11.49/11.69 tff(4041,plain,
% 11.49/11.69 ((~![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))),
% 11.49/11.69 inference(quant_inst,[status(thm)],[])).
% 11.49/11.69 tff(4042,plain,
% 11.49/11.69 ((~![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)),
% 11.49/11.69 inference(modus_ponens,[status(thm)],[4041, 4040])).
% 11.49/11.69 tff(4043,plain,
% 11.49/11.69 (node10(c_e_h_1, c_m, s3, s4) | node11(c_e_h_1, c_m, s3, s4)),
% 11.49/11.69 inference(unit_resolution,[status(thm)],[4042, 110, 1092])).
% 11.49/11.69 tff(4044,plain,
% 11.49/11.69 (node11(c_e_h_1, c_m, s3, s4)),
% 11.49/11.69 inference(unit_resolution,[status(thm)],[4043, 4039])).
% 11.49/11.69 tff(4045,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)), introduced(assumption)).
% 11.49/11.69 tff(4046,plain,
% 11.49/11.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, 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))),
% 11.49/11.69 inference(rewrite,[status(thm)],[])).
% 11.49/11.69 tff(4047,plain,
% 11.49/11.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, 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))),
% 11.49/11.69 inference(quant_inst,[status(thm)],[])).
% 11.49/11.69 tff(4048,plain,
% 11.49/11.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node11(c_e_h_1, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)),
% 11.49/11.69 inference(modus_ponens,[status(thm)],[4047, 4046])).
% 11.49/11.69 tff(4049,plain,
% 11.49/11.69 ($false),
% 11.49/11.69 inference(unit_resolution,[status(thm)],[4048, 147, 4021, 4045, 4044])).
% 11.49/11.69 tff(4050,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_m, s3)), inference(lemma,lemma(discharge,[]))).
% 11.49/11.69 tff(4051,plain,
% 11.49/11.69 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)),
% 11.49/11.69 inference(unit_resolution,[status(thm)],[4050, 3933])).
% 11.49/11.69 tff(4052,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)), introduced(assumption)).
% 11.49/11.69 tff(4053,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)), introduced(assumption)).
% 11.49/11.69 tff(4054,plain,
% 11.49/11.69 (((~![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))),
% 11.49/11.69 inference(rewrite,[status(thm)],[])).
% 11.49/11.69 tff(4055,plain,
% 11.49/11.69 ((~![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))),
% 11.49/11.69 inference(quant_inst,[status(thm)],[])).
% 11.49/11.69 tff(4056,plain,
% 11.49/11.69 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)),
% 11.49/11.69 inference(modus_ponens,[status(thm)],[4055, 4054])).
% 11.49/11.69 tff(4057,plain,
% 11.49/11.69 ($false),
% 11.49/11.69 inference(unit_resolution,[status(thm)],[4056, 3794, 4053, 4052])).
% 11.49/11.69 tff(4058,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)), inference(lemma,lemma(discharge,[]))).
% 11.49/11.69 tff(4059,plain,
% 11.49/11.69 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)),
% 11.49/11.69 inference(unit_resolution,[status(thm)],[4058, 4051])).
% 11.49/11.69 tff(4060,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)), introduced(assumption)).
% 11.49/11.69 tff(4061,assumption,(node10(c_e_h_1, c_n, s4, s5)), introduced(assumption)).
% 11.49/11.69 tff(4062,plain,
% 11.49/11.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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_in2(c_e_h_1, c_n, s4)) | (~node10(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in1(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, s5) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~node10(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)))),
% 11.55/11.69 inference(rewrite,[status(thm)],[])).
% 11.55/11.69 tff(4063,plain,
% 11.55/11.69 (((~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_in2(c_e_h_1, c_n, s4)) | (~node10(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)))),
% 11.55/11.69 inference(rewrite,[status(thm)],[])).
% 11.55/11.69 tff(4064,plain,
% 11.55/11.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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_in2(c_e_h_1, c_n, s4)) | (~node10(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4))))),
% 11.55/11.69 inference(monotonicity,[status(thm)],[4063])).
% 11.55/11.69 tff(4065,plain,
% 11.55/11.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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_in2(c_e_h_1, c_n, s4)) | (~node10(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)))),
% 11.55/11.69 inference(transitivity,[status(thm)],[4064, 4062])).
% 11.55/11.69 tff(4066,plain,
% 11.55/11.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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))),
% 11.55/11.69 inference(quant_inst,[status(thm)],[])).
% 11.55/11.69 tff(4067,plain,
% 11.55/11.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~node10(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4))),
% 11.55/11.69 inference(modus_ponens,[status(thm)],[4066, 4065])).
% 11.55/11.69 tff(4068,plain,
% 11.55/11.69 ($false),
% 11.55/11.69 inference(unit_resolution,[status(thm)],[4067, 3834, 4008, 4061, 4060, 4020])).
% 11.55/11.69 tff(4069,plain,((~node10(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_in2(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4))), inference(lemma,lemma(discharge,[]))).
% 11.55/11.69 tff(4070,plain,
% 11.55/11.69 ((~node10(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_in1(c_e_h_1, c_n, s4))),
% 11.55/11.69 inference(unit_resolution,[status(thm)],[4069, 4059])).
% 11.55/11.69 tff(4071,plain,
% 11.55/11.69 (~node10(c_e_h_1, c_n, s4, s5)),
% 11.55/11.69 inference(unit_resolution,[status(thm)],[4070, 4008, 4020])).
% 11.55/11.69 tff(4072,plain,
% 11.55/11.69 (((~![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))),
% 11.55/11.69 inference(rewrite,[status(thm)],[])).
% 11.55/11.69 tff(4073,plain,
% 11.55/11.69 ((~![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))),
% 11.55/11.69 inference(quant_inst,[status(thm)],[])).
% 11.55/11.69 tff(4074,plain,
% 11.55/11.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_1, c_n, s4, s5) | node11(c_e_h_1, c_n, s4, s5)),
% 11.55/11.69 inference(modus_ponens,[status(thm)],[4073, 4072])).
% 11.55/11.69 tff(4075,plain,
% 11.55/11.69 (node10(c_e_h_1, c_n, s4, s5) | node11(c_e_h_1, c_n, s4, s5)),
% 11.55/11.69 inference(unit_resolution,[status(thm)],[4074, 110, 1542])).
% 11.55/11.69 tff(4076,plain,
% 11.55/11.69 ($false),
% 11.55/11.69 inference(unit_resolution,[status(thm)],[4075, 4071, 4019])).
% 11.55/11.69 tff(4077,plain,(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))), inference(lemma,lemma(discharge,[]))).
% 11.55/11.69 tff(4078,plain,
% 11.55/11.69 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)),
% 11.55/11.69 inference(unit_resolution,[status(thm)],[4077, 3777])).
% 11.55/11.69 tff(4079,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)), introduced(assumption)).
% 11.55/11.69 tff(4080,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)), introduced(assumption)).
% 11.55/11.69 tff(4081,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)), introduced(assumption)).
% 11.55/11.69 tff(4082,plain,
% 11.55/11.69 (((~![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)))),
% 11.55/11.69 inference(rewrite,[status(thm)],[])).
% 11.55/11.69 tff(4083,plain,
% 11.55/11.69 ((~![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)))),
% 11.55/11.69 inference(quant_inst,[status(thm)],[])).
% 11.55/11.69 tff(4084,plain,
% 11.55/11.69 ((~![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))),
% 11.55/11.69 inference(modus_ponens,[status(thm)],[4083, 4082])).
% 11.55/11.69 tff(4085,plain,
% 11.55/11.69 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4)),
% 11.55/11.69 inference(unit_resolution,[status(thm)],[4084, 49, 4007])).
% 11.55/11.69 tff(4086,plain,
% 11.55/11.69 (((~![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))),
% 11.55/11.69 inference(rewrite,[status(thm)],[])).
% 11.55/11.69 tff(4087,plain,
% 11.55/11.69 ((~![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))),
% 11.55/11.69 inference(quant_inst,[status(thm)],[])).
% 11.55/11.69 tff(4088,plain,
% 11.55/11.69 ((~![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)),
% 11.55/11.69 inference(modus_ponens,[status(thm)],[4087, 4086])).
% 11.55/11.69 tff(4089,plain,
% 11.55/11.69 (~node9(c_e_h_1, c_m, s4)),
% 11.55/11.69 inference(unit_resolution,[status(thm)],[4088, 63, 4085])).
% 11.55/11.69 tff(4090,assumption,(node10(c_e_h_1, c_m, s4, s5)), introduced(assumption)).
% 11.55/11.69 tff(4091,plain,
% 11.55/11.69 (((~![Y: $i, I0: $i, 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))),
% 11.55/11.69 inference(rewrite,[status(thm)],[])).
% 11.55/11.69 tff(4092,plain,
% 11.55/11.69 ((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))),
% 11.55/11.69 inference(rewrite,[status(thm)],[])).
% 11.55/11.69 tff(4093,plain,
% 11.55/11.69 (((~![Y: $i, I0: $i, 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)))),
% 11.55/11.69 inference(monotonicity,[status(thm)],[4092])).
% 11.55/11.69 tff(4094,plain,
% 11.55/11.69 (((~![Y: $i, I0: $i, 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))),
% 11.55/11.69 inference(transitivity,[status(thm)],[4093, 4091])).
% 11.55/11.69 tff(4095,plain,
% 11.55/11.69 ((~![Y: $i, I0: $i, 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)))),
% 11.55/11.69 inference(quant_inst,[status(thm)],[])).
% 11.55/11.69 tff(4096,plain,
% 11.55/11.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node10(c_e_h_1, c_m, s4, s5)) | node9(c_e_h_1, c_m, s4)),
% 11.55/11.69 inference(modus_ponens,[status(thm)],[4095, 4094])).
% 11.55/11.69 tff(4097,plain,
% 11.55/11.69 ($false),
% 11.55/11.69 inference(unit_resolution,[status(thm)],[4096, 77, 4081, 4090, 4089])).
% 11.55/11.69 tff(4098,plain,((~node10(c_e_h_1, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))), inference(lemma,lemma(discharge,[]))).
% 11.55/11.69 tff(4099,plain,
% 11.55/11.69 (~node10(c_e_h_1, c_m, s4, s5)),
% 11.55/11.69 inference(unit_resolution,[status(thm)],[4098, 4081])).
% 11.55/11.69 tff(4100,plain,
% 11.55/11.69 (((~![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))),
% 11.55/11.69 inference(rewrite,[status(thm)],[])).
% 11.55/11.69 tff(4101,plain,
% 11.55/11.69 ((~![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))),
% 11.55/11.69 inference(quant_inst,[status(thm)],[])).
% 11.55/11.69 tff(4102,plain,
% 11.55/11.69 ((~![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)),
% 11.55/11.69 inference(modus_ponens,[status(thm)],[4101, 4100])).
% 11.55/11.69 tff(4103,plain,
% 11.55/11.69 (node10(c_e_h_1, c_m, s4, s5) | node11(c_e_h_1, c_m, s4, s5)),
% 11.55/11.69 inference(unit_resolution,[status(thm)],[4102, 110, 1542])).
% 11.55/11.69 tff(4104,plain,
% 11.55/11.69 (node11(c_e_h_1, c_m, s4, s5)),
% 11.55/11.69 inference(unit_resolution,[status(thm)],[4103, 4099])).
% 11.55/11.69 tff(4105,plain,
% 11.55/11.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, 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))),
% 11.55/11.69 inference(rewrite,[status(thm)],[])).
% 11.55/11.69 tff(4106,plain,
% 11.55/11.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, 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))),
% 11.55/11.69 inference(quant_inst,[status(thm)],[])).
% 11.55/11.69 tff(4107,plain,
% 11.55/11.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node11(c_e_h_1, c_m, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)),
% 11.55/11.69 inference(modus_ponens,[status(thm)],[4106, 4105])).
% 11.55/11.69 tff(4108,plain,
% 11.55/11.69 ($false),
% 11.55/11.69 inference(unit_resolution,[status(thm)],[4107, 147, 4051, 4081, 4104])).
% 11.55/11.69 tff(4109,plain,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)), inference(lemma,lemma(discharge,[]))).
% 11.55/11.69 tff(4110,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)), introduced(assumption)).
% 11.55/11.69 tff(4111,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)), introduced(assumption)).
% 11.55/11.69 tff(4112,plain,
% 11.55/11.69 (((~![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))),
% 11.55/11.69 inference(rewrite,[status(thm)],[])).
% 11.55/11.69 tff(4113,plain,
% 11.55/11.69 ((~![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))),
% 11.55/11.69 inference(quant_inst,[status(thm)],[])).
% 11.55/11.69 tff(4114,plain,
% 11.55/11.69 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)),
% 11.55/11.69 inference(modus_ponens,[status(thm)],[4113, 4112])).
% 11.55/11.69 tff(4115,plain,
% 11.55/11.69 ($false),
% 11.55/11.69 inference(unit_resolution,[status(thm)],[4114, 3794, 4111, 4110])).
% 11.55/11.69 tff(4116,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)), inference(lemma,lemma(discharge,[]))).
% 11.55/11.69 tff(4117,plain,
% 11.55/11.69 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)),
% 11.55/11.69 inference(unit_resolution,[status(thm)],[4116, 4109])).
% 11.55/11.69 tff(4118,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)), introduced(assumption)).
% 11.55/11.69 tff(4119,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)), introduced(assumption)).
% 11.55/11.69 tff(4120,assumption,(node10(c_e_h_1, c_n, s5, s6)), introduced(assumption)).
% 11.55/11.69 tff(4121,plain,
% 11.55/11.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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, 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)) | (~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_out(c_e_h_1, c_n, 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)) | (~node10(c_e_h_1, c_n, s5, s6)))),
% 11.55/11.69 inference(rewrite,[status(thm)],[])).
% 11.55/11.69 tff(4122,plain,
% 11.55/11.69 (((~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_out(c_e_h_1, c_n, 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)) | (~node10(c_e_h_1, c_n, s5, s6)))),
% 11.55/11.70 inference(rewrite,[status(thm)],[])).
% 11.55/11.70 tff(4123,plain,
% 11.55/11.70 (((~![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_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_out(c_e_h_1, c_n, 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)) | (~node10(c_e_h_1, c_n, s5, s6))))),
% 11.55/11.70 inference(monotonicity,[status(thm)],[4122])).
% 11.55/11.70 tff(4124,plain,
% 11.55/11.70 (((~![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_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_out(c_e_h_1, c_n, 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)) | (~node10(c_e_h_1, c_n, s5, s6)))),
% 11.55/11.70 inference(transitivity,[status(thm)],[4123, 4121])).
% 11.55/11.70 tff(4125,plain,
% 11.55/11.70 ((~![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_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))),
% 11.55/11.70 inference(quant_inst,[status(thm)],[])).
% 11.55/11.70 tff(4126,plain,
% 11.55/11.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | (~node10(c_e_h_1, c_n, s5, s6))),
% 11.55/11.70 inference(modus_ponens,[status(thm)],[4125, 4124])).
% 11.55/11.70 tff(4127,plain,
% 11.55/11.70 ($false),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4126, 3834, 4119, 4120, 4079, 4118])).
% 11.55/11.70 tff(4128,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,[]))).
% 11.55/11.70 tff(4129,plain,
% 11.55/11.70 (~node10(c_e_h_1, c_n, s5, s6)),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4128, 4119, 4079, 4118])).
% 11.55/11.70 tff(4130,plain,
% 11.55/11.70 (((~![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))),
% 11.55/11.70 inference(rewrite,[status(thm)],[])).
% 11.55/11.70 tff(4131,plain,
% 11.55/11.70 ((~![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))),
% 11.55/11.70 inference(quant_inst,[status(thm)],[])).
% 11.55/11.70 tff(4132,plain,
% 11.55/11.70 ((~![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)),
% 11.55/11.70 inference(modus_ponens,[status(thm)],[4131, 4130])).
% 11.55/11.70 tff(4133,plain,
% 11.55/11.70 (node10(c_e_h_1, c_n, s5, s6) | node11(c_e_h_1, c_n, s5, s6)),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4132, 110, 2348])).
% 11.55/11.70 tff(4134,plain,
% 11.55/11.70 (node11(c_e_h_1, c_n, s5, s6)),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4133, 4129])).
% 11.55/11.70 tff(4135,plain,
% 11.55/11.70 (((~![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_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) | (~node11(c_e_h_1, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)))),
% 11.55/11.70 inference(rewrite,[status(thm)],[])).
% 11.55/11.70 tff(4136,plain,
% 11.55/11.70 ((~![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_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)))),
% 11.55/11.70 inference(quant_inst,[status(thm)],[])).
% 11.55/11.70 tff(4137,plain,
% 11.55/11.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~node11(c_e_h_1, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5))),
% 11.55/11.70 inference(modus_ponens,[status(thm)],[4136, 4135])).
% 11.55/11.70 tff(4138,plain,
% 11.55/11.70 ($false),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4137, 3810, 4119, 4080, 4134])).
% 11.55/11.70 tff(4139,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,[]))).
% 11.55/11.70 tff(4140,plain,
% 11.55/11.70 (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))),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4139, 4117])).
% 11.55/11.70 tff(4141,plain,
% 11.55/11.70 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4140, 4080, 4079])).
% 11.55/11.70 tff(4142,plain,
% 11.55/11.70 (((~![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_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)))),
% 11.55/11.70 inference(rewrite,[status(thm)],[])).
% 11.55/11.70 tff(4143,plain,
% 11.55/11.70 ((~![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_1, c_m, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)))),
% 11.55/11.70 inference(quant_inst,[status(thm)],[])).
% 11.55/11.70 tff(4144,plain,
% 11.55/11.70 ((~![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_1, c_m, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6))),
% 11.55/11.70 inference(modus_ponens,[status(thm)],[4143, 4142])).
% 11.55/11.70 tff(4145,plain,
% 11.55/11.70 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s6)),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4144, 49, 4141])).
% 11.55/11.70 tff(4146,plain,
% 11.55/11.70 (((~![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_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))),
% 11.55/11.70 inference(rewrite,[status(thm)],[])).
% 11.55/11.70 tff(4147,plain,
% 11.55/11.70 ((~![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_1, c_m, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s6))),
% 11.55/11.70 inference(quant_inst,[status(thm)],[])).
% 11.55/11.70 tff(4148,plain,
% 11.55/11.70 ((~![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_1, c_m, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s6)),
% 11.55/11.70 inference(modus_ponens,[status(thm)],[4147, 4146])).
% 11.55/11.70 tff(4149,plain,
% 11.55/11.70 (~node9(c_e_h_1, c_m, s6)),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4148, 63, 4145])).
% 11.55/11.70 tff(4150,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)), introduced(assumption)).
% 11.55/11.70 tff(4151,plain,
% 11.55/11.70 (((~![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_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)))),
% 11.55/11.70 inference(rewrite,[status(thm)],[])).
% 11.55/11.70 tff(4152,plain,
% 11.55/11.70 ((~![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_1, c_m, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)))),
% 11.55/11.70 inference(quant_inst,[status(thm)],[])).
% 11.55/11.70 tff(4153,plain,
% 11.55/11.70 ((~![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_1, c_m, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5))),
% 11.55/11.70 inference(modus_ponens,[status(thm)],[4152, 4151])).
% 11.55/11.70 tff(4154,plain,
% 11.55/11.70 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5)),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4153, 49, 4080])).
% 11.55/11.70 tff(4155,plain,
% 11.55/11.70 (((~![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_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))),
% 11.55/11.70 inference(rewrite,[status(thm)],[])).
% 11.55/11.70 tff(4156,plain,
% 11.55/11.70 ((~![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_1, c_m, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5))),
% 11.55/11.70 inference(quant_inst,[status(thm)],[])).
% 11.55/11.70 tff(4157,plain,
% 11.55/11.70 ((~![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_1, c_m, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5)),
% 11.55/11.70 inference(modus_ponens,[status(thm)],[4156, 4155])).
% 11.55/11.70 tff(4158,plain,
% 11.55/11.70 (~node9(c_e_h_1, c_m, s5)),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4157, 63, 4154])).
% 11.55/11.70 tff(4159,assumption,(~node9(c_e_h_1, c_m, s5)), introduced(assumption)).
% 11.55/11.70 tff(4160,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)), introduced(assumption)).
% 11.55/11.70 tff(4161,assumption,(node11(c_e_h_1, c_m, s5, s6)), introduced(assumption)).
% 11.55/11.70 tff(4162,plain,
% 11.55/11.70 (((~![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_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))),
% 11.55/11.70 inference(rewrite,[status(thm)],[])).
% 11.55/11.70 tff(4163,plain,
% 11.55/11.70 ((~![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_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))),
% 11.55/11.70 inference(quant_inst,[status(thm)],[])).
% 11.55/11.70 tff(4164,plain,
% 11.55/11.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | (~node11(c_e_h_1, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)),
% 11.55/11.70 inference(modus_ponens,[status(thm)],[4163, 4162])).
% 11.55/11.70 tff(4165,plain,
% 11.55/11.70 ($false),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4164, 147, 4160, 4109, 4161])).
% 11.55/11.70 tff(4166,plain,((~node11(c_e_h_1, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))), inference(lemma,lemma(discharge,[]))).
% 11.55/11.70 tff(4167,plain,
% 11.55/11.70 (~node11(c_e_h_1, c_m, s5, s6)),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4166, 4160])).
% 11.55/11.70 tff(4168,plain,
% 11.55/11.70 (((~![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))),
% 11.55/11.70 inference(rewrite,[status(thm)],[])).
% 11.55/11.70 tff(4169,plain,
% 11.55/11.70 ((~![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))),
% 11.55/11.70 inference(quant_inst,[status(thm)],[])).
% 11.55/11.70 tff(4170,plain,
% 11.55/11.70 ((~![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)),
% 11.55/11.70 inference(modus_ponens,[status(thm)],[4169, 4168])).
% 11.55/11.70 tff(4171,plain,
% 11.55/11.70 (node10(c_e_h_1, c_m, s5, s6) | node11(c_e_h_1, c_m, s5, s6)),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4170, 110, 2348])).
% 11.55/11.70 tff(4172,plain,
% 11.55/11.70 (node10(c_e_h_1, c_m, s5, s6)),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4171, 4167])).
% 11.55/11.70 tff(4173,plain,
% 11.55/11.70 (((~![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_1, c_m, s6)) | (~node10(c_e_h_1, c_m, s5, s6)) | node9(c_e_h_1, 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_1, c_m, s6)) | (~node10(c_e_h_1, c_m, s5, s6)) | node9(c_e_h_1, c_m, s5))),
% 11.55/11.70 inference(rewrite,[status(thm)],[])).
% 11.55/11.70 tff(4174,plain,
% 11.55/11.70 ((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)) | (~node10(c_e_h_1, c_m, s5, s6)) | node9(c_e_h_1, c_m, s5))),
% 11.55/11.70 inference(rewrite,[status(thm)],[])).
% 11.55/11.70 tff(4175,plain,
% 11.55/11.70 (((~![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_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)) | (~node10(c_e_h_1, c_m, s5, s6)) | node9(c_e_h_1, c_m, s5)))),
% 11.55/11.70 inference(monotonicity,[status(thm)],[4174])).
% 11.55/11.70 tff(4176,plain,
% 11.55/11.70 (((~![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_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)) | (~node10(c_e_h_1, c_m, s5, s6)) | node9(c_e_h_1, c_m, s5))),
% 11.55/11.70 inference(transitivity,[status(thm)],[4175, 4173])).
% 11.55/11.70 tff(4177,plain,
% 11.55/11.70 ((~![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_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)))),
% 11.55/11.70 inference(quant_inst,[status(thm)],[])).
% 11.55/11.70 tff(4178,plain,
% 11.55/11.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | (~node10(c_e_h_1, c_m, s5, s6)) | node9(c_e_h_1, c_m, s5)),
% 11.55/11.70 inference(modus_ponens,[status(thm)],[4177, 4176])).
% 11.55/11.70 tff(4179,plain,
% 11.55/11.70 ($false),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4178, 77, 4160, 4172, 4159])).
% 11.55/11.70 tff(4180,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | node9(c_e_h_1, c_m, s5)), inference(lemma,lemma(discharge,[]))).
% 11.55/11.70 tff(4181,plain,
% 11.55/11.70 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4180, 4158])).
% 11.55/11.70 tff(4182,assumption,(node11(c_e_h_1, c_m, s6, s7)), introduced(assumption)).
% 11.55/11.70 tff(4183,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)), introduced(assumption)).
% 11.55/11.70 tff(4184,plain,
% 11.55/11.70 (((~![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_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))),
% 11.55/11.70 inference(rewrite,[status(thm)],[])).
% 11.55/11.70 tff(4185,plain,
% 11.55/11.70 ((~![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_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))),
% 11.55/11.70 inference(quant_inst,[status(thm)],[])).
% 11.55/11.70 tff(4186,plain,
% 11.55/11.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | (~node11(c_e_h_1, c_m, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)),
% 11.55/11.70 inference(modus_ponens,[status(thm)],[4185, 4184])).
% 11.55/11.70 tff(4187,plain,
% 11.55/11.70 ($false),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4186, 147, 4150, 4183, 4182])).
% 11.55/11.70 tff(4188,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,[]))).
% 11.55/11.70 tff(4189,plain,
% 11.55/11.70 (~node11(c_e_h_1, c_m, s6, s7)),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4188, 4181, 4150])).
% 11.55/11.70 tff(4190,plain,
% 11.55/11.70 (((~![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))),
% 11.55/11.70 inference(rewrite,[status(thm)],[])).
% 11.55/11.70 tff(4191,plain,
% 11.55/11.70 ((~![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))),
% 11.55/11.70 inference(quant_inst,[status(thm)],[])).
% 11.55/11.70 tff(4192,plain,
% 11.55/11.70 ((~![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)),
% 11.55/11.70 inference(modus_ponens,[status(thm)],[4191, 4190])).
% 11.55/11.70 tff(4193,plain,
% 11.55/11.70 (node10(c_e_h_1, c_m, s6, s7) | node11(c_e_h_1, c_m, s6, s7)),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4192, 110, 2649])).
% 11.55/11.70 tff(4194,plain,
% 11.55/11.70 (node10(c_e_h_1, c_m, s6, s7)),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4193, 4189])).
% 11.55/11.70 tff(4195,plain,
% 11.55/11.70 (((~![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_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)))),
% 11.55/11.70 inference(rewrite,[status(thm)],[])).
% 11.55/11.70 tff(4196,plain,
% 11.55/11.70 ((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)))),
% 11.55/11.70 inference(rewrite,[status(thm)],[])).
% 11.55/11.70 tff(4197,plain,
% 11.55/11.70 (((~![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_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))))),
% 11.55/11.70 inference(monotonicity,[status(thm)],[4196])).
% 11.55/11.70 tff(4198,plain,
% 11.55/11.70 (((~![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_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)))),
% 11.55/11.70 inference(transitivity,[status(thm)],[4197, 4195])).
% 11.55/11.70 tff(4199,plain,
% 11.55/11.70 ((~![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_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)))),
% 11.55/11.70 inference(quant_inst,[status(thm)],[])).
% 11.55/11.70 tff(4200,plain,
% 11.55/11.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | node9(c_e_h_1, c_m, s6) | (~node10(c_e_h_1, c_m, s6, s7))),
% 11.55/11.70 inference(modus_ponens,[status(thm)],[4199, 4198])).
% 11.55/11.70 tff(4201,plain,
% 11.55/11.70 ($false),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4200, 77, 4150, 4194, 4149])).
% 11.55/11.70 tff(4202,plain,((~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_m, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5))), inference(lemma,lemma(discharge,[]))).
% 11.55/11.70 tff(4203,plain,
% 11.55/11.70 ((~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, s5))),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4202, 4078])).
% 11.55/11.70 tff(4204,plain,
% 11.55/11.70 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4203, 3770])).
% 11.55/11.70 tff(4205,plain,
% 11.55/11.70 (^[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)))),
% 11.55/11.70 inference(bind,[status(th)],[])).
% 11.55/11.70 tff(4206,plain,
% 11.55/11.70 (![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)) <=> ![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))),
% 11.55/11.70 inference(quant_intro,[status(thm)],[4205])).
% 11.55/11.70 tff(4207,plain,
% 11.55/11.70 (![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)) <=> ![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))),
% 11.55/11.70 inference(rewrite,[status(thm)],[])).
% 11.55/11.70 tff(4208,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')).
% 11.55/11.70 tff(4209,plain,
% 11.55/11.70 (![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))),
% 11.55/11.70 inference(modus_ponens,[status(thm)],[4208, 4207])).
% 11.55/11.70 tff(4210,plain,(
% 11.55/11.70 ![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))),
% 11.55/11.70 inference(skolemize,[status(sab)],[4209])).
% 11.55/11.70 tff(4211,plain,
% 11.55/11.70 (![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))),
% 11.55/11.70 inference(modus_ponens,[status(thm)],[4210, 4206])).
% 11.55/11.70 tff(4212,plain,
% 11.55/11.70 (((~![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_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))),
% 11.55/11.70 inference(rewrite,[status(thm)],[])).
% 11.55/11.70 tff(4213,plain,
% 11.55/11.70 ((~![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_1, c_r, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))),
% 11.55/11.70 inference(quant_inst,[status(thm)],[])).
% 11.55/11.70 tff(4214,plain,
% 11.55/11.70 ((~![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_1, c_r, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)),
% 11.55/11.70 inference(modus_ponens,[status(thm)],[4213, 4212])).
% 11.55/11.70 tff(4215,plain,
% 11.55/11.70 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s7)),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4214, 4211, 4204])).
% 11.55/11.70 tff(4216,plain,
% 11.55/11.70 (((~![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))),
% 11.55/11.70 inference(rewrite,[status(thm)],[])).
% 11.55/11.70 tff(4217,plain,
% 11.55/11.70 ((~![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))),
% 11.55/11.70 inference(quant_inst,[status(thm)],[])).
% 11.55/11.70 tff(4218,plain,
% 11.55/11.70 ((~![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)),
% 11.55/11.70 inference(modus_ponens,[status(thm)],[4217, 4216])).
% 11.55/11.70 tff(4219,plain,
% 11.55/11.70 (~node20(c_e_h_1, c_r, s7)),
% 11.55/11.70 inference(unit_resolution,[status(thm)],[4218, 173, 4215])).
% 11.55/11.71 tff(4220,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s2)), introduced(assumption)).
% 11.55/11.71 tff(4221,plain,
% 11.55/11.71 (((~![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_1, c_r, s1)) | m_c_h_element_v_out(c_e_h_1, 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_1, c_r, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s1))),
% 11.55/11.71 inference(rewrite,[status(thm)],[])).
% 11.55/11.71 tff(4222,plain,
% 11.55/11.71 ((~![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_1, c_r, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s1))),
% 11.55/11.71 inference(quant_inst,[status(thm)],[])).
% 11.55/11.71 tff(4223,plain,
% 11.55/11.71 ((~![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_1, c_r, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s1)),
% 11.55/11.71 inference(modus_ponens,[status(thm)],[4222, 4221])).
% 11.55/11.71 tff(4224,plain,
% 11.55/11.71 (~m_and_h_gate_v_in1(c_e_h_1, c_r, s1)),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4223, 2431, 3518])).
% 11.55/11.71 tff(4225,plain,
% 11.55/11.71 (((~![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_r, s1)) | m_and_h_gate_v_in1(c_e_h_1, 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_1, c_r, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s1))),
% 11.55/11.71 inference(rewrite,[status(thm)],[])).
% 11.55/11.71 tff(4226,plain,
% 11.55/11.71 ((~![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_r, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s1))),
% 11.55/11.71 inference(quant_inst,[status(thm)],[])).
% 11.55/11.71 tff(4227,plain,
% 11.55/11.71 ((~![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_r, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s1)),
% 11.55/11.71 inference(modus_ponens,[status(thm)],[4226, 4225])).
% 11.55/11.71 tff(4228,plain,
% 11.55/11.71 (~node20(c_e_h_1, c_r, s1)),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4227, 213, 4224])).
% 11.55/11.71 tff(4229,plain,
% 11.55/11.71 (((~![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)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | node20(c_e_h_1, c_r, s1) | (~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)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | node20(c_e_h_1, c_r, s1) | (~node21(c_e_h_1, c_r, s1, s2)))),
% 11.55/11.71 inference(rewrite,[status(thm)],[])).
% 11.55/11.71 tff(4230,plain,
% 11.55/11.71 ((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))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | node20(c_e_h_1, c_r, s1) | (~node21(c_e_h_1, c_r, s1, s2)))),
% 11.55/11.71 inference(rewrite,[status(thm)],[])).
% 11.55/11.71 tff(4231,plain,
% 11.55/11.71 (((~![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_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)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | node20(c_e_h_1, c_r, s1) | (~node21(c_e_h_1, c_r, s1, s2))))),
% 11.55/11.71 inference(monotonicity,[status(thm)],[4230])).
% 11.55/11.71 tff(4232,plain,
% 11.55/11.71 (((~![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_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)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | node20(c_e_h_1, c_r, s1) | (~node21(c_e_h_1, c_r, s1, s2)))),
% 11.55/11.71 inference(transitivity,[status(thm)],[4231, 4229])).
% 11.55/11.71 tff(4233,plain,
% 11.55/11.71 ((~![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_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)))),
% 11.55/11.71 inference(quant_inst,[status(thm)],[])).
% 11.55/11.71 tff(4234,plain,
% 11.55/11.71 ((~![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)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | node20(c_e_h_1, c_r, s1) | (~node21(c_e_h_1, c_r, s1, s2))),
% 11.55/11.71 inference(modus_ponens,[status(thm)],[4233, 4232])).
% 11.55/11.71 tff(4235,plain,
% 11.55/11.71 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node21(c_e_h_1, c_r, s1, s2))),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4234, 228, 4228])).
% 11.55/11.71 tff(4236,plain,
% 11.55/11.71 (~node21(c_e_h_1, c_r, s1, s2)),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4235, 4220])).
% 11.55/11.71 tff(4237,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s1)), introduced(assumption)).
% 11.55/11.71 tff(4238,assumption,(node22(c_e_h_1, c_r, s0, s1)), introduced(assumption)).
% 11.55/11.71 tff(4239,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s0)), introduced(assumption)).
% 11.55/11.71 tff(4240,plain,
% 11.55/11.71 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s0))),
% 11.55/11.71 inference(quant_inst,[status(thm)],[])).
% 11.55/11.71 tff(4241,plain,
% 11.55/11.71 ($false),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4240, 260, 4239])).
% 11.55/11.71 tff(4242,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s0)), inference(lemma,lemma(discharge,[]))).
% 11.55/11.71 tff(4243,plain,
% 11.55/11.71 (((~![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_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))),
% 11.55/11.71 inference(rewrite,[status(thm)],[])).
% 11.55/11.71 tff(4244,plain,
% 11.55/11.71 ((~![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_r, s1)) | (~node22(c_e_h_1, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0))),
% 11.55/11.71 inference(quant_inst,[status(thm)],[])).
% 11.55/11.71 tff(4245,plain,
% 11.55/11.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node22(c_e_h_1, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0)),
% 11.55/11.71 inference(modus_ponens,[status(thm)],[4244, 4243])).
% 11.55/11.71 tff(4246,plain,
% 11.55/11.71 ($false),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4245, 273, 4242, 4237, 4238])).
% 11.55/11.71 tff(4247,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,[]))).
% 11.55/11.71 tff(4248,plain,
% 11.55/11.71 (~node22(c_e_h_1, c_r, s0, s1)),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4247, 4237])).
% 11.55/11.71 tff(4249,plain,
% 11.55/11.71 (((~![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))),
% 11.55/11.71 inference(rewrite,[status(thm)],[])).
% 11.55/11.71 tff(4250,plain,
% 11.55/11.71 ((~![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))),
% 11.55/11.71 inference(quant_inst,[status(thm)],[])).
% 11.55/11.71 tff(4251,plain,
% 11.55/11.71 ((~![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)),
% 11.55/11.71 inference(modus_ponens,[status(thm)],[4250, 4249])).
% 11.55/11.71 tff(4252,plain,
% 11.55/11.71 (node21(c_e_h_1, c_r, s0, s1) | node22(c_e_h_1, c_r, s0, s1)),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4251, 247, 100])).
% 11.55/11.71 tff(4253,plain,
% 11.55/11.71 (node21(c_e_h_1, c_r, s0, s1)),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4252, 4248])).
% 11.55/11.71 tff(4254,plain,
% 11.55/11.71 (((~![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_1, c_r, s0)) | m_c_h_element_v_out(c_e_h_1, 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_1, c_r, s0)) | m_c_h_element_v_out(c_e_h_1, c_e, s0))),
% 11.55/11.71 inference(rewrite,[status(thm)],[])).
% 11.55/11.71 tff(4255,plain,
% 11.55/11.71 ((~![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_1, c_r, s0)) | m_c_h_element_v_out(c_e_h_1, c_e, s0))),
% 11.55/11.71 inference(quant_inst,[status(thm)],[])).
% 11.55/11.71 tff(4256,plain,
% 11.55/11.71 ((~![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_1, c_r, s0)) | m_c_h_element_v_out(c_e_h_1, c_e, s0)),
% 11.55/11.71 inference(modus_ponens,[status(thm)],[4255, 4254])).
% 11.55/11.71 tff(4257,plain,
% 11.55/11.71 (~m_and_h_gate_v_in1(c_e_h_1, c_r, s0)),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4256, 2431, 3482])).
% 11.55/11.71 tff(4258,plain,
% 11.55/11.71 (((~![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_r, s0)) | m_and_h_gate_v_in1(c_e_h_1, 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_1, c_r, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s0))),
% 11.55/11.71 inference(rewrite,[status(thm)],[])).
% 11.55/11.71 tff(4259,plain,
% 11.55/11.71 ((~![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_r, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s0))),
% 11.55/11.71 inference(quant_inst,[status(thm)],[])).
% 11.55/11.71 tff(4260,plain,
% 11.55/11.71 ((~![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_r, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s0)),
% 11.55/11.71 inference(modus_ponens,[status(thm)],[4259, 4258])).
% 11.55/11.71 tff(4261,plain,
% 11.55/11.71 (~node20(c_e_h_1, c_r, s0)),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4260, 213, 4257])).
% 11.55/11.71 tff(4262,plain,
% 11.55/11.71 (((~![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_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)))),
% 11.55/11.71 inference(rewrite,[status(thm)],[])).
% 11.55/11.71 tff(4263,plain,
% 11.55/11.71 ((~![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_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)))),
% 11.55/11.71 inference(quant_inst,[status(thm)],[])).
% 11.55/11.71 tff(4264,plain,
% 11.55/11.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node21(c_e_h_1, c_r, s0, s1))),
% 11.55/11.71 inference(modus_ponens,[status(thm)],[4263, 4262])).
% 11.55/11.71 tff(4265,plain,
% 11.55/11.71 ($false),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4264, 228, 4237, 4261, 4253])).
% 11.55/11.71 tff(4266,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s1)), inference(lemma,lemma(discharge,[]))).
% 11.55/11.71 tff(4267,plain,
% 11.55/11.71 (((~![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_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))),
% 11.55/11.71 inference(rewrite,[status(thm)],[])).
% 11.55/11.71 tff(4268,plain,
% 11.55/11.71 ((~![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_r, s2)) | (~node22(c_e_h_1, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1))),
% 11.55/11.71 inference(quant_inst,[status(thm)],[])).
% 11.55/11.71 tff(4269,plain,
% 11.55/11.71 ((~![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_r, s2)) | (~node22(c_e_h_1, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1)),
% 11.55/11.71 inference(modus_ponens,[status(thm)],[4268, 4267])).
% 11.55/11.71 tff(4270,plain,
% 11.55/11.71 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node22(c_e_h_1, c_r, s1, s2))),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4269, 273, 4266])).
% 11.55/11.71 tff(4271,plain,
% 11.55/11.71 (~node22(c_e_h_1, c_r, s1, s2)),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4270, 4220])).
% 11.55/11.71 tff(4272,plain,
% 11.55/11.71 (((~![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))),
% 11.55/11.71 inference(rewrite,[status(thm)],[])).
% 11.55/11.71 tff(4273,plain,
% 11.55/11.71 ((~![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))),
% 11.55/11.71 inference(quant_inst,[status(thm)],[])).
% 11.55/11.71 tff(4274,plain,
% 11.55/11.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_r, s1, s2) | node22(c_e_h_1, c_r, s1, s2)),
% 11.55/11.71 inference(modus_ponens,[status(thm)],[4273, 4272])).
% 11.55/11.71 tff(4275,plain,
% 11.55/11.71 ($false),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4274, 247, 470, 4271, 4236])).
% 11.55/11.71 tff(4276,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s2)), inference(lemma,lemma(discharge,[]))).
% 11.55/11.71 tff(4277,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s3)), introduced(assumption)).
% 11.55/11.71 tff(4278,assumption,(node21(c_e_h_1, c_r, s2, s3)), introduced(assumption)).
% 11.55/11.71 tff(4279,plain,
% 11.55/11.71 (((~![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_1, c_r, s2)) | m_c_h_element_v_out(c_e_h_1, 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_1, c_r, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s2))),
% 11.55/11.71 inference(rewrite,[status(thm)],[])).
% 11.55/11.71 tff(4280,plain,
% 11.55/11.71 ((~![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_1, c_r, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s2))),
% 11.55/11.71 inference(quant_inst,[status(thm)],[])).
% 11.55/11.71 tff(4281,plain,
% 11.55/11.71 ((~![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_1, c_r, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s2)),
% 11.55/11.71 inference(modus_ponens,[status(thm)],[4280, 4279])).
% 11.55/11.71 tff(4282,plain,
% 11.55/11.71 (~m_and_h_gate_v_in1(c_e_h_1, c_r, s2)),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4281, 2431, 3556])).
% 11.55/11.71 tff(4283,plain,
% 11.55/11.71 (((~![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_r, s2)) | m_and_h_gate_v_in1(c_e_h_1, 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_1, c_r, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s2))),
% 11.55/11.71 inference(rewrite,[status(thm)],[])).
% 11.55/11.71 tff(4284,plain,
% 11.55/11.71 ((~![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_r, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s2))),
% 11.55/11.71 inference(quant_inst,[status(thm)],[])).
% 11.55/11.71 tff(4285,plain,
% 11.55/11.71 ((~![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_r, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s2)),
% 11.55/11.71 inference(modus_ponens,[status(thm)],[4284, 4283])).
% 11.55/11.71 tff(4286,plain,
% 11.55/11.71 (~node20(c_e_h_1, c_r, s2)),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4285, 213, 4282])).
% 11.55/11.71 tff(4287,plain,
% 11.55/11.71 (((~![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_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)))) | 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)))),
% 11.55/11.71 inference(rewrite,[status(thm)],[])).
% 11.55/11.71 tff(4288,plain,
% 11.55/11.71 ((~![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_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)))),
% 11.55/11.71 inference(quant_inst,[status(thm)],[])).
% 11.55/11.71 tff(4289,plain,
% 11.55/11.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3))),
% 11.55/11.71 inference(modus_ponens,[status(thm)],[4288, 4287])).
% 11.55/11.71 tff(4290,plain,
% 11.55/11.71 ($false),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4289, 228, 4277, 4286, 4278])).
% 11.55/11.71 tff(4291,plain,((~node21(c_e_h_1, c_r, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3))), inference(lemma,lemma(discharge,[]))).
% 11.55/11.71 tff(4292,plain,
% 11.55/11.71 (~node21(c_e_h_1, c_r, s2, s3)),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4291, 4277])).
% 11.55/11.71 tff(4293,plain,
% 11.55/11.71 (((~![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_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))),
% 11.55/11.71 inference(rewrite,[status(thm)],[])).
% 11.55/11.71 tff(4294,plain,
% 11.55/11.71 ((~![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_r, s2, s3) | node22(c_e_h_1, c_r, s2, s3))),
% 11.55/11.71 inference(quant_inst,[status(thm)],[])).
% 11.55/11.71 tff(4295,plain,
% 11.55/11.71 ((~![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_r, s2, s3) | node22(c_e_h_1, c_r, s2, s3)),
% 11.55/11.71 inference(modus_ponens,[status(thm)],[4294, 4293])).
% 11.55/11.71 tff(4296,plain,
% 11.55/11.71 (node21(c_e_h_1, c_r, s2, s3) | node22(c_e_h_1, c_r, s2, s3)),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4295, 247, 604])).
% 11.55/11.71 tff(4297,plain,
% 11.55/11.71 (node22(c_e_h_1, c_r, s2, s3)),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4296, 4292])).
% 11.55/11.71 tff(4298,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s2)), introduced(assumption)).
% 11.55/11.71 tff(4299,plain,
% 11.55/11.71 (((~![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_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))),
% 11.55/11.71 inference(rewrite,[status(thm)],[])).
% 11.55/11.71 tff(4300,plain,
% 11.55/11.71 ((~![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_r, s3)) | (~node22(c_e_h_1, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2))),
% 11.55/11.71 inference(quant_inst,[status(thm)],[])).
% 11.55/11.71 tff(4301,plain,
% 11.55/11.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node22(c_e_h_1, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2)),
% 11.55/11.71 inference(modus_ponens,[status(thm)],[4300, 4299])).
% 11.55/11.71 tff(4302,plain,
% 11.55/11.71 ($false),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4301, 273, 4298, 4277, 4297])).
% 11.55/11.71 tff(4303,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2)), inference(lemma,lemma(discharge,[]))).
% 11.55/11.71 tff(4304,plain,
% 11.55/11.71 (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4303, 4276])).
% 11.55/11.71 tff(4305,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s4)), introduced(assumption)).
% 11.55/11.71 tff(4306,plain,
% 11.55/11.71 (((~![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))),
% 11.55/11.71 inference(rewrite,[status(thm)],[])).
% 11.55/11.71 tff(4307,plain,
% 11.55/11.71 ((~![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))),
% 11.55/11.71 inference(quant_inst,[status(thm)],[])).
% 11.55/11.71 tff(4308,plain,
% 11.55/11.71 ((~![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)),
% 11.55/11.71 inference(modus_ponens,[status(thm)],[4307, 4306])).
% 11.55/11.71 tff(4309,plain,
% 11.55/11.71 ((~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)),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4308, 4211])).
% 11.55/11.71 tff(4310,plain,
% 11.55/11.71 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s3)),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4309, 3933])).
% 11.55/11.71 tff(4311,plain,
% 11.55/11.71 (((~![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))),
% 11.55/11.71 inference(rewrite,[status(thm)],[])).
% 11.55/11.71 tff(4312,plain,
% 11.55/11.71 ((~![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))),
% 11.55/11.71 inference(quant_inst,[status(thm)],[])).
% 11.55/11.71 tff(4313,plain,
% 11.55/11.71 ((~![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)),
% 11.55/11.71 inference(modus_ponens,[status(thm)],[4312, 4311])).
% 11.55/11.71 tff(4314,plain,
% 11.55/11.71 (~node20(c_e_h_1, c_r, s3)),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4313, 173, 4310])).
% 11.55/11.71 tff(4315,assumption,(~node20(c_e_h_1, c_r, s3)), introduced(assumption)).
% 11.55/11.71 tff(4316,assumption,(node21(c_e_h_1, c_r, s3, s4)), introduced(assumption)).
% 11.55/11.71 tff(4317,plain,
% 11.55/11.71 (((~![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_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)))) | 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)))),
% 11.55/11.71 inference(rewrite,[status(thm)],[])).
% 11.55/11.71 tff(4318,plain,
% 11.55/11.71 ((~![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_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)))),
% 11.55/11.71 inference(quant_inst,[status(thm)],[])).
% 11.55/11.71 tff(4319,plain,
% 11.55/11.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node21(c_e_h_1, c_r, s3, s4))),
% 11.55/11.71 inference(modus_ponens,[status(thm)],[4318, 4317])).
% 11.55/11.71 tff(4320,plain,
% 11.55/11.71 ($false),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4319, 228, 4316, 4305, 4315])).
% 11.55/11.71 tff(4321,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 11.55/11.71 tff(4322,plain,
% 11.55/11.71 ((~node21(c_e_h_1, c_r, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4))),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4321, 4314])).
% 11.55/11.71 tff(4323,plain,
% 11.55/11.71 (~node21(c_e_h_1, c_r, s3, s4)),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4322, 4305])).
% 11.55/11.71 tff(4324,plain,
% 11.55/11.71 (((~![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))),
% 11.55/11.71 inference(rewrite,[status(thm)],[])).
% 11.55/11.71 tff(4325,plain,
% 11.55/11.71 ((~![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))),
% 11.55/11.71 inference(quant_inst,[status(thm)],[])).
% 11.55/11.71 tff(4326,plain,
% 11.55/11.71 ((~![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)),
% 11.55/11.71 inference(modus_ponens,[status(thm)],[4325, 4324])).
% 11.55/11.71 tff(4327,plain,
% 11.55/11.71 (node21(c_e_h_1, c_r, s3, s4) | node22(c_e_h_1, c_r, s3, s4)),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4326, 247, 1092])).
% 11.55/11.71 tff(4328,plain,
% 11.55/11.71 (node22(c_e_h_1, c_r, s3, s4)),
% 11.55/11.71 inference(unit_resolution,[status(thm)],[4327, 4323])).
% 11.55/11.71 tff(4329,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s3)), introduced(assumption)).
% 11.55/11.71 tff(4330,plain,
% 11.55/11.71 (((~![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_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))),
% 11.55/11.71 inference(rewrite,[status(thm)],[])).
% 11.55/11.71 tff(4331,plain,
% 11.55/11.71 ((~![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_r, s4)) | (~node22(c_e_h_1, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3))),
% 11.55/11.72 inference(quant_inst,[status(thm)],[])).
% 11.55/11.72 tff(4332,plain,
% 11.55/11.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node22(c_e_h_1, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3)),
% 11.55/11.72 inference(modus_ponens,[status(thm)],[4331, 4330])).
% 11.55/11.72 tff(4333,plain,
% 11.55/11.72 ($false),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4332, 273, 4329, 4328, 4305])).
% 11.55/11.72 tff(4334,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,[]))).
% 11.55/11.72 tff(4335,plain,
% 11.55/11.72 (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4334, 4304])).
% 11.55/11.72 tff(4336,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s5)), introduced(assumption)).
% 11.55/11.72 tff(4337,plain,
% 11.55/11.72 (((~![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))),
% 11.55/11.72 inference(rewrite,[status(thm)],[])).
% 11.55/11.72 tff(4338,plain,
% 11.55/11.72 ((~![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))),
% 11.55/11.72 inference(quant_inst,[status(thm)],[])).
% 11.55/11.72 tff(4339,plain,
% 11.55/11.72 ((~![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)),
% 11.55/11.72 inference(modus_ponens,[status(thm)],[4338, 4337])).
% 11.55/11.72 tff(4340,plain,
% 11.55/11.72 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s4)),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4339, 4211, 4051])).
% 11.55/11.72 tff(4341,plain,
% 11.55/11.72 (((~![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))),
% 11.55/11.72 inference(rewrite,[status(thm)],[])).
% 11.55/11.72 tff(4342,plain,
% 11.55/11.72 ((~![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))),
% 11.55/11.72 inference(quant_inst,[status(thm)],[])).
% 11.55/11.72 tff(4343,plain,
% 11.55/11.72 ((~![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)),
% 11.55/11.72 inference(modus_ponens,[status(thm)],[4342, 4341])).
% 11.55/11.72 tff(4344,plain,
% 11.55/11.72 (~node20(c_e_h_1, c_r, s4)),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4343, 173, 4340])).
% 11.55/11.72 tff(4345,plain,
% 11.55/11.72 (((~![Y: $i, I0: $i, X: $i, 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)))) | 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)))),
% 11.55/11.72 inference(rewrite,[status(thm)],[])).
% 11.55/11.72 tff(4346,plain,
% 11.55/11.72 ((~![Y: $i, I0: $i, X: $i, 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)))),
% 11.55/11.72 inference(quant_inst,[status(thm)],[])).
% 11.55/11.72 tff(4347,plain,
% 11.55/11.72 ((~![Y: $i, I0: $i, X: $i, 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))),
% 11.55/11.72 inference(modus_ponens,[status(thm)],[4346, 4345])).
% 11.55/11.72 tff(4348,plain,
% 11.55/11.72 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | (~node21(c_e_h_1, c_r, s4, s5))),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4347, 228, 4344])).
% 11.55/11.72 tff(4349,plain,
% 11.55/11.72 (~node21(c_e_h_1, c_r, s4, s5)),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4348, 4336])).
% 11.55/11.72 tff(4350,plain,
% 11.55/11.72 (((~![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))),
% 11.55/11.72 inference(rewrite,[status(thm)],[])).
% 11.55/11.72 tff(4351,plain,
% 11.55/11.72 ((~![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))),
% 11.55/11.72 inference(quant_inst,[status(thm)],[])).
% 11.55/11.72 tff(4352,plain,
% 11.55/11.72 ((~![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)),
% 11.55/11.72 inference(modus_ponens,[status(thm)],[4351, 4350])).
% 11.55/11.72 tff(4353,plain,
% 11.55/11.72 (node22(c_e_h_1, c_r, s4, s5)),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4352, 247, 1542, 4349])).
% 11.55/11.72 tff(4354,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s4)), introduced(assumption)).
% 11.55/11.72 tff(4355,plain,
% 11.55/11.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, 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))),
% 11.55/11.72 inference(rewrite,[status(thm)],[])).
% 11.55/11.72 tff(4356,plain,
% 11.55/11.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, 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))),
% 11.55/11.72 inference(quant_inst,[status(thm)],[])).
% 11.55/11.72 tff(4357,plain,
% 11.55/11.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | (~node22(c_e_h_1, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4)),
% 11.55/11.72 inference(modus_ponens,[status(thm)],[4356, 4355])).
% 11.55/11.72 tff(4358,plain,
% 11.55/11.72 ($false),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4357, 273, 4336, 4354, 4353])).
% 11.55/11.72 tff(4359,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,[]))).
% 11.55/11.72 tff(4360,plain,
% 11.55/11.72 (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4359, 4335])).
% 11.55/11.72 tff(4361,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s6)), introduced(assumption)).
% 11.55/11.72 tff(4362,plain,
% 11.55/11.72 (((~![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))),
% 11.55/11.72 inference(rewrite,[status(thm)],[])).
% 11.55/11.72 tff(4363,plain,
% 11.55/11.72 ((~![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))),
% 11.55/11.72 inference(quant_inst,[status(thm)],[])).
% 11.55/11.72 tff(4364,plain,
% 11.55/11.72 ((~![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)),
% 11.55/11.72 inference(modus_ponens,[status(thm)],[4363, 4362])).
% 11.55/11.72 tff(4365,plain,
% 11.55/11.72 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s5)),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4364, 4211, 4109])).
% 11.55/11.72 tff(4366,plain,
% 11.55/11.72 (((~![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))),
% 11.55/11.72 inference(rewrite,[status(thm)],[])).
% 11.55/11.72 tff(4367,plain,
% 11.55/11.72 ((~![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))),
% 11.55/11.72 inference(quant_inst,[status(thm)],[])).
% 11.55/11.72 tff(4368,plain,
% 11.55/11.72 ((~![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)),
% 11.55/11.72 inference(modus_ponens,[status(thm)],[4367, 4366])).
% 11.55/11.72 tff(4369,plain,
% 11.55/11.72 (~node20(c_e_h_1, c_r, s5)),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4368, 173, 4365])).
% 11.55/11.72 tff(4370,plain,
% 11.55/11.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, 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)) | node20(c_e_h_1, c_r, s5) | (~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)) | node20(c_e_h_1, c_r, s5) | (~node21(c_e_h_1, c_r, s5, s6)))),
% 11.55/11.72 inference(rewrite,[status(thm)],[])).
% 11.55/11.72 tff(4371,plain,
% 11.55/11.72 ((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)) | node20(c_e_h_1, c_r, s5) | (~node21(c_e_h_1, c_r, s5, s6)))),
% 11.55/11.72 inference(rewrite,[status(thm)],[])).
% 11.55/11.72 tff(4372,plain,
% 11.55/11.72 (((~![Y: $i, I0: $i, X: $i, 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)) | node20(c_e_h_1, c_r, s5) | (~node21(c_e_h_1, c_r, s5, s6))))),
% 11.55/11.72 inference(monotonicity,[status(thm)],[4371])).
% 11.55/11.72 tff(4373,plain,
% 11.55/11.72 (((~![Y: $i, I0: $i, X: $i, 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)) | node20(c_e_h_1, c_r, s5) | (~node21(c_e_h_1, c_r, s5, s6)))),
% 11.55/11.72 inference(transitivity,[status(thm)],[4372, 4370])).
% 11.55/11.72 tff(4374,plain,
% 11.55/11.72 ((~![Y: $i, I0: $i, X: $i, 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)))),
% 11.55/11.72 inference(quant_inst,[status(thm)],[])).
% 11.55/11.72 tff(4375,plain,
% 11.55/11.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, 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)) | node20(c_e_h_1, c_r, s5) | (~node21(c_e_h_1, c_r, s5, s6))),
% 11.55/11.72 inference(modus_ponens,[status(thm)],[4374, 4373])).
% 11.55/11.72 tff(4376,plain,
% 11.55/11.72 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node21(c_e_h_1, c_r, s5, s6))),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4375, 228, 4369])).
% 11.55/11.72 tff(4377,plain,
% 11.55/11.72 (~node21(c_e_h_1, c_r, s5, s6)),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4376, 4361])).
% 11.55/11.72 tff(4378,plain,
% 11.55/11.72 (((~![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))),
% 11.55/11.72 inference(rewrite,[status(thm)],[])).
% 11.55/11.72 tff(4379,plain,
% 11.55/11.72 ((~![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))),
% 11.55/11.72 inference(quant_inst,[status(thm)],[])).
% 11.55/11.72 tff(4380,plain,
% 11.55/11.72 ((~![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)),
% 11.55/11.72 inference(modus_ponens,[status(thm)],[4379, 4378])).
% 11.55/11.72 tff(4381,plain,
% 11.55/11.72 (node22(c_e_h_1, c_r, s5, s6)),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4380, 247, 2348, 4377])).
% 11.55/11.72 tff(4382,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s5)), introduced(assumption)).
% 11.55/11.72 tff(4383,plain,
% 11.55/11.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, 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))),
% 11.55/11.72 inference(rewrite,[status(thm)],[])).
% 11.55/11.72 tff(4384,plain,
% 11.55/11.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, 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))),
% 11.55/11.72 inference(quant_inst,[status(thm)],[])).
% 11.55/11.72 tff(4385,plain,
% 11.55/11.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node22(c_e_h_1, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_r, s5)),
% 11.55/11.72 inference(modus_ponens,[status(thm)],[4384, 4383])).
% 11.55/11.72 tff(4386,plain,
% 11.55/11.72 ($false),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4385, 273, 4361, 4382, 4381])).
% 11.55/11.72 tff(4387,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 11.55/11.72 tff(4388,plain,
% 11.55/11.72 (~m_and_h_gate_v_out(c_e_h_1, c_r, s6)),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4387, 4360])).
% 11.55/11.72 tff(4389,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s6)), introduced(assumption)).
% 11.55/11.72 tff(4390,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s7)), introduced(assumption)).
% 11.55/11.72 tff(4391,assumption,(node22(c_e_h_1, c_r, s6, s7)), introduced(assumption)).
% 11.55/11.72 tff(4392,plain,
% 11.55/11.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, 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))),
% 11.55/11.72 inference(rewrite,[status(thm)],[])).
% 11.55/11.72 tff(4393,plain,
% 11.55/11.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, 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))),
% 11.55/11.72 inference(quant_inst,[status(thm)],[])).
% 11.55/11.72 tff(4394,plain,
% 11.55/11.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | (~node22(c_e_h_1, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_r, s6)),
% 11.55/11.72 inference(modus_ponens,[status(thm)],[4393, 4392])).
% 11.55/11.72 tff(4395,plain,
% 11.55/11.72 ($false),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4394, 273, 4390, 4389, 4391])).
% 11.55/11.72 tff(4396,plain,((~node22(c_e_h_1, c_r, s6, s7)) | (~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,[]))).
% 11.55/11.72 tff(4397,plain,
% 11.55/11.72 (~node22(c_e_h_1, c_r, s6, s7)),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4396, 4390, 4389])).
% 11.55/11.72 tff(4398,plain,
% 11.55/11.72 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5)),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4153, 49, 4078])).
% 11.55/11.72 tff(4399,plain,
% 11.55/11.72 (~node9(c_e_h_1, c_m, s5)),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4157, 63, 4398])).
% 11.55/11.72 tff(4400,plain,
% 11.55/11.72 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4180, 4399])).
% 11.55/11.72 tff(4401,plain,
% 11.55/11.72 (((~![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))),
% 11.55/11.72 inference(rewrite,[status(thm)],[])).
% 11.55/11.72 tff(4402,plain,
% 11.55/11.72 ((~![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))),
% 11.55/11.72 inference(quant_inst,[status(thm)],[])).
% 11.55/11.72 tff(4403,plain,
% 11.55/11.72 ((~![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)),
% 11.55/11.72 inference(modus_ponens,[status(thm)],[4402, 4401])).
% 11.55/11.72 tff(4404,plain,
% 11.55/11.72 ((~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)),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4403, 4211])).
% 11.55/11.72 tff(4405,plain,
% 11.55/11.72 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s6)),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4404, 4400])).
% 11.55/11.72 tff(4406,plain,
% 11.55/11.72 (((~![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))),
% 11.55/11.72 inference(rewrite,[status(thm)],[])).
% 11.55/11.72 tff(4407,plain,
% 11.55/11.72 ((~![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))),
% 11.55/11.72 inference(quant_inst,[status(thm)],[])).
% 11.55/11.72 tff(4408,plain,
% 11.55/11.72 ((~![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)),
% 11.55/11.72 inference(modus_ponens,[status(thm)],[4407, 4406])).
% 11.55/11.72 tff(4409,plain,
% 11.55/11.72 (~node20(c_e_h_1, c_r, s6)),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4408, 173, 4405])).
% 11.55/11.72 tff(4410,plain,
% 11.55/11.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, 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, s7)) | node20(c_e_h_1, c_r, s6) | (~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)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | node20(c_e_h_1, c_r, s6) | (~node21(c_e_h_1, c_r, s6, s7)))),
% 11.55/11.72 inference(rewrite,[status(thm)],[])).
% 11.55/11.72 tff(4411,plain,
% 11.55/11.72 ((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))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | node20(c_e_h_1, c_r, s6) | (~node21(c_e_h_1, c_r, s6, s7)))),
% 11.55/11.72 inference(rewrite,[status(thm)],[])).
% 11.55/11.72 tff(4412,plain,
% 11.55/11.72 (((~![Y: $i, I0: $i, X: $i, 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)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | node20(c_e_h_1, c_r, s6) | (~node21(c_e_h_1, c_r, s6, s7))))),
% 11.55/11.72 inference(monotonicity,[status(thm)],[4411])).
% 11.55/11.72 tff(4413,plain,
% 11.55/11.72 (((~![Y: $i, I0: $i, X: $i, 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)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | node20(c_e_h_1, c_r, s6) | (~node21(c_e_h_1, c_r, s6, s7)))),
% 11.55/11.72 inference(transitivity,[status(thm)],[4412, 4410])).
% 11.55/11.72 tff(4414,plain,
% 11.55/11.72 ((~![Y: $i, I0: $i, X: $i, 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)))),
% 11.55/11.72 inference(quant_inst,[status(thm)],[])).
% 11.55/11.72 tff(4415,plain,
% 11.55/11.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, 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, s7)) | node20(c_e_h_1, c_r, s6) | (~node21(c_e_h_1, c_r, s6, s7))),
% 11.55/11.72 inference(modus_ponens,[status(thm)],[4414, 4413])).
% 11.55/11.72 tff(4416,plain,
% 11.55/11.72 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | node20(c_e_h_1, c_r, s6) | (~node21(c_e_h_1, c_r, s6, s7))),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4415, 228])).
% 11.55/11.72 tff(4417,plain,
% 11.55/11.72 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | (~node21(c_e_h_1, c_r, s6, s7))),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4416, 4409])).
% 11.55/11.72 tff(4418,plain,
% 11.55/11.72 (~node21(c_e_h_1, c_r, s6, s7)),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4417, 4390])).
% 11.55/11.72 tff(4419,assumption,(~node22(c_e_h_1, c_r, s6, s7)), introduced(assumption)).
% 11.55/11.72 tff(4420,assumption,(~node21(c_e_h_1, c_r, s6, s7)), introduced(assumption)).
% 11.55/11.72 tff(4421,plain,
% 11.55/11.72 (((~![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))),
% 11.55/11.72 inference(rewrite,[status(thm)],[])).
% 11.55/11.72 tff(4422,plain,
% 11.55/11.72 ((~![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))),
% 11.55/11.72 inference(quant_inst,[status(thm)],[])).
% 11.55/11.72 tff(4423,plain,
% 11.55/11.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_1, c_r, s6, s7) | node22(c_e_h_1, c_r, s6, s7)),
% 11.55/11.72 inference(modus_ponens,[status(thm)],[4422, 4421])).
% 11.55/11.72 tff(4424,plain,
% 11.55/11.72 ($false),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4423, 247, 2649, 4420, 4419])).
% 11.55/11.72 tff(4425,plain,(node21(c_e_h_1, c_r, s6, s7) | node22(c_e_h_1, c_r, s6, s7)), inference(lemma,lemma(discharge,[]))).
% 11.55/11.72 tff(4426,plain,
% 11.55/11.72 ($false),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4425, 4418, 4397])).
% 11.55/11.72 tff(4427,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,[]))).
% 11.55/11.72 tff(4428,plain,
% 11.55/11.72 (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)),
% 11.55/11.72 inference(unit_resolution,[status(thm)],[4427, 4388])).
% 11.55/11.72 tff(4429,assumption,(~node20(c_e_h_1, c_r, s7)), introduced(assumption)).
% 11.55/11.72 tff(4430,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s8)), introduced(assumption)).
% 11.55/11.72 tff(4431,plain,
% 11.55/11.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, 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)))),
% 11.55/11.72 inference(rewrite,[status(thm)],[])).
% 11.55/11.72 tff(4432,plain,
% 11.55/11.72 ((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)))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4433,plain,
% 11.55/11.73 (((~![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_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))))),
% 11.55/11.73 inference(monotonicity,[status(thm)],[4432])).
% 11.55/11.73 tff(4434,plain,
% 11.55/11.73 (((~![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_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)))),
% 11.55/11.73 inference(transitivity,[status(thm)],[4433, 4431])).
% 11.55/11.73 tff(4435,plain,
% 11.55/11.73 ((~![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_r, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | (~node21(c_e_h_1, c_r, s7, s8)))),
% 11.55/11.73 inference(quant_inst,[status(thm)],[])).
% 11.55/11.73 tff(4436,plain,
% 11.55/11.73 ((~![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)))) | (~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))),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4435, 4434])).
% 11.55/11.73 tff(4437,plain,
% 11.55/11.73 ((~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))),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4436, 228])).
% 11.55/11.73 tff(4438,plain,
% 11.55/11.73 (~node21(c_e_h_1, c_r, s7, s8)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4437, 4430, 4429])).
% 11.55/11.73 tff(4439,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s7)), introduced(assumption)).
% 11.55/11.73 tff(4440,plain,
% 11.55/11.73 (((~![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_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))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4441,plain,
% 11.55/11.73 ((~![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_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))),
% 11.55/11.73 inference(quant_inst,[status(thm)],[])).
% 11.55/11.73 tff(4442,plain,
% 11.55/11.73 ((~![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_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)),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4441, 4440])).
% 11.55/11.73 tff(4443,plain,
% 11.55/11.73 ((~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)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4442, 273])).
% 11.55/11.73 tff(4444,plain,
% 11.55/11.73 (~node22(c_e_h_1, c_r, s7, s8)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4443, 4430, 4439])).
% 11.55/11.73 tff(4445,plain,
% 11.55/11.73 (((~![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))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4446,plain,
% 11.55/11.73 ((~![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))),
% 11.55/11.73 inference(quant_inst,[status(thm)],[])).
% 11.55/11.73 tff(4447,plain,
% 11.55/11.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_1, c_r, s7, s8) | node22(c_e_h_1, c_r, s7, s8)),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4446, 4445])).
% 11.55/11.73 tff(4448,plain,
% 11.55/11.73 ($false),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4447, 247, 2669, 4444, 4438])).
% 11.55/11.73 tff(4449,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | node20(c_e_h_1, c_r, s7) | m_and_h_gate_v_out(c_e_h_1, c_r, s7)), inference(lemma,lemma(discharge,[]))).
% 11.55/11.73 tff(4450,plain,
% 11.55/11.73 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | node20(c_e_h_1, c_r, s7)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4449, 4428])).
% 11.55/11.73 tff(4451,plain,
% 11.55/11.73 (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4450, 4219])).
% 11.55/11.73 tff(4452,plain,
% 11.55/11.73 (^[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)))),
% 11.55/11.73 inference(bind,[status(th)],[])).
% 11.55/11.73 tff(4453,plain,
% 11.55/11.73 (![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))),
% 11.55/11.73 inference(quant_intro,[status(thm)],[4452])).
% 11.55/11.73 tff(4454,plain,
% 11.55/11.73 (![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))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4455,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')).
% 11.55/11.73 tff(4456,plain,
% 11.55/11.73 (![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4455, 4454])).
% 11.55/11.73 tff(4457,plain,(
% 11.55/11.73 ![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))),
% 11.55/11.73 inference(skolemize,[status(sab)],[4456])).
% 11.55/11.73 tff(4458,plain,
% 11.55/11.73 (![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4457, 4453])).
% 11.55/11.73 tff(4459,plain,
% 11.55/11.73 (((~![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))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4460,plain,
% 11.55/11.73 ((~![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))),
% 11.55/11.73 inference(quant_inst,[status(thm)],[])).
% 11.55/11.73 tff(4461,plain,
% 11.55/11.73 ((~![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)),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4460, 4459])).
% 11.55/11.73 tff(4462,plain,
% 11.55/11.73 (~m_user_v_ack(c_e_h_1, c_u, s8)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4461, 4458, 4451])).
% 11.55/11.73 tff(4463,plain,
% 11.55/11.73 (^[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))))),
% 11.55/11.73 inference(bind,[status(th)],[])).
% 11.55/11.73 tff(4464,plain,
% 11.55/11.73 (![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)))),
% 11.55/11.73 inference(quant_intro,[status(thm)],[4463])).
% 11.55/11.73 tff(4465,plain,
% 11.55/11.73 (![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)))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4466,axiom,(![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty1')).
% 11.55/11.73 tff(4467,plain,
% 11.55/11.73 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4466, 4465])).
% 11.55/11.73 tff(4468,plain,(
% 11.55/11.73 ![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))),
% 11.55/11.73 inference(skolemize,[status(sab)],[4467])).
% 11.55/11.73 tff(4469,plain,
% 11.55/11.73 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4468, 4464])).
% 11.55/11.73 tff(4470,plain,
% 11.55/11.73 (((~![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)))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4471,plain,
% 11.55/11.73 ((~![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)))),
% 11.55/11.73 inference(quant_inst,[status(thm)],[])).
% 11.55/11.73 tff(4472,plain,
% 11.55/11.73 ((~![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))),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4471, 4470])).
% 11.55/11.73 tff(4473,plain,
% 11.55/11.73 (~node23(s8)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4472, 4469, 4462])).
% 11.55/11.73 tff(4474,assumption,(~m_c_h_element_v_out(c_e_h_3, c_h, s5)), introduced(assumption)).
% 11.55/11.73 tff(4475,plain,
% 11.55/11.73 (((~![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)))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4476,plain,
% 11.55/11.73 ((~![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)))),
% 11.55/11.73 inference(quant_inst,[status(thm)],[])).
% 11.55/11.73 tff(4477,plain,
% 11.55/11.73 ((~![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))),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4476, 4475])).
% 11.55/11.73 tff(4478,plain,
% 11.55/11.73 (~node23(s9)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4477, 4469, 1557])).
% 11.55/11.73 tff(4479,assumption,(~node23(s8)), introduced(assumption)).
% 11.55/11.73 tff(4480,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s8)), introduced(assumption)).
% 11.55/11.73 tff(4481,plain,
% 11.55/11.73 (((~![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))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4482,plain,
% 11.55/11.73 ((~![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))),
% 11.55/11.73 inference(quant_inst,[status(thm)],[])).
% 11.55/11.73 tff(4483,plain,
% 11.55/11.73 ((~![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)),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4482, 4481])).
% 11.55/11.73 tff(4484,plain,
% 11.55/11.73 (~m_user_v_ack(c_e_h_3, c_u, s8)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4483, 4458, 4480])).
% 11.55/11.73 tff(4485,plain,
% 11.55/11.73 (^[X: $i] : refl(((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X)) <=> ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X)))),
% 11.55/11.73 inference(bind,[status(th)],[])).
% 11.55/11.73 tff(4486,plain,
% 11.55/11.73 (![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X)) <=> ![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))),
% 11.55/11.73 inference(quant_intro,[status(thm)],[4485])).
% 11.55/11.73 tff(4487,plain,
% 11.55/11.73 (![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X)) <=> ![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4488,plain,
% 11.55/11.73 (^[X: $i] : rewrite((m_user_v_ack(c_e_h_3, c_u, X) | (~node24(X))) <=> ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X)))),
% 11.55/11.73 inference(bind,[status(th)],[])).
% 11.55/11.73 tff(4489,plain,
% 11.55/11.73 (![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node24(X))) <=> ![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))),
% 11.55/11.73 inference(quant_intro,[status(thm)],[4488])).
% 11.55/11.73 tff(4490,axiom,(![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node24(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty4')).
% 11.55/11.73 tff(4491,plain,
% 11.55/11.73 (![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4490, 4489])).
% 11.55/11.73 tff(4492,plain,
% 11.55/11.73 (![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4491, 4487])).
% 11.55/11.73 tff(4493,plain,(
% 11.55/11.73 ![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))),
% 11.55/11.73 inference(skolemize,[status(sab)],[4492])).
% 11.55/11.73 tff(4494,plain,
% 11.55/11.73 (![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4493, 4486])).
% 11.55/11.73 tff(4495,plain,
% 11.55/11.73 (((~![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))) | ((~node24(s8)) | m_user_v_ack(c_e_h_3, c_u, s8))) <=> ((~![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))) | (~node24(s8)) | m_user_v_ack(c_e_h_3, c_u, s8))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4496,plain,
% 11.55/11.73 ((~![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))) | ((~node24(s8)) | m_user_v_ack(c_e_h_3, c_u, s8))),
% 11.55/11.73 inference(quant_inst,[status(thm)],[])).
% 11.55/11.73 tff(4497,plain,
% 11.55/11.73 ((~![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))) | (~node24(s8)) | m_user_v_ack(c_e_h_3, c_u, s8)),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4496, 4495])).
% 11.55/11.73 tff(4498,plain,
% 11.55/11.73 (~node24(s8)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4497, 4494, 4484])).
% 11.55/11.73 tff(4499,plain,
% 11.55/11.73 (^[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))))),
% 11.55/11.73 inference(bind,[status(th)],[])).
% 11.55/11.73 tff(4500,plain,
% 11.55/11.73 (![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)))),
% 11.55/11.73 inference(quant_intro,[status(thm)],[4499])).
% 11.55/11.73 tff(4501,plain,
% 11.55/11.73 (![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)))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4502,axiom,(![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty3')).
% 11.55/11.73 tff(4503,plain,
% 11.55/11.73 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4502, 4501])).
% 11.55/11.73 tff(4504,plain,(
% 11.55/11.73 ![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))),
% 11.55/11.73 inference(skolemize,[status(sab)],[4503])).
% 11.55/11.73 tff(4505,plain,
% 11.55/11.73 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4504, 4500])).
% 11.55/11.73 tff(4506,plain,
% 11.55/11.73 (((~![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)))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4507,plain,
% 11.55/11.73 ((~![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)))),
% 11.55/11.73 inference(quant_inst,[status(thm)],[])).
% 11.55/11.73 tff(4508,plain,
% 11.55/11.73 ((~![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))),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4507, 4506])).
% 11.55/11.73 tff(4509,plain,
% 11.55/11.73 (~node24(s9)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4508, 4505, 1557])).
% 11.55/11.73 tff(4510,plain,
% 11.55/11.73 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s5)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[2803, 503, 4474])).
% 11.55/11.73 tff(4511,plain,
% 11.55/11.73 (~node20(c_e_h_3, c_i, s5)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[2799, 213, 4510])).
% 11.55/11.73 tff(4512,plain,
% 11.55/11.73 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s4)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[1799, 503, 1795])).
% 11.55/11.73 tff(4513,plain,
% 11.55/11.73 (~node20(c_e_h_3, c_i, s4)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[1803, 213, 4512])).
% 11.55/11.73 tff(4514,plain,
% 11.55/11.73 (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[1957, 4513])).
% 11.55/11.73 tff(4515,plain,
% 11.55/11.73 ((~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | node20(c_e_h_3, c_i, s5)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[2795, 4514])).
% 11.55/11.73 tff(4516,plain,
% 11.55/11.73 (~m_and_h_gate_v_out(c_e_h_3, c_i, s6)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4515, 4511])).
% 11.55/11.73 tff(4517,plain,
% 11.55/11.73 (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[2773, 4516])).
% 11.55/11.73 tff(4518,plain,
% 11.55/11.73 (~m_c_h_element_v_in2(c_e_h_3, c_e, s5)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[1968, 1965, 4514])).
% 11.55/11.73 tff(4519,plain,
% 11.55/11.73 (~m_c_h_element_v_out(c_e_h_3, c_e, s6)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[2420, 4518])).
% 11.55/11.73 tff(4520,plain,
% 11.55/11.73 (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, s7))),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[2765, 4519])).
% 11.55/11.73 tff(4521,plain,
% 11.55/11.73 (~m_c_h_element_v_out(c_e_h_3, c_e, s7)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4520, 4517])).
% 11.55/11.73 tff(4522,plain,
% 11.55/11.73 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s7)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[2695, 4521])).
% 11.55/11.73 tff(4523,plain,
% 11.55/11.73 (~node20(c_e_h_3, c_r, s7)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[2687, 4522])).
% 11.55/11.73 tff(4524,plain,
% 11.55/11.73 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s6)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[2436, 4519])).
% 11.55/11.73 tff(4525,assumption,(node20(c_e_h_3, c_r, s6)), introduced(assumption)).
% 11.55/11.73 tff(4526,plain,
% 11.55/11.73 ($false),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[2440, 213, 4525, 4524])).
% 11.55/11.73 tff(4527,plain,(~node20(c_e_h_3, c_r, s6)), inference(lemma,lemma(discharge,[]))).
% 11.55/11.73 tff(4528,plain,
% 11.55/11.73 (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[2655, 4527])).
% 11.55/11.73 tff(4529,plain,
% 11.55/11.73 ((~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | node20(c_e_h_3, c_r, s7)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[2679, 4528])).
% 11.55/11.73 tff(4530,plain,
% 11.55/11.73 (~m_and_h_gate_v_out(c_e_h_3, c_r, s8)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4529, 4523])).
% 11.55/11.73 tff(4531,plain,
% 11.55/11.73 (~m_user_v_ack(c_e_h_3, c_u, s8)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4483, 4458, 4530])).
% 11.55/11.73 tff(4532,plain,
% 11.55/11.73 (^[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))))),
% 11.55/11.73 inference(bind,[status(th)],[])).
% 11.55/11.73 tff(4533,plain,
% 11.55/11.73 (![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)))),
% 11.55/11.73 inference(quant_intro,[status(thm)],[4532])).
% 11.55/11.73 tff(4534,plain,
% 11.55/11.73 (![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)))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4535,axiom,(![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty6')).
% 11.55/11.73 tff(4536,plain,
% 11.55/11.73 (![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4535, 4534])).
% 11.55/11.73 tff(4537,plain,(
% 11.55/11.73 ![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))),
% 11.55/11.73 inference(skolemize,[status(sab)],[4536])).
% 11.55/11.73 tff(4538,plain,
% 11.55/11.73 (![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4537, 4533])).
% 11.55/11.73 tff(4539,plain,
% 11.55/11.73 (((~![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)))) | m_user_v_ack(c_e_h_3, c_u, s8) | (~node25(s8)))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4540,plain,
% 11.55/11.73 ((~![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)))),
% 11.55/11.73 inference(quant_inst,[status(thm)],[])).
% 11.55/11.73 tff(4541,plain,
% 11.55/11.73 ((~![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))),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4540, 4539])).
% 11.55/11.73 tff(4542,plain,
% 11.55/11.73 (~node25(s8)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4541, 4538, 4531])).
% 11.55/11.73 tff(4543,assumption,(~node24(s8)), introduced(assumption)).
% 11.55/11.73 tff(4544,plain,
% 11.55/11.73 (^[X: $i] : refl((node23(X) | node24(X) | node25(X) | (~node26(X))) <=> (node23(X) | node24(X) | node25(X) | (~node26(X))))),
% 11.55/11.73 inference(bind,[status(th)],[])).
% 11.55/11.73 tff(4545,plain,
% 11.55/11.73 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X))) <=> ![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 11.55/11.73 inference(quant_intro,[status(thm)],[4544])).
% 11.55/11.73 tff(4546,plain,
% 11.55/11.73 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X))) <=> ![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4547,plain,
% 11.55/11.73 (^[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)))))),
% 11.55/11.73 inference(bind,[status(th)],[])).
% 11.55/11.73 tff(4548,plain,
% 11.55/11.73 (![X: $i] : (((node23(X) | node24(X)) | node25(X)) | (~node26(X))) <=> ![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 11.55/11.73 inference(quant_intro,[status(thm)],[4547])).
% 11.55/11.73 tff(4549,axiom,(![X: $i] : (((node23(X) | node24(X)) | node25(X)) | (~node26(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty7')).
% 11.55/11.73 tff(4550,plain,
% 11.55/11.73 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4549, 4548])).
% 11.55/11.73 tff(4551,plain,
% 11.55/11.73 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4550, 4546])).
% 11.55/11.73 tff(4552,plain,(
% 11.55/11.73 ![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 11.55/11.73 inference(skolemize,[status(sab)],[4551])).
% 11.55/11.73 tff(4553,plain,
% 11.55/11.73 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4552, 4545])).
% 11.55/11.73 tff(4554,plain,
% 11.55/11.73 (((~![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)))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4555,plain,
% 11.55/11.73 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s8) | node24(s8) | node25(s8) | (~node26(s8)))),
% 11.55/11.73 inference(quant_inst,[status(thm)],[])).
% 11.55/11.73 tff(4556,plain,
% 11.55/11.73 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s8) | node24(s8) | node25(s8) | (~node26(s8))),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4555, 4554])).
% 11.55/11.73 tff(4557,plain,
% 11.55/11.73 (node25(s8) | (~node26(s8))),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4556, 4553, 4479, 4543])).
% 11.55/11.73 tff(4558,plain,
% 11.55/11.73 (~node26(s8)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4557, 4542])).
% 11.55/11.73 tff(4559,plain,
% 11.55/11.73 (((~![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))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4560,plain,
% 11.55/11.73 ((~![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))),
% 11.55/11.73 inference(quant_inst,[status(thm)],[])).
% 11.55/11.73 tff(4561,plain,
% 11.55/11.73 ((~![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)),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4560, 4559])).
% 11.55/11.73 tff(4562,plain,
% 11.55/11.73 (~m_user_v_ack(c_e_h_1, c_u, s6)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4561, 4458, 4388])).
% 11.55/11.73 tff(4563,plain,
% 11.55/11.73 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | ((~node23(s6)) | m_user_v_ack(c_e_h_1, c_u, s6))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s6)) | m_user_v_ack(c_e_h_1, c_u, s6))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4564,plain,
% 11.55/11.73 ((m_user_v_ack(c_e_h_1, c_u, s6) | (~node23(s6))) <=> ((~node23(s6)) | m_user_v_ack(c_e_h_1, c_u, s6))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4565,plain,
% 11.55/11.73 (((~![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)))) | ((~node23(s6)) | m_user_v_ack(c_e_h_1, c_u, s6)))),
% 11.55/11.73 inference(monotonicity,[status(thm)],[4564])).
% 11.55/11.73 tff(4566,plain,
% 11.55/11.73 (((~![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)))) | (~node23(s6)) | m_user_v_ack(c_e_h_1, c_u, s6))),
% 11.55/11.73 inference(transitivity,[status(thm)],[4565, 4563])).
% 11.55/11.73 tff(4567,plain,
% 11.55/11.73 ((~![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)))),
% 11.55/11.73 inference(quant_inst,[status(thm)],[])).
% 11.55/11.73 tff(4568,plain,
% 11.55/11.73 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s6)) | m_user_v_ack(c_e_h_1, c_u, s6)),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4567, 4566])).
% 11.55/11.73 tff(4569,plain,
% 11.55/11.73 (~node23(s6)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4568, 4469, 4562])).
% 11.55/11.73 tff(4570,plain,
% 11.55/11.73 (((~![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, s6)) | m_and_h_gate_v_out(c_e_h_3, 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_3, c_u, s6)) | m_and_h_gate_v_out(c_e_h_3, c_r, s6))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4571,plain,
% 11.55/11.73 ((~![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, s6)) | m_and_h_gate_v_out(c_e_h_3, c_r, s6))),
% 11.55/11.73 inference(quant_inst,[status(thm)],[])).
% 11.55/11.73 tff(4572,plain,
% 11.55/11.73 ((~![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, s6)) | m_and_h_gate_v_out(c_e_h_3, c_r, s6)),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4571, 4570])).
% 11.55/11.73 tff(4573,plain,
% 11.55/11.73 (~m_user_v_ack(c_e_h_3, c_u, s6)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4572, 4458, 2622])).
% 11.55/11.73 tff(4574,plain,
% 11.55/11.73 (((~![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))) | ((~node24(s6)) | m_user_v_ack(c_e_h_3, c_u, s6))) <=> ((~![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))) | (~node24(s6)) | m_user_v_ack(c_e_h_3, c_u, s6))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4575,plain,
% 11.55/11.73 ((~![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))) | ((~node24(s6)) | m_user_v_ack(c_e_h_3, c_u, s6))),
% 11.55/11.73 inference(quant_inst,[status(thm)],[])).
% 11.55/11.73 tff(4576,plain,
% 11.55/11.73 ((~![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))) | (~node24(s6)) | m_user_v_ack(c_e_h_3, c_u, s6)),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4575, 4574])).
% 11.55/11.73 tff(4577,plain,
% 11.55/11.73 (~node24(s6)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4576, 4494, 4573])).
% 11.55/11.73 tff(4578,plain,
% 11.55/11.73 (((~![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, s6) | (~node25(s6)))) <=> ((~![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, s6) | (~node25(s6)))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4579,plain,
% 11.55/11.73 ((~![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, s6) | (~node25(s6)))),
% 11.55/11.73 inference(quant_inst,[status(thm)],[])).
% 11.55/11.73 tff(4580,plain,
% 11.55/11.73 ((~![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, s6) | (~node25(s6))),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4579, 4578])).
% 11.55/11.73 tff(4581,plain,
% 11.55/11.73 (~node25(s6)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4580, 4538, 4573])).
% 11.55/11.73 tff(4582,plain,
% 11.55/11.73 (((~![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)))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4583,plain,
% 11.55/11.73 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s6) | node24(s6) | node25(s6) | (~node26(s6)))),
% 11.55/11.73 inference(quant_inst,[status(thm)],[])).
% 11.55/11.73 tff(4584,plain,
% 11.55/11.73 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s6) | node24(s6) | node25(s6) | (~node26(s6))),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4583, 4582])).
% 11.55/11.73 tff(4585,plain,
% 11.55/11.73 (node23(s6) | (~node26(s6))),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4584, 4553, 4581, 4577])).
% 11.55/11.73 tff(4586,plain,
% 11.55/11.73 (~node26(s6)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4585, 4569])).
% 11.55/11.73 tff(4587,plain,
% 11.55/11.73 (((~![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))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4588,plain,
% 11.55/11.73 ((~![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))),
% 11.55/11.73 inference(quant_inst,[status(thm)],[])).
% 11.55/11.73 tff(4589,plain,
% 11.55/11.73 ((~![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)),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4588, 4587])).
% 11.55/11.73 tff(4590,plain,
% 11.55/11.73 (~m_user_v_ack(c_e_h_1, c_u, s5)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4589, 4458, 4360])).
% 11.55/11.73 tff(4591,plain,
% 11.55/11.73 (((~![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)))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4592,plain,
% 11.55/11.73 ((~![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)))),
% 11.55/11.73 inference(quant_inst,[status(thm)],[])).
% 11.55/11.73 tff(4593,plain,
% 11.55/11.73 ((~![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))),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4592, 4591])).
% 11.55/11.73 tff(4594,plain,
% 11.55/11.73 (~node23(s5)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4593, 4469, 4590])).
% 11.55/11.73 tff(4595,assumption,(m_user_v_ack(c_e_h_3, c_u, s7)), introduced(assumption)).
% 11.55/11.73 tff(4596,plain,
% 11.55/11.73 (((~![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))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4597,plain,
% 11.55/11.73 ((~![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))),
% 11.55/11.73 inference(quant_inst,[status(thm)],[])).
% 11.55/11.73 tff(4598,plain,
% 11.55/11.73 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s7)) | m_and_h_gate_v_out(c_e_h_3, c_r, s7)),
% 11.55/11.73 inference(modus_ponens,[status(thm)],[4597, 4596])).
% 11.55/11.73 tff(4599,plain,
% 11.55/11.73 ($false),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4598, 4458, 4595, 2674])).
% 11.55/11.73 tff(4600,plain,((~m_user_v_ack(c_e_h_3, c_u, s7)) | m_and_h_gate_v_out(c_e_h_3, c_r, s7)), inference(lemma,lemma(discharge,[]))).
% 11.55/11.73 tff(4601,plain,
% 11.55/11.73 (~m_user_v_ack(c_e_h_3, c_u, s7)),
% 11.55/11.73 inference(unit_resolution,[status(thm)],[4600, 4528])).
% 11.55/11.73 tff(4602,plain,
% 11.55/11.73 (((~![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)))),
% 11.55/11.73 inference(rewrite,[status(thm)],[])).
% 11.55/11.73 tff(4603,plain,
% 11.55/11.73 ((~![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)))),
% 11.55/11.73 inference(quant_inst,[status(thm)],[])).
% 11.55/11.73 tff(4604,plain,
% 11.55/11.73 ((~![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))),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4603, 4602])).
% 11.55/11.74 tff(4605,plain,
% 11.55/11.74 (~node25(s7)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4604, 4538, 4601])).
% 11.55/11.74 tff(4606,plain,
% 11.55/11.74 (((~![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))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4607,plain,
% 11.55/11.74 ((~![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))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4608,plain,
% 11.55/11.74 ((~![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)),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4607, 4606])).
% 11.55/11.74 tff(4609,plain,
% 11.55/11.74 (~m_user_v_ack(c_e_h_1, c_u, s7)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4608, 4458, 4428])).
% 11.55/11.74 tff(4610,plain,
% 11.55/11.74 (((~![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)))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4611,plain,
% 11.55/11.74 ((~![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)))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4612,plain,
% 11.55/11.74 ((~![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))),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4611, 4610])).
% 11.55/11.74 tff(4613,plain,
% 11.55/11.74 (~node24(s7)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4612, 4505, 4609])).
% 11.55/11.74 tff(4614,plain,
% 11.55/11.74 (((~![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)))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4615,plain,
% 11.55/11.74 ((~![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)))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4616,plain,
% 11.55/11.74 ((~![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))),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4615, 4614])).
% 11.55/11.74 tff(4617,plain,
% 11.55/11.74 (~node23(s7)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4616, 4469, 4609])).
% 11.55/11.74 tff(4618,plain,
% 11.55/11.74 (((~![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)))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4619,plain,
% 11.55/11.74 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s7) | node24(s7) | node25(s7) | (~node26(s7)))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4620,plain,
% 11.55/11.74 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s7) | node24(s7) | node25(s7) | (~node26(s7))),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4619, 4618])).
% 11.55/11.74 tff(4621,plain,
% 11.55/11.74 (node25(s7) | (~node26(s7))),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4620, 4553, 4617, 4613])).
% 11.55/11.74 tff(4622,plain,
% 11.55/11.74 (~node26(s7)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4621, 4605])).
% 11.55/11.74 tff(4623,assumption,(m_user_v_ack(c_e_h_1, c_u, s2)), introduced(assumption)).
% 11.55/11.74 tff(4624,plain,
% 11.55/11.74 (((~![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))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4625,plain,
% 11.55/11.74 ((~![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))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4626,plain,
% 11.55/11.74 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2)),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4625, 4624])).
% 11.55/11.74 tff(4627,plain,
% 11.55/11.74 ($false),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4626, 4458, 4623, 4298])).
% 11.55/11.74 tff(4628,plain,((~m_user_v_ack(c_e_h_1, c_u, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2)), inference(lemma,lemma(discharge,[]))).
% 11.55/11.74 tff(4629,plain,
% 11.55/11.74 (~m_user_v_ack(c_e_h_1, c_u, s2)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4628, 4276])).
% 11.55/11.74 tff(4630,plain,
% 11.55/11.74 (((~![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, s5)) | m_and_h_gate_v_out(c_e_h_3, 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_3, c_u, s5)) | m_and_h_gate_v_out(c_e_h_3, c_r, s5))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4631,plain,
% 11.55/11.74 ((~![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, s5)) | m_and_h_gate_v_out(c_e_h_3, c_r, s5))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4632,plain,
% 11.55/11.74 ((~![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, s5)) | m_and_h_gate_v_out(c_e_h_3, c_r, s5)),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4631, 4630])).
% 11.55/11.74 tff(4633,plain,
% 11.55/11.74 (~m_user_v_ack(c_e_h_3, c_u, s5)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4632, 4458, 2585])).
% 11.55/11.74 tff(4634,plain,
% 11.55/11.74 (((~![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, s5) | (~node25(s5)))) <=> ((~![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, s5) | (~node25(s5)))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4635,plain,
% 11.55/11.74 ((~![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, s5) | (~node25(s5)))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4636,plain,
% 11.55/11.74 ((~![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, s5) | (~node25(s5))),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4635, 4634])).
% 11.55/11.74 tff(4637,plain,
% 11.55/11.74 (~node25(s5)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4636, 4538, 4633])).
% 11.55/11.74 tff(4638,assumption,(~m_user_v_ack(c_e_h_1, c_u, s2)), introduced(assumption)).
% 11.55/11.74 tff(4639,assumption,(~node26(s6)), introduced(assumption)).
% 11.55/11.74 tff(4640,assumption,(~node26(s9)), introduced(assumption)).
% 11.55/11.74 tff(4641,assumption,(m_user_v_ack(c_e_h_1, c_u, s3)), introduced(assumption)).
% 11.55/11.74 tff(4642,plain,
% 11.55/11.74 (((~![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))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4643,plain,
% 11.55/11.74 ((~![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))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4644,plain,
% 11.55/11.74 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3)),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4643, 4642])).
% 11.55/11.74 tff(4645,plain,
% 11.55/11.74 ($false),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4644, 4458, 4641, 4329])).
% 11.55/11.74 tff(4646,plain,((~m_user_v_ack(c_e_h_1, c_u, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 11.55/11.74 tff(4647,plain,
% 11.55/11.74 (~m_user_v_ack(c_e_h_1, c_u, s3)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4646, 4329])).
% 11.55/11.74 tff(4648,plain,
% 11.55/11.74 (((~![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)))) | m_user_v_ack(c_e_h_1, c_u, s3) | (~node23(s3)))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4649,plain,
% 11.55/11.74 ((~![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)))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4650,plain,
% 11.55/11.74 ((~![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))),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4649, 4648])).
% 11.55/11.74 tff(4651,plain,
% 11.55/11.74 (~node23(s3)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4650, 4469, 4647])).
% 11.55/11.74 tff(4652,assumption,(~node26(s7)), introduced(assumption)).
% 11.55/11.74 tff(4653,assumption,(~node26(s8)), introduced(assumption)).
% 11.55/11.74 tff(4654,assumption,(m_user_v_ack(c_e_h_1, c_u, s4)), introduced(assumption)).
% 11.55/11.74 tff(4655,plain,
% 11.55/11.74 (((~![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))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4656,plain,
% 11.55/11.74 ((~![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))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4657,plain,
% 11.55/11.74 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4)),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4656, 4655])).
% 11.55/11.74 tff(4658,plain,
% 11.55/11.74 ($false),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4657, 4458, 4654, 4354])).
% 11.55/11.74 tff(4659,plain,((~m_user_v_ack(c_e_h_1, c_u, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4)), inference(lemma,lemma(discharge,[]))).
% 11.55/11.74 tff(4660,plain,
% 11.55/11.74 (~m_user_v_ack(c_e_h_1, c_u, s4)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4659, 4354])).
% 11.55/11.74 tff(4661,plain,
% 11.55/11.74 (((~![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)))) | m_user_v_ack(c_e_h_1, c_u, s4) | (~node23(s4)))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4662,plain,
% 11.55/11.74 ((~![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)))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4663,plain,
% 11.55/11.74 ((~![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))),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4662, 4661])).
% 11.55/11.74 tff(4664,plain,
% 11.55/11.74 (~node23(s4)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4663, 4469, 4660])).
% 11.55/11.74 tff(4665,plain,
% 11.55/11.74 (((~![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, s4)) | m_and_h_gate_v_out(c_e_h_3, 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_3, c_u, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s4))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4666,plain,
% 11.55/11.74 ((~![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, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s4))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4667,plain,
% 11.55/11.74 ((~![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, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s4)),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4666, 4665])).
% 11.55/11.74 tff(4668,plain,
% 11.55/11.74 (~m_user_v_ack(c_e_h_3, c_u, s4)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4667, 4458, 2555])).
% 11.55/11.74 tff(4669,plain,
% 11.55/11.74 (((~![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, s4) | (~node25(s4)))) <=> ((~![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, s4) | (~node25(s4)))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4670,plain,
% 11.55/11.74 ((~![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, s4) | (~node25(s4)))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4671,plain,
% 11.55/11.74 ((~![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, s4) | (~node25(s4))),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4670, 4669])).
% 11.55/11.74 tff(4672,plain,
% 11.55/11.74 (~node25(s4)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4671, 4538, 4668])).
% 11.55/11.74 tff(4673,plain,
% 11.55/11.74 (((~![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))) | ((~node24(s4)) | m_user_v_ack(c_e_h_3, c_u, s4))) <=> ((~![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))) | (~node24(s4)) | m_user_v_ack(c_e_h_3, c_u, s4))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4674,plain,
% 11.55/11.74 ((~![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))) | ((~node24(s4)) | m_user_v_ack(c_e_h_3, c_u, s4))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4675,plain,
% 11.55/11.74 ((~![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))) | (~node24(s4)) | m_user_v_ack(c_e_h_3, c_u, s4)),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4674, 4673])).
% 11.55/11.74 tff(4676,plain,
% 11.55/11.74 (~node24(s4)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4675, 4494, 4668])).
% 11.55/11.74 tff(4677,plain,
% 11.55/11.74 (((~![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)))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4678,plain,
% 11.55/11.74 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s4) | node24(s4) | node25(s4) | (~node26(s4)))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4679,plain,
% 11.55/11.74 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s4) | node24(s4) | node25(s4) | (~node26(s4))),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4678, 4677])).
% 11.55/11.74 tff(4680,plain,
% 11.55/11.74 (node23(s4) | (~node26(s4))),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4679, 4553, 4676, 4672])).
% 11.55/11.74 tff(4681,plain,
% 11.55/11.74 (~node26(s4)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4680, 4664])).
% 11.55/11.74 tff(4682,plain,
% 11.55/11.74 (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4359, 4354])).
% 11.55/11.74 tff(4683,plain,
% 11.55/11.74 (~m_user_v_ack(c_e_h_1, c_u, s5)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4589, 4458, 4682])).
% 11.55/11.74 tff(4684,plain,
% 11.55/11.74 (((~![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)))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4685,plain,
% 11.55/11.74 ((~![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)))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4686,plain,
% 11.55/11.74 ((~![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))),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4685, 4684])).
% 11.55/11.74 tff(4687,plain,
% 11.55/11.74 (~node24(s5)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4686, 4505, 4683])).
% 11.55/11.74 tff(4688,assumption,(~node25(s5)), introduced(assumption)).
% 11.55/11.74 tff(4689,assumption,(~node23(s5)), introduced(assumption)).
% 11.55/11.74 tff(4690,plain,
% 11.55/11.74 (((~![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)))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4691,plain,
% 11.55/11.74 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s5) | node24(s5) | node25(s5) | (~node26(s5)))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4692,plain,
% 11.55/11.74 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s5) | node24(s5) | node25(s5) | (~node26(s5))),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4691, 4690])).
% 11.55/11.74 tff(4693,plain,
% 11.55/11.74 (node24(s5) | (~node26(s5))),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4692, 4553, 4689, 4688])).
% 11.55/11.74 tff(4694,plain,
% 11.55/11.74 (~node26(s5)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4693, 4687])).
% 11.55/11.74 tff(4695,plain,
% 11.55/11.74 (((~![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, s3)) | m_and_h_gate_v_out(c_e_h_3, 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_3, c_u, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4696,plain,
% 11.55/11.74 ((~![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, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4697,plain,
% 11.55/11.74 ((~![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, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3)),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4696, 4695])).
% 11.55/11.74 tff(4698,plain,
% 11.55/11.74 (~m_user_v_ack(c_e_h_3, c_u, s3)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4697, 4458, 2550])).
% 11.55/11.74 tff(4699,plain,
% 11.55/11.74 (((~![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, s3) | (~node25(s3)))) <=> ((~![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, s3) | (~node25(s3)))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4700,plain,
% 11.55/11.74 ((~![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, s3) | (~node25(s3)))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4701,plain,
% 11.55/11.74 ((~![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, s3) | (~node25(s3))),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4700, 4699])).
% 11.55/11.74 tff(4702,plain,
% 11.55/11.74 (~node25(s3)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4701, 4538, 4698])).
% 11.55/11.74 tff(4703,assumption,(~node26(s5)), introduced(assumption)).
% 11.55/11.74 tff(4704,assumption,(~node26(s4)), introduced(assumption)).
% 11.55/11.74 tff(4705,plain,
% 11.55/11.74 (((~![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)))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4706,plain,
% 11.55/11.74 ((~![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)))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4707,plain,
% 11.55/11.74 ((~![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))),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4706, 4705])).
% 11.55/11.74 tff(4708,plain,
% 11.55/11.74 (~node23(s2)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4707, 4469, 4638])).
% 11.55/11.74 tff(4709,plain,
% 11.55/11.74 (((~![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, s2)) | m_and_h_gate_v_out(c_e_h_3, 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_3, c_u, s2)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4710,plain,
% 11.55/11.74 ((~![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, s2)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4711,plain,
% 11.55/11.74 ((~![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, s2)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2)),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4710, 4709])).
% 11.55/11.74 tff(4712,plain,
% 11.55/11.74 (~m_user_v_ack(c_e_h_3, c_u, s2)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4711, 4458, 2523])).
% 11.55/11.74 tff(4713,plain,
% 11.55/11.74 (((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | ((~node25(s2)) | m_user_v_ack(c_e_h_3, c_u, s2))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (~node25(s2)) | m_user_v_ack(c_e_h_3, c_u, s2))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4714,plain,
% 11.55/11.74 ((m_user_v_ack(c_e_h_3, c_u, s2) | (~node25(s2))) <=> ((~node25(s2)) | m_user_v_ack(c_e_h_3, c_u, s2))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4715,plain,
% 11.55/11.74 (((~![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, s2) | (~node25(s2)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | ((~node25(s2)) | m_user_v_ack(c_e_h_3, c_u, s2)))),
% 11.55/11.74 inference(monotonicity,[status(thm)],[4714])).
% 11.55/11.74 tff(4716,plain,
% 11.55/11.74 (((~![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, s2) | (~node25(s2)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (~node25(s2)) | m_user_v_ack(c_e_h_3, c_u, s2))),
% 11.55/11.74 inference(transitivity,[status(thm)],[4715, 4713])).
% 11.55/11.74 tff(4717,plain,
% 11.55/11.74 ((~![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, s2) | (~node25(s2)))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4718,plain,
% 11.55/11.74 ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (~node25(s2)) | m_user_v_ack(c_e_h_3, c_u, s2)),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4717, 4716])).
% 11.55/11.74 tff(4719,plain,
% 11.55/11.74 (~node25(s2)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4718, 4538, 4712])).
% 11.55/11.74 tff(4720,plain,
% 11.55/11.74 (((~![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))) | ((~node24(s2)) | m_user_v_ack(c_e_h_3, c_u, s2))) <=> ((~![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))) | (~node24(s2)) | m_user_v_ack(c_e_h_3, c_u, s2))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4721,plain,
% 11.55/11.74 ((~![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))) | ((~node24(s2)) | m_user_v_ack(c_e_h_3, c_u, s2))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4722,plain,
% 11.55/11.74 ((~![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))) | (~node24(s2)) | m_user_v_ack(c_e_h_3, c_u, s2)),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4721, 4720])).
% 11.55/11.74 tff(4723,plain,
% 11.55/11.74 (~node24(s2)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4722, 4494, 4712])).
% 11.55/11.74 tff(4724,plain,
% 11.55/11.74 (((~![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)))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4725,plain,
% 11.55/11.74 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s2) | node24(s2) | node25(s2) | (~node26(s2)))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4726,plain,
% 11.55/11.74 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s2) | node24(s2) | node25(s2) | (~node26(s2))),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4725, 4724])).
% 11.55/11.74 tff(4727,plain,
% 11.55/11.74 (node23(s2) | (~node26(s2))),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4726, 4553, 4723, 4719])).
% 11.55/11.74 tff(4728,plain,
% 11.55/11.74 (~node26(s2)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4727, 4708])).
% 11.55/11.74 tff(4729,plain,
% 11.55/11.74 (~m_user_v_ack(c_e_h_1, c_u, s3)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4644, 4458, 4329])).
% 11.55/11.74 tff(4730,plain,
% 11.55/11.74 (((~![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)))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4731,plain,
% 11.55/11.74 ((~![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)))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4732,plain,
% 11.55/11.74 ((~![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))),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4731, 4730])).
% 11.55/11.74 tff(4733,plain,
% 11.55/11.74 (~node24(s3)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4732, 4505, 4729])).
% 11.55/11.74 tff(4734,assumption,(~node25(s3)), introduced(assumption)).
% 11.55/11.74 tff(4735,assumption,(~node23(s3)), introduced(assumption)).
% 11.55/11.74 tff(4736,plain,
% 11.55/11.74 (((~![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)))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4737,plain,
% 11.55/11.74 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s3) | node24(s3) | node25(s3) | (~node26(s3)))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4738,plain,
% 11.55/11.74 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s3) | node24(s3) | node25(s3) | (~node26(s3))),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4737, 4736])).
% 11.55/11.74 tff(4739,plain,
% 11.55/11.74 (node24(s3) | (~node26(s3))),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4738, 4553, 4735, 4734])).
% 11.55/11.74 tff(4740,plain,
% 11.55/11.74 (~node26(s3)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4739, 4733])).
% 11.55/11.74 tff(4741,assumption,(~node26(s2)), introduced(assumption)).
% 11.55/11.74 tff(4742,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s1)), introduced(assumption)).
% 11.55/11.74 tff(4743,plain,
% 11.55/11.74 (^[X: $i] : refl((~m_cell_v_token(c_e_h_2, X)) <=> (~m_cell_v_token(c_e_h_2, X)))),
% 11.55/11.74 inference(bind,[status(th)],[])).
% 11.55/11.74 tff(4744,plain,
% 11.55/11.74 (![X: $i] : (~m_cell_v_token(c_e_h_2, X)) <=> ![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 11.55/11.74 inference(quant_intro,[status(thm)],[4743])).
% 11.55/11.74 tff(4745,plain,
% 11.55/11.74 (![X: $i] : (~m_cell_v_token(c_e_h_2, X)) <=> ![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4746,axiom,(![X: $i] : (~m_cell_v_token(c_e_h_2, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_6')).
% 11.55/11.74 tff(4747,plain,
% 11.55/11.74 (![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4746, 4745])).
% 11.55/11.74 tff(4748,plain,(
% 11.55/11.74 ![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 11.55/11.74 inference(skolemize,[status(sab)],[4747])).
% 11.55/11.74 tff(4749,plain,
% 11.55/11.74 (![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4748, 4744])).
% 11.55/11.74 tff(4750,plain,
% 11.55/11.74 ((~![X: $i] : (~m_cell_v_token(c_e_h_2, X))) | (~m_cell_v_token(c_e_h_2, s0))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4751,plain,
% 11.55/11.74 (~m_cell_v_token(c_e_h_2, s0)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4750, 4749])).
% 11.55/11.74 tff(4752,plain,
% 11.55/11.74 (((~![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))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4753,plain,
% 11.55/11.74 ((~![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))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4754,plain,
% 11.55/11.74 ((~![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)),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4753, 4752])).
% 11.55/11.74 tff(4755,plain,
% 11.55/11.74 (~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_m, s0)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4754, 122, 4751])).
% 11.55/11.74 tff(4756,plain,
% 11.55/11.74 (((~![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))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4757,plain,
% 11.55/11.74 ((~![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))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4758,plain,
% 11.55/11.74 ((~![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)),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4757, 4756])).
% 11.55/11.74 tff(4759,plain,
% 11.55/11.74 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4758, 133, 4755])).
% 11.55/11.74 tff(4760,plain,
% 11.55/11.74 (((~![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))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4761,plain,
% 11.55/11.74 ((~![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))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4762,plain,
% 11.55/11.74 ((~![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)),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4761, 4760])).
% 11.55/11.74 tff(4763,plain,
% 11.55/11.74 (~m_and_h_gate_v_in2(c_e_h_2, c_r, s0)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4762, 4211, 4759])).
% 11.55/11.74 tff(4764,plain,
% 11.55/11.74 (((~![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))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4765,plain,
% 11.55/11.74 ((~![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))),
% 11.55/11.74 inference(quant_inst,[status(thm)],[])).
% 11.55/11.74 tff(4766,plain,
% 11.55/11.74 ((~![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)),
% 11.55/11.74 inference(modus_ponens,[status(thm)],[4765, 4764])).
% 11.55/11.74 tff(4767,plain,
% 11.55/11.74 (~node20(c_e_h_2, c_r, s0)),
% 11.55/11.74 inference(unit_resolution,[status(thm)],[4766, 173, 4763])).
% 11.55/11.74 tff(4768,plain,
% 11.55/11.74 (((~![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_r, s0) | (~node21(c_e_h_2, c_r, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, 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)))) | node20(c_e_h_2, c_r, s0) | (~node21(c_e_h_2, c_r, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4769,plain,
% 11.55/11.74 ((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))) <=> (node20(c_e_h_2, c_r, s0) | (~node21(c_e_h_2, c_r, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)))),
% 11.55/11.74 inference(rewrite,[status(thm)],[])).
% 11.55/11.74 tff(4770,plain,
% 11.55/11.74 (((~![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_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)))) | (node20(c_e_h_2, c_r, s0) | (~node21(c_e_h_2, c_r, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1))))),
% 11.55/11.74 inference(monotonicity,[status(thm)],[4769])).
% 11.55/11.74 tff(4771,plain,
% 11.55/11.74 (((~![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_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)))) | node20(c_e_h_2, c_r, s0) | (~node21(c_e_h_2, c_r, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)))),
% 11.55/11.75 inference(transitivity,[status(thm)],[4770, 4768])).
% 11.55/11.75 tff(4772,plain,
% 11.55/11.75 ((~![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_r, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | (~node21(c_e_h_2, c_r, s0, s1)))),
% 11.55/11.75 inference(quant_inst,[status(thm)],[])).
% 11.55/11.75 tff(4773,plain,
% 11.55/11.75 ((~![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_r, s0) | (~node21(c_e_h_2, c_r, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1))),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4772, 4771])).
% 11.55/11.75 tff(4774,plain,
% 11.55/11.75 ((~node21(c_e_h_2, c_r, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1))),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4773, 228, 4767])).
% 11.55/11.75 tff(4775,plain,
% 11.55/11.75 (~node21(c_e_h_2, c_r, s0, s1)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4774, 4742])).
% 11.55/11.75 tff(4776,plain,
% 11.55/11.75 (((~![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))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4777,plain,
% 11.55/11.75 ((~![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))),
% 11.55/11.75 inference(quant_inst,[status(thm)],[])).
% 11.55/11.75 tff(4778,plain,
% 11.55/11.75 ((~![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)),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4777, 4776])).
% 11.55/11.75 tff(4779,plain,
% 11.55/11.75 (node22(c_e_h_2, c_r, s0, s1)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4778, 247, 100, 4775])).
% 11.55/11.75 tff(4780,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s0)), introduced(assumption)).
% 11.55/11.75 tff(4781,plain,
% 11.55/11.75 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s0))),
% 11.55/11.75 inference(quant_inst,[status(thm)],[])).
% 11.55/11.75 tff(4782,plain,
% 11.55/11.75 ($false),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4781, 260, 4780])).
% 11.55/11.75 tff(4783,plain,(~m_and_h_gate_v_out(c_e_h_2, c_r, s0)), inference(lemma,lemma(discharge,[]))).
% 11.55/11.75 tff(4784,plain,
% 11.55/11.75 (((~![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_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))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4785,plain,
% 11.55/11.75 ((~![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_r, s1)) | (~node22(c_e_h_2, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_r, s0))),
% 11.55/11.75 inference(quant_inst,[status(thm)],[])).
% 11.55/11.75 tff(4786,plain,
% 11.55/11.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | (~node22(c_e_h_2, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_r, s0)),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4785, 4784])).
% 11.55/11.75 tff(4787,plain,
% 11.55/11.75 ($false),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4786, 273, 4783, 4742, 4779])).
% 11.55/11.75 tff(4788,plain,(~m_and_h_gate_v_out(c_e_h_2, c_r, s1)), inference(lemma,lemma(discharge,[]))).
% 11.55/11.75 tff(4789,plain,
% 11.55/11.75 (((~![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, s1)) | m_and_h_gate_v_out(c_e_h_2, 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_2, c_u, s1)) | m_and_h_gate_v_out(c_e_h_2, c_r, s1))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4790,plain,
% 11.55/11.75 ((~![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, s1)) | m_and_h_gate_v_out(c_e_h_2, c_r, s1))),
% 11.55/11.75 inference(quant_inst,[status(thm)],[])).
% 11.55/11.75 tff(4791,plain,
% 11.55/11.75 ((~![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, s1)) | m_and_h_gate_v_out(c_e_h_2, c_r, s1)),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4790, 4789])).
% 11.55/11.75 tff(4792,plain,
% 11.55/11.75 (~m_user_v_ack(c_e_h_2, c_u, s1)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4791, 4458, 4788])).
% 11.55/11.75 tff(4793,plain,
% 11.55/11.75 (^[X: $i] : refl(((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X)) <=> ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X)))),
% 11.55/11.75 inference(bind,[status(th)],[])).
% 11.55/11.75 tff(4794,plain,
% 11.55/11.75 (![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X)) <=> ![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))),
% 11.55/11.75 inference(quant_intro,[status(thm)],[4793])).
% 11.55/11.75 tff(4795,plain,
% 11.55/11.75 (![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X)) <=> ![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4796,plain,
% 11.55/11.75 (^[X: $i] : rewrite((m_user_v_ack(c_e_h_2, c_u, X) | (~node23(X))) <=> ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X)))),
% 11.55/11.75 inference(bind,[status(th)],[])).
% 11.55/11.75 tff(4797,plain,
% 11.55/11.75 (![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node23(X))) <=> ![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))),
% 11.55/11.75 inference(quant_intro,[status(thm)],[4796])).
% 11.55/11.75 tff(4798,axiom,(![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node23(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty2')).
% 11.55/11.75 tff(4799,plain,
% 11.55/11.75 (![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4798, 4797])).
% 11.55/11.75 tff(4800,plain,
% 11.55/11.75 (![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4799, 4795])).
% 11.55/11.75 tff(4801,plain,(
% 11.55/11.75 ![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))),
% 11.55/11.75 inference(skolemize,[status(sab)],[4800])).
% 11.55/11.75 tff(4802,plain,
% 11.55/11.75 (![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4801, 4794])).
% 11.55/11.75 tff(4803,plain,
% 11.55/11.75 (((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | ((~node23(s1)) | m_user_v_ack(c_e_h_2, c_u, s1))) <=> ((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | (~node23(s1)) | m_user_v_ack(c_e_h_2, c_u, s1))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4804,plain,
% 11.55/11.75 ((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | ((~node23(s1)) | m_user_v_ack(c_e_h_2, c_u, s1))),
% 11.55/11.75 inference(quant_inst,[status(thm)],[])).
% 11.55/11.75 tff(4805,plain,
% 11.55/11.75 ((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | (~node23(s1)) | m_user_v_ack(c_e_h_2, c_u, s1)),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4804, 4803])).
% 11.55/11.75 tff(4806,plain,
% 11.55/11.75 (~node23(s1)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4805, 4802, 4792])).
% 11.55/11.75 tff(4807,plain,
% 11.55/11.75 (((~![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))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4808,plain,
% 11.55/11.75 ((~![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))),
% 11.55/11.75 inference(quant_inst,[status(thm)],[])).
% 11.55/11.75 tff(4809,plain,
% 11.55/11.75 ((~![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)),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4808, 4807])).
% 11.55/11.75 tff(4810,plain,
% 11.55/11.75 (~m_user_v_ack(c_e_h_3, c_u, s1)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4809, 4458, 2502])).
% 11.55/11.75 tff(4811,plain,
% 11.55/11.75 (((~![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)))) | m_user_v_ack(c_e_h_3, c_u, s1) | (~node25(s1)))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4812,plain,
% 11.55/11.75 ((~![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)))),
% 11.55/11.75 inference(quant_inst,[status(thm)],[])).
% 11.55/11.75 tff(4813,plain,
% 11.55/11.75 ((~![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))),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4812, 4811])).
% 11.55/11.75 tff(4814,plain,
% 11.55/11.75 (~node25(s1)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4813, 4538, 4810])).
% 11.55/11.75 tff(4815,plain,
% 11.55/11.75 (((~![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))) | ((~node24(s1)) | m_user_v_ack(c_e_h_3, c_u, s1))) <=> ((~![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))) | (~node24(s1)) | m_user_v_ack(c_e_h_3, c_u, s1))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4816,plain,
% 11.55/11.75 ((~![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))) | ((~node24(s1)) | m_user_v_ack(c_e_h_3, c_u, s1))),
% 11.55/11.75 inference(quant_inst,[status(thm)],[])).
% 11.55/11.75 tff(4817,plain,
% 11.55/11.75 ((~![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))) | (~node24(s1)) | m_user_v_ack(c_e_h_3, c_u, s1)),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4816, 4815])).
% 11.55/11.75 tff(4818,plain,
% 11.55/11.75 (~node24(s1)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4817, 4494, 4810])).
% 11.55/11.75 tff(4819,plain,
% 11.55/11.75 (((~![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)))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4820,plain,
% 11.55/11.75 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s1) | node24(s1) | node25(s1) | (~node26(s1)))),
% 11.55/11.75 inference(quant_inst,[status(thm)],[])).
% 11.55/11.75 tff(4821,plain,
% 11.55/11.75 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s1) | node24(s1) | node25(s1) | (~node26(s1))),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4820, 4819])).
% 11.55/11.75 tff(4822,plain,
% 11.55/11.75 (node23(s1) | (~node26(s1))),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4821, 4553, 4818, 4814])).
% 11.55/11.75 tff(4823,plain,
% 11.55/11.75 (~node26(s1)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4822, 4806])).
% 11.55/11.75 tff(4824,plain,
% 11.55/11.75 (((~![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))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4825,plain,
% 11.55/11.75 ((~![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))),
% 11.55/11.75 inference(quant_inst,[status(thm)],[])).
% 11.55/11.75 tff(4826,plain,
% 11.55/11.75 ((~![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)),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4825, 4824])).
% 11.55/11.75 tff(4827,plain,
% 11.55/11.75 (~m_user_v_ack(c_e_h_1, c_u, s0)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4826, 4458, 4242])).
% 11.55/11.75 tff(4828,assumption,(node24(s0)), introduced(assumption)).
% 11.55/11.75 tff(4829,plain,
% 11.55/11.75 (((~![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)))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4830,plain,
% 11.55/11.75 ((~![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)))),
% 11.55/11.75 inference(quant_inst,[status(thm)],[])).
% 11.55/11.75 tff(4831,plain,
% 11.55/11.75 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s0) | (~node24(s0))),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4830, 4829])).
% 11.55/11.75 tff(4832,plain,
% 11.55/11.75 ($false),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4831, 4505, 4828, 4827])).
% 11.55/11.75 tff(4833,plain,(~node24(s0)), inference(lemma,lemma(discharge,[]))).
% 11.55/11.75 tff(4834,plain,
% 11.55/11.75 (((~![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))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4835,plain,
% 11.55/11.75 ((~![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))),
% 11.55/11.75 inference(quant_inst,[status(thm)],[])).
% 11.55/11.75 tff(4836,plain,
% 11.55/11.75 ((~![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)),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4835, 4834])).
% 11.55/11.75 tff(4837,plain,
% 11.55/11.75 (~m_user_v_ack(c_e_h_2, c_u, s0)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4836, 4458, 4783])).
% 11.55/11.75 tff(4838,plain,
% 11.55/11.75 (^[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))))),
% 11.55/11.75 inference(bind,[status(th)],[])).
% 11.55/11.75 tff(4839,plain,
% 11.55/11.75 (![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)))),
% 11.55/11.75 inference(quant_intro,[status(thm)],[4838])).
% 11.55/11.75 tff(4840,plain,
% 11.55/11.75 (![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)))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4841,axiom,(![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty5')).
% 11.55/11.75 tff(4842,plain,
% 11.55/11.75 (![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4841, 4840])).
% 11.55/11.75 tff(4843,plain,(
% 11.55/11.75 ![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))),
% 11.55/11.75 inference(skolemize,[status(sab)],[4842])).
% 11.55/11.75 tff(4844,plain,
% 11.55/11.75 (![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4843, 4839])).
% 11.55/11.75 tff(4845,plain,
% 11.55/11.75 (((~![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)))) | m_user_v_ack(c_e_h_2, c_u, s0) | (~node25(s0)))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4846,plain,
% 11.55/11.75 ((~![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)))),
% 11.55/11.75 inference(quant_inst,[status(thm)],[])).
% 11.55/11.75 tff(4847,plain,
% 11.55/11.75 ((~![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))),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4846, 4845])).
% 11.55/11.75 tff(4848,plain,
% 11.55/11.75 (~node25(s0)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4847, 4844, 4837])).
% 11.55/11.75 tff(4849,plain,
% 11.55/11.75 (((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | ((~node23(s0)) | m_user_v_ack(c_e_h_2, c_u, s0))) <=> ((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | (~node23(s0)) | m_user_v_ack(c_e_h_2, c_u, s0))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4850,plain,
% 11.55/11.75 ((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | ((~node23(s0)) | m_user_v_ack(c_e_h_2, c_u, s0))),
% 11.55/11.75 inference(quant_inst,[status(thm)],[])).
% 11.55/11.75 tff(4851,plain,
% 11.55/11.75 ((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | (~node23(s0)) | m_user_v_ack(c_e_h_2, c_u, s0)),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4850, 4849])).
% 11.55/11.75 tff(4852,plain,
% 11.55/11.75 (~node23(s0)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4851, 4802, 4837])).
% 11.55/11.75 tff(4853,plain,
% 11.55/11.75 (((~![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)))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4854,plain,
% 11.55/11.75 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s0) | node24(s0) | node25(s0) | (~node26(s0)))),
% 11.55/11.75 inference(quant_inst,[status(thm)],[])).
% 11.55/11.75 tff(4855,plain,
% 11.55/11.75 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s0) | node24(s0) | node25(s0) | (~node26(s0))),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4854, 4853])).
% 11.55/11.75 tff(4856,plain,
% 11.55/11.75 (node24(s0) | (~node26(s0))),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4855, 4553, 4852, 4848])).
% 11.55/11.75 tff(4857,plain,
% 11.55/11.75 (~node26(s0)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4856, 4833])).
% 11.55/11.75 tff(4858,plain,
% 11.55/11.75 (until27(s0) <=> until27(s0)),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4859,axiom,(until27(s0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty15')).
% 11.55/11.75 tff(4860,plain,
% 11.55/11.75 (until27(s0)),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4859, 4858])).
% 11.55/11.75 tff(4861,plain,
% 11.55/11.75 (^[X: $i] : refl(((~until27(X)) | node26(X) | xuntil28(X)) <=> ((~until27(X)) | node26(X) | xuntil28(X)))),
% 11.55/11.75 inference(bind,[status(th)],[])).
% 11.55/11.75 tff(4862,plain,
% 11.55/11.75 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X)) <=> ![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 11.55/11.75 inference(quant_intro,[status(thm)],[4861])).
% 11.55/11.75 tff(4863,plain,
% 11.55/11.75 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X)) <=> ![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4864,plain,
% 11.55/11.75 (^[X: $i] : rewrite(((node26(X) | xuntil28(X)) | (~until27(X))) <=> ((~until27(X)) | node26(X) | xuntil28(X)))),
% 11.55/11.75 inference(bind,[status(th)],[])).
% 11.55/11.75 tff(4865,plain,
% 11.55/11.75 (![X: $i] : ((node26(X) | xuntil28(X)) | (~until27(X))) <=> ![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 11.55/11.75 inference(quant_intro,[status(thm)],[4864])).
% 11.55/11.75 tff(4866,axiom,(![X: $i] : ((node26(X) | xuntil28(X)) | (~until27(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty8')).
% 11.55/11.75 tff(4867,plain,
% 11.55/11.75 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4866, 4865])).
% 11.55/11.75 tff(4868,plain,
% 11.55/11.75 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4867, 4863])).
% 11.55/11.75 tff(4869,plain,(
% 11.55/11.75 ![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 11.55/11.75 inference(skolemize,[status(sab)],[4868])).
% 11.55/11.75 tff(4870,plain,
% 11.55/11.75 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4869, 4862])).
% 11.55/11.75 tff(4871,plain,
% 11.55/11.75 (((~![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))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4872,plain,
% 11.55/11.75 (((~until27(s0)) | node26(s0) | xuntil28(s0)) <=> (xuntil28(s0) | (~until27(s0)) | node26(s0))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4873,plain,
% 11.55/11.75 (((~![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)))),
% 11.55/11.75 inference(monotonicity,[status(thm)],[4872])).
% 11.55/11.75 tff(4874,plain,
% 11.55/11.75 (((~![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))),
% 11.55/11.75 inference(transitivity,[status(thm)],[4873, 4871])).
% 11.55/11.75 tff(4875,plain,
% 11.55/11.75 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s0)) | node26(s0) | xuntil28(s0))),
% 11.55/11.75 inference(quant_inst,[status(thm)],[])).
% 11.55/11.75 tff(4876,plain,
% 11.55/11.75 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s0) | (~until27(s0)) | node26(s0)),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4875, 4874])).
% 11.55/11.75 tff(4877,plain,
% 11.55/11.75 (xuntil28(s0) | node26(s0)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4876, 4870, 4860])).
% 11.55/11.75 tff(4878,plain,
% 11.55/11.75 (xuntil28(s0)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4877, 4857])).
% 11.55/11.75 tff(4879,plain,
% 11.55/11.75 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)) <=> ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)))),
% 11.55/11.75 inference(bind,[status(th)],[])).
% 11.55/11.75 tff(4880,plain,
% 11.55/11.75 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 11.55/11.75 inference(quant_intro,[status(thm)],[4879])).
% 11.55/11.75 tff(4881,plain,
% 11.55/11.75 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4882,plain,
% 11.55/11.75 (^[Y: $i, X: $i] : rewrite(((until27(Y) | (~succ(X, Y))) | (~xuntil28(X))) <=> ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)))),
% 11.55/11.75 inference(bind,[status(th)],[])).
% 11.55/11.75 tff(4883,plain,
% 11.55/11.75 (![Y: $i, X: $i] : ((until27(Y) | (~succ(X, Y))) | (~xuntil28(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 11.55/11.75 inference(quant_intro,[status(thm)],[4882])).
% 11.55/11.75 tff(4884,axiom,(![Y: $i, X: $i] : ((until27(Y) | (~succ(X, Y))) | (~xuntil28(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty9')).
% 11.55/11.75 tff(4885,plain,
% 11.55/11.75 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4884, 4883])).
% 11.55/11.75 tff(4886,plain,
% 11.55/11.75 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4885, 4881])).
% 11.55/11.75 tff(4887,plain,(
% 11.55/11.75 ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 11.55/11.75 inference(skolemize,[status(sab)],[4886])).
% 11.55/11.75 tff(4888,plain,
% 11.55/11.75 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4887, 4880])).
% 11.55/11.75 tff(4889,plain,
% 11.55/11.75 (((~![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))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4890,plain,
% 11.55/11.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s0, s1)) | (~xuntil28(s0)) | until27(s1))),
% 11.55/11.75 inference(quant_inst,[status(thm)],[])).
% 11.55/11.75 tff(4891,plain,
% 11.55/11.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s0, s1)) | (~xuntil28(s0)) | until27(s1)),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4890, 4889])).
% 11.55/11.75 tff(4892,plain,
% 11.55/11.75 ((~xuntil28(s0)) | until27(s1)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4891, 96, 4888])).
% 11.55/11.75 tff(4893,plain,
% 11.55/11.75 (until27(s1)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4892, 4878])).
% 11.55/11.75 tff(4894,plain,
% 11.55/11.75 (((~![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)))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4895,plain,
% 11.55/11.75 (((~until27(s1)) | node26(s1) | xuntil28(s1)) <=> (xuntil28(s1) | node26(s1) | (~until27(s1)))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4896,plain,
% 11.55/11.75 (((~![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))))),
% 11.55/11.75 inference(monotonicity,[status(thm)],[4895])).
% 11.55/11.75 tff(4897,plain,
% 11.55/11.75 (((~![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)))),
% 11.55/11.75 inference(transitivity,[status(thm)],[4896, 4894])).
% 11.55/11.75 tff(4898,plain,
% 11.55/11.75 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s1)) | node26(s1) | xuntil28(s1))),
% 11.55/11.75 inference(quant_inst,[status(thm)],[])).
% 11.55/11.75 tff(4899,plain,
% 11.55/11.75 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s1) | node26(s1) | (~until27(s1))),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4898, 4897])).
% 11.55/11.75 tff(4900,plain,
% 11.55/11.75 (xuntil28(s1) | node26(s1)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4899, 4870, 4893])).
% 11.55/11.75 tff(4901,plain,
% 11.55/11.75 (xuntil28(s1)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4900, 4823])).
% 11.55/11.75 tff(4902,plain,
% 11.55/11.75 (((~![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))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4903,plain,
% 11.55/11.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s1, s2)) | (~xuntil28(s1)) | until27(s2))),
% 11.55/11.75 inference(quant_inst,[status(thm)],[])).
% 11.55/11.75 tff(4904,plain,
% 11.55/11.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s1, s2)) | (~xuntil28(s1)) | until27(s2)),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4903, 4902])).
% 11.55/11.75 tff(4905,plain,
% 11.55/11.75 ((~xuntil28(s1)) | until27(s2)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4904, 466, 4888])).
% 11.55/11.75 tff(4906,plain,
% 11.55/11.75 (until27(s2)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4905, 4901])).
% 11.55/11.75 tff(4907,plain,
% 11.55/11.75 (((~![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)))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4908,plain,
% 11.55/11.75 (((~until27(s2)) | node26(s2) | xuntil28(s2)) <=> (xuntil28(s2) | node26(s2) | (~until27(s2)))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4909,plain,
% 11.55/11.75 (((~![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))))),
% 11.55/11.75 inference(monotonicity,[status(thm)],[4908])).
% 11.55/11.75 tff(4910,plain,
% 11.55/11.75 (((~![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)))),
% 11.55/11.75 inference(transitivity,[status(thm)],[4909, 4907])).
% 11.55/11.75 tff(4911,plain,
% 11.55/11.75 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s2)) | node26(s2) | xuntil28(s2))),
% 11.55/11.75 inference(quant_inst,[status(thm)],[])).
% 11.55/11.75 tff(4912,plain,
% 11.55/11.75 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s2) | node26(s2) | (~until27(s2))),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4911, 4910])).
% 11.55/11.75 tff(4913,plain,
% 11.55/11.75 (xuntil28(s2) | node26(s2)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4912, 4870, 4906])).
% 11.55/11.75 tff(4914,plain,
% 11.55/11.75 (xuntil28(s2)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4913, 4741])).
% 11.55/11.75 tff(4915,plain,
% 11.55/11.75 (((~![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))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4916,plain,
% 11.55/11.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s2, s3)) | (~xuntil28(s2)) | until27(s3))),
% 11.55/11.75 inference(quant_inst,[status(thm)],[])).
% 11.55/11.75 tff(4917,plain,
% 11.55/11.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s2, s3)) | (~xuntil28(s2)) | until27(s3)),
% 11.55/11.75 inference(modus_ponens,[status(thm)],[4916, 4915])).
% 11.55/11.75 tff(4918,plain,
% 11.55/11.75 ((~xuntil28(s2)) | until27(s3)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4917, 600, 4888])).
% 11.55/11.75 tff(4919,plain,
% 11.55/11.75 (until27(s3)),
% 11.55/11.75 inference(unit_resolution,[status(thm)],[4918, 4914])).
% 11.55/11.75 tff(4920,assumption,(~node26(s3)), introduced(assumption)).
% 11.55/11.75 tff(4921,plain,
% 11.55/11.75 (((~![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))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.55/11.75 tff(4922,plain,
% 11.55/11.75 (((~until27(s3)) | node26(s3) | xuntil28(s3)) <=> (xuntil28(s3) | (~until27(s3)) | node26(s3))),
% 11.55/11.75 inference(rewrite,[status(thm)],[])).
% 11.61/11.75 tff(4923,plain,
% 11.61/11.75 (((~![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)))),
% 11.61/11.75 inference(monotonicity,[status(thm)],[4922])).
% 11.61/11.75 tff(4924,plain,
% 11.61/11.75 (((~![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))),
% 11.61/11.75 inference(transitivity,[status(thm)],[4923, 4921])).
% 11.61/11.75 tff(4925,plain,
% 11.61/11.75 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s3)) | node26(s3) | xuntil28(s3))),
% 11.61/11.75 inference(quant_inst,[status(thm)],[])).
% 11.61/11.75 tff(4926,plain,
% 11.61/11.75 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s3) | (~until27(s3)) | node26(s3)),
% 11.61/11.75 inference(modus_ponens,[status(thm)],[4925, 4924])).
% 11.61/11.75 tff(4927,plain,
% 11.61/11.75 (xuntil28(s3) | (~until27(s3))),
% 11.61/11.75 inference(unit_resolution,[status(thm)],[4926, 4870, 4920])).
% 11.61/11.75 tff(4928,plain,
% 11.61/11.75 (xuntil28(s3)),
% 11.61/11.75 inference(unit_resolution,[status(thm)],[4927, 4919])).
% 11.61/11.75 tff(4929,plain,
% 11.61/11.75 (((~![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))),
% 11.61/11.75 inference(rewrite,[status(thm)],[])).
% 11.61/11.75 tff(4930,plain,
% 11.61/11.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s3, s4)) | (~xuntil28(s3)) | until27(s4))),
% 11.61/11.75 inference(quant_inst,[status(thm)],[])).
% 11.61/11.75 tff(4931,plain,
% 11.61/11.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s3, s4)) | (~xuntil28(s3)) | until27(s4)),
% 11.61/11.75 inference(modus_ponens,[status(thm)],[4930, 4929])).
% 11.61/11.75 tff(4932,plain,
% 11.61/11.75 ((~xuntil28(s3)) | until27(s4)),
% 11.61/11.75 inference(unit_resolution,[status(thm)],[4931, 1088, 4888])).
% 11.61/11.75 tff(4933,plain,
% 11.61/11.75 (until27(s4)),
% 11.61/11.75 inference(unit_resolution,[status(thm)],[4932, 4928])).
% 11.61/11.75 tff(4934,plain,
% 11.61/11.75 (((~![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))),
% 11.61/11.75 inference(rewrite,[status(thm)],[])).
% 11.61/11.75 tff(4935,plain,
% 11.61/11.75 (((~until27(s4)) | node26(s4) | xuntil28(s4)) <=> (xuntil28(s4) | (~until27(s4)) | node26(s4))),
% 11.61/11.75 inference(rewrite,[status(thm)],[])).
% 11.61/11.75 tff(4936,plain,
% 11.61/11.75 (((~![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)))),
% 11.61/11.75 inference(monotonicity,[status(thm)],[4935])).
% 11.61/11.75 tff(4937,plain,
% 11.61/11.75 (((~![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))),
% 11.61/11.75 inference(transitivity,[status(thm)],[4936, 4934])).
% 11.61/11.75 tff(4938,plain,
% 11.61/11.75 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s4)) | node26(s4) | xuntil28(s4))),
% 11.61/11.75 inference(quant_inst,[status(thm)],[])).
% 11.61/11.75 tff(4939,plain,
% 11.61/11.75 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s4) | (~until27(s4)) | node26(s4)),
% 11.61/11.75 inference(modus_ponens,[status(thm)],[4938, 4937])).
% 11.61/11.75 tff(4940,plain,
% 11.61/11.75 (xuntil28(s4) | (~until27(s4))),
% 11.61/11.75 inference(unit_resolution,[status(thm)],[4939, 4870, 4704])).
% 11.61/11.75 tff(4941,plain,
% 11.61/11.75 (xuntil28(s4)),
% 11.61/11.75 inference(unit_resolution,[status(thm)],[4940, 4933])).
% 11.61/11.75 tff(4942,plain,
% 11.61/11.75 (((~![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))),
% 11.61/11.75 inference(rewrite,[status(thm)],[])).
% 11.61/11.75 tff(4943,plain,
% 11.61/11.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s4, s5)) | (~xuntil28(s4)) | until27(s5))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(4944,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s4, s5)) | (~xuntil28(s4)) | until27(s5)),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[4943, 4942])).
% 11.61/11.76 tff(4945,plain,
% 11.61/11.76 ((~xuntil28(s4)) | until27(s5)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[4944, 1538, 4888])).
% 11.61/11.76 tff(4946,plain,
% 11.61/11.76 (until27(s5)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[4945, 4941])).
% 11.61/11.76 tff(4947,plain,
% 11.61/11.76 (((~![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))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(4948,plain,
% 11.61/11.76 (((~until27(s5)) | node26(s5) | xuntil28(s5)) <=> (xuntil28(s5) | (~until27(s5)) | node26(s5))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(4949,plain,
% 11.61/11.76 (((~![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)))),
% 11.61/11.76 inference(monotonicity,[status(thm)],[4948])).
% 11.61/11.76 tff(4950,plain,
% 11.61/11.76 (((~![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))),
% 11.61/11.76 inference(transitivity,[status(thm)],[4949, 4947])).
% 11.61/11.76 tff(4951,plain,
% 11.61/11.76 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s5)) | node26(s5) | xuntil28(s5))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(4952,plain,
% 11.61/11.76 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s5) | (~until27(s5)) | node26(s5)),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[4951, 4950])).
% 11.61/11.76 tff(4953,plain,
% 11.61/11.76 (xuntil28(s5) | (~until27(s5))),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[4952, 4870, 4703])).
% 11.61/11.76 tff(4954,plain,
% 11.61/11.76 (xuntil28(s5)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[4953, 4946])).
% 11.61/11.76 tff(4955,plain,
% 11.61/11.76 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s5, s6)) | (~xuntil28(s5)) | until27(s6))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s5, s6)) | (~xuntil28(s5)) | until27(s6))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(4956,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s5, s6)) | (~xuntil28(s5)) | until27(s6))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(4957,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s5, s6)) | (~xuntil28(s5)) | until27(s6)),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[4956, 4955])).
% 11.61/11.76 tff(4958,plain,
% 11.61/11.76 ((~xuntil28(s5)) | until27(s6)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[4957, 2344, 4888])).
% 11.61/11.76 tff(4959,plain,
% 11.61/11.76 (until27(s6)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[4958, 4954])).
% 11.61/11.76 tff(4960,plain,
% 11.61/11.76 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s6) | node26(s6) | (~until27(s6)))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s6) | node26(s6) | (~until27(s6)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(4961,plain,
% 11.61/11.76 (((~until27(s6)) | node26(s6) | xuntil28(s6)) <=> (xuntil28(s6) | node26(s6) | (~until27(s6)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(4962,plain,
% 11.61/11.76 (((~![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))))),
% 11.61/11.76 inference(monotonicity,[status(thm)],[4961])).
% 11.61/11.76 tff(4963,plain,
% 11.61/11.76 (((~![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)))),
% 11.61/11.76 inference(transitivity,[status(thm)],[4962, 4960])).
% 11.61/11.76 tff(4964,plain,
% 11.61/11.76 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s6)) | node26(s6) | xuntil28(s6))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(4965,plain,
% 11.61/11.76 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s6) | node26(s6) | (~until27(s6))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[4964, 4963])).
% 11.61/11.76 tff(4966,plain,
% 11.61/11.76 (xuntil28(s6) | node26(s6)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[4965, 4870, 4959])).
% 11.61/11.76 tff(4967,plain,
% 11.61/11.76 (xuntil28(s6)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[4966, 4639])).
% 11.61/11.76 tff(4968,plain,
% 11.61/11.76 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s6, s7)) | (~xuntil28(s6)) | until27(s7))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s6, s7)) | (~xuntil28(s6)) | until27(s7))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(4969,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s6, s7)) | (~xuntil28(s6)) | until27(s7))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(4970,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s6, s7)) | (~xuntil28(s6)) | until27(s7)),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[4969, 4968])).
% 11.61/11.76 tff(4971,plain,
% 11.61/11.76 ((~xuntil28(s6)) | until27(s7)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[4970, 2645, 4888])).
% 11.61/11.76 tff(4972,plain,
% 11.61/11.76 (until27(s7)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[4971, 4967])).
% 11.61/11.76 tff(4973,plain,
% 11.61/11.76 (((~![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)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(4974,plain,
% 11.61/11.76 (((~until27(s7)) | node26(s7) | xuntil28(s7)) <=> (xuntil28(s7) | node26(s7) | (~until27(s7)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(4975,plain,
% 11.61/11.76 (((~![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))))),
% 11.61/11.76 inference(monotonicity,[status(thm)],[4974])).
% 11.61/11.76 tff(4976,plain,
% 11.61/11.76 (((~![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)))),
% 11.61/11.76 inference(transitivity,[status(thm)],[4975, 4973])).
% 11.61/11.76 tff(4977,plain,
% 11.61/11.76 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s7)) | node26(s7) | xuntil28(s7))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(4978,plain,
% 11.61/11.76 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s7) | node26(s7) | (~until27(s7))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[4977, 4976])).
% 11.61/11.76 tff(4979,plain,
% 11.61/11.76 (xuntil28(s7) | node26(s7)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[4978, 4870, 4972])).
% 11.61/11.76 tff(4980,plain,
% 11.61/11.76 (xuntil28(s7)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[4979, 4652])).
% 11.61/11.76 tff(4981,plain,
% 11.61/11.76 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s7, s8)) | (~xuntil28(s7)) | until27(s8))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s7, s8)) | (~xuntil28(s7)) | until27(s8))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(4982,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s7, s8)) | (~xuntil28(s7)) | until27(s8))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(4983,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s7, s8)) | (~xuntil28(s7)) | until27(s8)),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[4982, 4981])).
% 11.61/11.76 tff(4984,plain,
% 11.61/11.76 ((~xuntil28(s7)) | until27(s8)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[4983, 2665, 4888])).
% 11.61/11.76 tff(4985,plain,
% 11.61/11.76 (until27(s8)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[4984, 4980])).
% 11.61/11.76 tff(4986,plain,
% 11.61/11.76 (((~![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)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(4987,plain,
% 11.61/11.76 (((~until27(s8)) | node26(s8) | xuntil28(s8)) <=> (xuntil28(s8) | node26(s8) | (~until27(s8)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(4988,plain,
% 11.61/11.76 (((~![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))))),
% 11.61/11.76 inference(monotonicity,[status(thm)],[4987])).
% 11.61/11.76 tff(4989,plain,
% 11.61/11.76 (((~![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)))),
% 11.61/11.76 inference(transitivity,[status(thm)],[4988, 4986])).
% 11.61/11.76 tff(4990,plain,
% 11.61/11.76 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s8)) | node26(s8) | xuntil28(s8))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(4991,plain,
% 11.61/11.76 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s8) | node26(s8) | (~until27(s8))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[4990, 4989])).
% 11.61/11.76 tff(4992,plain,
% 11.61/11.76 (xuntil28(s8) | (~until27(s8))),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[4991, 4870, 4653])).
% 11.61/11.76 tff(4993,plain,
% 11.61/11.76 (xuntil28(s8)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[4992, 4985])).
% 11.61/11.76 tff(4994,plain,
% 11.61/11.76 (succ(s8, s9) <=> succ(s8, s9)),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(4995,axiom,(succ(s8, s9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound9')).
% 11.61/11.76 tff(4996,plain,
% 11.61/11.76 (succ(s8, s9)),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[4995, 4994])).
% 11.61/11.76 tff(4997,plain,
% 11.61/11.76 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s8, s9)) | (~xuntil28(s8)) | until27(s9))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s8, s9)) | (~xuntil28(s8)) | until27(s9))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(4998,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s8, s9)) | (~xuntil28(s8)) | until27(s9))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(4999,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s8, s9)) | (~xuntil28(s8)) | until27(s9)),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[4998, 4997])).
% 11.61/11.76 tff(5000,plain,
% 11.61/11.76 ((~xuntil28(s8)) | until27(s9)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[4999, 4996, 4888])).
% 11.61/11.76 tff(5001,plain,
% 11.61/11.76 (until27(s9)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5000, 4993])).
% 11.61/11.76 tff(5002,plain,
% 11.61/11.76 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s9) | node26(s9) | (~until27(s9)))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s9) | node26(s9) | (~until27(s9)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5003,plain,
% 11.61/11.76 (((~until27(s9)) | node26(s9) | xuntil28(s9)) <=> (xuntil28(s9) | node26(s9) | (~until27(s9)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5004,plain,
% 11.61/11.76 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s9)) | node26(s9) | xuntil28(s9))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s9) | node26(s9) | (~until27(s9))))),
% 11.61/11.76 inference(monotonicity,[status(thm)],[5003])).
% 11.61/11.76 tff(5005,plain,
% 11.61/11.76 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s9)) | node26(s9) | xuntil28(s9))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s9) | node26(s9) | (~until27(s9)))),
% 11.61/11.76 inference(transitivity,[status(thm)],[5004, 5002])).
% 11.61/11.76 tff(5006,plain,
% 11.61/11.76 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s9)) | node26(s9) | xuntil28(s9))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(5007,plain,
% 11.61/11.76 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s9) | node26(s9) | (~until27(s9))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5006, 5005])).
% 11.61/11.76 tff(5008,plain,
% 11.61/11.76 (xuntil28(s9) | node26(s9)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5007, 4870, 5001])).
% 11.61/11.76 tff(5009,plain,
% 11.61/11.76 (xuntil28(s9)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5008, 4640])).
% 11.61/11.76 tff(5010,plain,
% 11.61/11.76 (^[X: $i] : refl(((~last(X)) | (~xuntil2p30(X))) <=> ((~last(X)) | (~xuntil2p30(X))))),
% 11.61/11.76 inference(bind,[status(th)],[])).
% 11.61/11.76 tff(5011,plain,
% 11.61/11.76 (![X: $i] : ((~last(X)) | (~xuntil2p30(X))) <=> ![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 11.61/11.76 inference(quant_intro,[status(thm)],[5010])).
% 11.61/11.76 tff(5012,plain,
% 11.61/11.76 (![X: $i] : ((~last(X)) | (~xuntil2p30(X))) <=> ![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5013,axiom,(![X: $i] : ((~last(X)) | (~xuntil2p30(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty14')).
% 11.61/11.76 tff(5014,plain,
% 11.61/11.76 (![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5013, 5012])).
% 11.61/11.76 tff(5015,plain,(
% 11.61/11.76 ![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 11.61/11.76 inference(skolemize,[status(sab)],[5014])).
% 11.61/11.76 tff(5016,plain,
% 11.61/11.76 (![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5015, 5011])).
% 11.61/11.76 tff(5017,plain,
% 11.61/11.76 (last(s9) <=> last(s9)),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5018,axiom,(last(s9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound10')).
% 11.61/11.76 tff(5019,plain,
% 11.61/11.76 (last(s9)),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5018, 5017])).
% 11.61/11.76 tff(5020,plain,
% 11.61/11.76 (((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | ((~last(s9)) | (~xuntil2p30(s9)))) <=> ((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | (~last(s9)) | (~xuntil2p30(s9)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5021,plain,
% 11.61/11.76 ((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | ((~last(s9)) | (~xuntil2p30(s9)))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(5022,plain,
% 11.61/11.76 ((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | (~last(s9)) | (~xuntil2p30(s9))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5021, 5020])).
% 11.61/11.76 tff(5023,plain,
% 11.61/11.76 (~xuntil2p30(s9)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5022, 5019, 5016])).
% 11.61/11.76 tff(5024,plain,
% 11.61/11.76 (^[X: $i] : refl((node26(X) | xuntil2p30(X) | (~until2p29(X))) <=> (node26(X) | xuntil2p30(X) | (~until2p29(X))))),
% 11.61/11.76 inference(bind,[status(th)],[])).
% 11.61/11.76 tff(5025,plain,
% 11.61/11.76 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X))) <=> ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 11.61/11.76 inference(quant_intro,[status(thm)],[5024])).
% 11.61/11.76 tff(5026,plain,
% 11.61/11.76 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X))) <=> ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5027,plain,
% 11.61/11.76 (^[X: $i] : rewrite(((node26(X) | xuntil2p30(X)) | (~until2p29(X))) <=> (node26(X) | xuntil2p30(X) | (~until2p29(X))))),
% 11.61/11.76 inference(bind,[status(th)],[])).
% 11.61/11.76 tff(5028,plain,
% 11.61/11.76 (![X: $i] : ((node26(X) | xuntil2p30(X)) | (~until2p29(X))) <=> ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 11.61/11.76 inference(quant_intro,[status(thm)],[5027])).
% 11.61/11.76 tff(5029,axiom,(![X: $i] : ((node26(X) | xuntil2p30(X)) | (~until2p29(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty12')).
% 11.61/11.76 tff(5030,plain,
% 11.61/11.76 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5029, 5028])).
% 11.61/11.76 tff(5031,plain,
% 11.61/11.76 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5030, 5026])).
% 11.61/11.76 tff(5032,plain,(
% 11.61/11.76 ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 11.61/11.76 inference(skolemize,[status(sab)],[5031])).
% 11.61/11.76 tff(5033,plain,
% 11.61/11.76 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5032, 5025])).
% 11.61/11.76 tff(5034,plain,
% 11.61/11.76 (((~![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)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5035,plain,
% 11.61/11.76 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s9) | xuntil2p30(s9) | (~until2p29(s9)))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(5036,plain,
% 11.61/11.76 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s9) | xuntil2p30(s9) | (~until2p29(s9))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5035, 5034])).
% 11.61/11.76 tff(5037,plain,
% 11.61/11.76 (node26(s9) | (~until2p29(s9))),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5036, 5033, 5023])).
% 11.61/11.76 tff(5038,plain,
% 11.61/11.76 (~until2p29(s9)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5037, 4640])).
% 11.61/11.76 tff(5039,plain,
% 11.61/11.76 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))) <=> ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))))),
% 11.61/11.76 inference(bind,[status(th)],[])).
% 11.61/11.76 tff(5040,plain,
% 11.61/11.76 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 11.61/11.76 inference(quant_intro,[status(thm)],[5039])).
% 11.61/11.76 tff(5041,plain,
% 11.61/11.76 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5042,plain,
% 11.61/11.76 (^[Y: $i, X: $i] : rewrite(((until2p29(Y) | (~succ(X, Y))) | (~xuntil2p30(X))) <=> ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))))),
% 11.61/11.76 inference(bind,[status(th)],[])).
% 11.61/11.76 tff(5043,plain,
% 11.61/11.76 (![Y: $i, X: $i] : ((until2p29(Y) | (~succ(X, Y))) | (~xuntil2p30(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 11.61/11.76 inference(quant_intro,[status(thm)],[5042])).
% 11.61/11.76 tff(5044,axiom,(![Y: $i, X: $i] : ((until2p29(Y) | (~succ(X, Y))) | (~xuntil2p30(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty13')).
% 11.61/11.76 tff(5045,plain,
% 11.61/11.76 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5044, 5043])).
% 11.61/11.76 tff(5046,plain,
% 11.61/11.76 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5045, 5041])).
% 11.61/11.76 tff(5047,plain,(
% 11.61/11.76 ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 11.61/11.76 inference(skolemize,[status(sab)],[5046])).
% 11.61/11.76 tff(5048,plain,
% 11.61/11.76 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5047, 5040])).
% 11.61/11.76 tff(5049,plain,
% 11.61/11.76 (((~![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)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5050,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s8, s9)) | until2p29(s9) | (~xuntil2p30(s8)))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(5051,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s8, s9)) | until2p29(s9) | (~xuntil2p30(s8))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5050, 5049])).
% 11.61/11.76 tff(5052,plain,
% 11.61/11.76 (until2p29(s9) | (~xuntil2p30(s8))),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5051, 4996, 5048])).
% 11.61/11.76 tff(5053,plain,
% 11.61/11.76 (~xuntil2p30(s8)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5052, 5038])).
% 11.61/11.76 tff(5054,plain,
% 11.61/11.76 (((~![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)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5055,plain,
% 11.61/11.76 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s8) | xuntil2p30(s8) | (~until2p29(s8)))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(5056,plain,
% 11.61/11.76 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s8) | xuntil2p30(s8) | (~until2p29(s8))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5055, 5054])).
% 11.61/11.76 tff(5057,plain,
% 11.61/11.76 (xuntil2p30(s8) | (~until2p29(s8))),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5056, 5033, 4653])).
% 11.61/11.76 tff(5058,plain,
% 11.61/11.76 (~until2p29(s8)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5057, 5053])).
% 11.61/11.76 tff(5059,plain,
% 11.61/11.76 (^[Y: $i, X: $i] : refl(((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y)) <=> ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y)))),
% 11.61/11.76 inference(bind,[status(th)],[])).
% 11.61/11.76 tff(5060,plain,
% 11.61/11.76 (![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))),
% 11.61/11.76 inference(quant_intro,[status(thm)],[5059])).
% 11.61/11.76 tff(5061,plain,
% 11.61/11.76 (![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))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5062,plain,
% 11.61/11.76 (^[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))))),
% 11.61/11.76 inference(bind,[status(th)],[])).
% 11.61/11.76 tff(5063,plain,
% 11.61/11.76 (![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))),
% 11.61/11.76 inference(quant_intro,[status(thm)],[5062])).
% 11.61/11.76 tff(5064,axiom,(![Y: $i, X: $i] : (((until2p29(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil28(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty11')).
% 11.61/11.76 tff(5065,plain,
% 11.61/11.76 (![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5064, 5063])).
% 11.61/11.76 tff(5066,plain,
% 11.61/11.76 (![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5065, 5061])).
% 11.61/11.76 tff(5067,plain,(
% 11.61/11.76 ![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 11.61/11.76 inference(skolemize,[status(sab)],[5066])).
% 11.61/11.76 tff(5068,plain,
% 11.61/11.76 (![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5067, 5060])).
% 11.61/11.76 tff(5069,plain,
% 11.61/11.76 (((~![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)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5070,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s7, s8)) | until2p29(s8) | (~xuntil2p30(s7)))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(5071,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s7, s8)) | until2p29(s8) | (~xuntil2p30(s7))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5070, 5069])).
% 11.61/11.76 tff(5072,plain,
% 11.61/11.76 (until2p29(s8) | (~xuntil2p30(s7))),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5071, 2665, 5048])).
% 11.61/11.76 tff(5073,plain,
% 11.61/11.76 (~xuntil2p30(s7)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5072, 5058])).
% 11.61/11.76 tff(5074,plain,
% 11.61/11.76 (((~![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)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5075,plain,
% 11.61/11.76 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s7) | xuntil2p30(s7) | (~until2p29(s7)))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(5076,plain,
% 11.61/11.76 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s7) | xuntil2p30(s7) | (~until2p29(s7))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5075, 5074])).
% 11.61/11.76 tff(5077,plain,
% 11.61/11.76 (xuntil2p30(s7) | (~until2p29(s7))),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5076, 5033, 4652])).
% 11.61/11.76 tff(5078,plain,
% 11.61/11.76 (~until2p29(s7)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5077, 5073])).
% 11.61/11.76 tff(5079,assumption,(xuntil28(s9)), introduced(assumption)).
% 11.61/11.76 tff(5080,assumption,(~until2p29(s7)), introduced(assumption)).
% 11.61/11.76 tff(5081,assumption,(trans(s9, s7)), introduced(assumption)).
% 11.61/11.76 tff(5082,plain,
% 11.61/11.76 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s7) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s7)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s7) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s7)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5083,plain,
% 11.61/11.76 (((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s7)) | until2p29(s7)) <=> (until2p29(s7) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s7)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5084,plain,
% 11.61/11.76 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s7)) | until2p29(s7))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s7) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s7))))),
% 11.61/11.76 inference(monotonicity,[status(thm)],[5083])).
% 11.61/11.76 tff(5085,plain,
% 11.61/11.76 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s7)) | until2p29(s7))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s7) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s7)))),
% 11.61/11.76 inference(transitivity,[status(thm)],[5084, 5082])).
% 11.61/11.76 tff(5086,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s7)) | until2p29(s7))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(5087,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s7) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s7))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5086, 5085])).
% 11.61/11.76 tff(5088,plain,
% 11.61/11.76 ($false),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5087, 5019, 5081, 5068, 5080, 5079])).
% 11.61/11.76 tff(5089,plain,((~trans(s9, s7)) | until2p29(s7) | (~xuntil28(s9))), inference(lemma,lemma(discharge,[]))).
% 11.61/11.76 tff(5090,plain,
% 11.61/11.76 (~trans(s9, s7)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5089, 5078, 5009])).
% 11.61/11.76 tff(5091,plain,
% 11.61/11.76 (((~![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)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5092,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s6, s7)) | until2p29(s7) | (~xuntil2p30(s6)))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(5093,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s6, s7)) | until2p29(s7) | (~xuntil2p30(s6))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5092, 5091])).
% 11.61/11.76 tff(5094,plain,
% 11.61/11.76 (until2p29(s7) | (~xuntil2p30(s6))),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5093, 2645, 5048])).
% 11.61/11.76 tff(5095,plain,
% 11.61/11.76 (~xuntil2p30(s6)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5094, 5078])).
% 11.61/11.76 tff(5096,plain,
% 11.61/11.76 (((~![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)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5097,plain,
% 11.61/11.76 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s6) | xuntil2p30(s6) | (~until2p29(s6)))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(5098,plain,
% 11.61/11.76 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s6) | xuntil2p30(s6) | (~until2p29(s6))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5097, 5096])).
% 11.61/11.76 tff(5099,plain,
% 11.61/11.76 (xuntil2p30(s6) | (~until2p29(s6))),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5098, 5033, 4639])).
% 11.61/11.76 tff(5100,plain,
% 11.61/11.76 (~until2p29(s6)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5099, 5095])).
% 11.61/11.76 tff(5101,assumption,(~until2p29(s6)), introduced(assumption)).
% 11.61/11.76 tff(5102,assumption,(trans(s9, s6)), introduced(assumption)).
% 11.61/11.76 tff(5103,plain,
% 11.61/11.76 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s6) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s6)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s6) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s6)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5104,plain,
% 11.61/11.76 (((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s6)) | until2p29(s6)) <=> (until2p29(s6) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s6)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5105,plain,
% 11.61/11.76 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s6)) | until2p29(s6))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s6) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s6))))),
% 11.61/11.76 inference(monotonicity,[status(thm)],[5104])).
% 11.61/11.76 tff(5106,plain,
% 11.61/11.76 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s6)) | until2p29(s6))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s6) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s6)))),
% 11.61/11.76 inference(transitivity,[status(thm)],[5105, 5103])).
% 11.61/11.76 tff(5107,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s6)) | until2p29(s6))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(5108,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s6) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s6))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5107, 5106])).
% 11.61/11.76 tff(5109,plain,
% 11.61/11.76 ($false),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5108, 5019, 5102, 5068, 5101, 5079])).
% 11.61/11.76 tff(5110,plain,((~trans(s9, s6)) | until2p29(s6) | (~xuntil28(s9))), inference(lemma,lemma(discharge,[]))).
% 11.61/11.76 tff(5111,plain,
% 11.61/11.76 (~trans(s9, s6)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5110, 5100, 5009])).
% 11.61/11.76 tff(5112,plain,
% 11.61/11.76 (((~![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)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5113,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s5, s6)) | until2p29(s6) | (~xuntil2p30(s5)))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(5114,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s5, s6)) | until2p29(s6) | (~xuntil2p30(s5))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5113, 5112])).
% 11.61/11.76 tff(5115,plain,
% 11.61/11.76 (until2p29(s6) | (~xuntil2p30(s5))),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5114, 2344, 5048])).
% 11.61/11.76 tff(5116,plain,
% 11.61/11.76 (~xuntil2p30(s5)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5115, 5100])).
% 11.61/11.76 tff(5117,plain,
% 11.61/11.76 (((~![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)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5118,plain,
% 11.61/11.76 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s5) | xuntil2p30(s5) | (~until2p29(s5)))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(5119,plain,
% 11.61/11.76 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s5) | xuntil2p30(s5) | (~until2p29(s5))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5118, 5117])).
% 11.61/11.76 tff(5120,plain,
% 11.61/11.76 (xuntil2p30(s5) | (~until2p29(s5))),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5119, 5033, 4703])).
% 11.61/11.76 tff(5121,plain,
% 11.61/11.76 (~until2p29(s5)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5120, 5116])).
% 11.61/11.76 tff(5122,plain,
% 11.61/11.76 (((~![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)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5123,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s4, s5)) | until2p29(s5) | (~xuntil2p30(s4)))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(5124,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s4, s5)) | until2p29(s5) | (~xuntil2p30(s4))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5123, 5122])).
% 11.61/11.76 tff(5125,plain,
% 11.61/11.76 (until2p29(s5) | (~xuntil2p30(s4))),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5124, 1538, 5048])).
% 11.61/11.76 tff(5126,plain,
% 11.61/11.76 (~xuntil2p30(s4)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5125, 5121])).
% 11.61/11.76 tff(5127,plain,
% 11.61/11.76 (((~![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)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5128,plain,
% 11.61/11.76 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s4) | xuntil2p30(s4) | (~until2p29(s4)))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(5129,plain,
% 11.61/11.76 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s4) | xuntil2p30(s4) | (~until2p29(s4))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5128, 5127])).
% 11.61/11.76 tff(5130,plain,
% 11.61/11.76 (xuntil2p30(s4) | (~until2p29(s4))),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5129, 5033, 4704])).
% 11.61/11.76 tff(5131,plain,
% 11.61/11.76 (~until2p29(s4)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5130, 5126])).
% 11.61/11.76 tff(5132,plain,
% 11.61/11.76 (((~![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)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5133,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s3, s4)) | until2p29(s4) | (~xuntil2p30(s3)))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(5134,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s3, s4)) | until2p29(s4) | (~xuntil2p30(s3))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5133, 5132])).
% 11.61/11.76 tff(5135,plain,
% 11.61/11.76 (until2p29(s4) | (~xuntil2p30(s3))),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5134, 1088, 5048])).
% 11.61/11.76 tff(5136,plain,
% 11.61/11.76 (~xuntil2p30(s3)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5135, 5131])).
% 11.61/11.76 tff(5137,plain,
% 11.61/11.76 (((~![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)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5138,plain,
% 11.61/11.76 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s3) | xuntil2p30(s3) | (~until2p29(s3)))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(5139,plain,
% 11.61/11.76 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s3) | xuntil2p30(s3) | (~until2p29(s3))),
% 11.61/11.76 inference(modus_ponens,[status(thm)],[5138, 5137])).
% 11.61/11.76 tff(5140,plain,
% 11.61/11.76 (xuntil2p30(s3) | (~until2p29(s3))),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5139, 5033, 4920])).
% 11.61/11.76 tff(5141,plain,
% 11.61/11.76 (~until2p29(s3)),
% 11.61/11.76 inference(unit_resolution,[status(thm)],[5140, 5136])).
% 11.61/11.76 tff(5142,plain,
% 11.61/11.76 (((~![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)))),
% 11.61/11.76 inference(rewrite,[status(thm)],[])).
% 11.61/11.76 tff(5143,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s2, s3)) | until2p29(s3) | (~xuntil2p30(s2)))),
% 11.61/11.76 inference(quant_inst,[status(thm)],[])).
% 11.61/11.76 tff(5144,plain,
% 11.61/11.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s2, s3)) | until2p29(s3) | (~xuntil2p30(s2))),
% 11.61/11.77 inference(modus_ponens,[status(thm)],[5143, 5142])).
% 11.61/11.77 tff(5145,plain,
% 11.61/11.77 (until2p29(s3) | (~xuntil2p30(s2))),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5144, 600, 5048])).
% 11.61/11.77 tff(5146,plain,
% 11.61/11.77 (~xuntil2p30(s2)),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5145, 5141])).
% 11.61/11.77 tff(5147,plain,
% 11.61/11.77 (((~![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)))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5148,plain,
% 11.61/11.77 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s2) | xuntil2p30(s2) | (~until2p29(s2)))),
% 11.61/11.77 inference(quant_inst,[status(thm)],[])).
% 11.61/11.77 tff(5149,plain,
% 11.61/11.77 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s2) | xuntil2p30(s2) | (~until2p29(s2))),
% 11.61/11.77 inference(modus_ponens,[status(thm)],[5148, 5147])).
% 11.61/11.77 tff(5150,plain,
% 11.61/11.77 (xuntil2p30(s2) | (~until2p29(s2))),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5149, 5033, 4741])).
% 11.61/11.77 tff(5151,plain,
% 11.61/11.77 (~until2p29(s2)),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5150, 5146])).
% 11.61/11.77 tff(5152,assumption,(~until2p29(s2)), introduced(assumption)).
% 11.61/11.77 tff(5153,assumption,(trans(s9, s2)), introduced(assumption)).
% 11.61/11.77 tff(5154,plain,
% 11.61/11.77 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s2) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s2)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s2) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s2)))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5155,plain,
% 11.61/11.77 (((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s2)) | until2p29(s2)) <=> (until2p29(s2) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s2)))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5156,plain,
% 11.61/11.77 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s2)) | until2p29(s2))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s2) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s2))))),
% 11.61/11.77 inference(monotonicity,[status(thm)],[5155])).
% 11.61/11.77 tff(5157,plain,
% 11.61/11.77 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s2)) | until2p29(s2))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s2) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s2)))),
% 11.61/11.77 inference(transitivity,[status(thm)],[5156, 5154])).
% 11.61/11.77 tff(5158,plain,
% 11.61/11.77 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s2)) | until2p29(s2))),
% 11.61/11.77 inference(quant_inst,[status(thm)],[])).
% 11.61/11.77 tff(5159,plain,
% 11.61/11.77 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s2) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s2))),
% 11.61/11.77 inference(modus_ponens,[status(thm)],[5158, 5157])).
% 11.61/11.77 tff(5160,plain,
% 11.61/11.77 ($false),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5159, 5019, 5153, 5068, 5152, 5079])).
% 11.61/11.77 tff(5161,plain,((~trans(s9, s2)) | until2p29(s2) | (~xuntil28(s9))), inference(lemma,lemma(discharge,[]))).
% 11.61/11.77 tff(5162,plain,
% 11.61/11.77 (~trans(s9, s2)),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5161, 5151, 5009])).
% 11.61/11.77 tff(5163,plain,
% 11.61/11.77 (((~![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)))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5164,plain,
% 11.61/11.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s1, s2)) | until2p29(s2) | (~xuntil2p30(s1)))),
% 11.61/11.77 inference(quant_inst,[status(thm)],[])).
% 11.61/11.77 tff(5165,plain,
% 11.61/11.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s1, s2)) | until2p29(s2) | (~xuntil2p30(s1))),
% 11.61/11.77 inference(modus_ponens,[status(thm)],[5164, 5163])).
% 11.61/11.77 tff(5166,plain,
% 11.61/11.77 (until2p29(s2) | (~xuntil2p30(s1))),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5165, 466, 5048])).
% 11.61/11.77 tff(5167,plain,
% 11.61/11.77 (~xuntil2p30(s1)),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5166, 5151])).
% 11.61/11.77 tff(5168,plain,
% 11.61/11.77 (((~![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)))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5169,plain,
% 11.61/11.77 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s1) | xuntil2p30(s1) | (~until2p29(s1)))),
% 11.61/11.77 inference(quant_inst,[status(thm)],[])).
% 11.61/11.77 tff(5170,plain,
% 11.61/11.77 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s1) | xuntil2p30(s1) | (~until2p29(s1))),
% 11.61/11.77 inference(modus_ponens,[status(thm)],[5169, 5168])).
% 11.61/11.77 tff(5171,plain,
% 11.61/11.77 (xuntil2p30(s1) | (~until2p29(s1))),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5170, 5033, 4823])).
% 11.61/11.77 tff(5172,plain,
% 11.61/11.77 (~until2p29(s1)),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5171, 5167])).
% 11.61/11.77 tff(5173,assumption,(~until2p29(s1)), introduced(assumption)).
% 11.61/11.77 tff(5174,assumption,(trans(s9, s1)), introduced(assumption)).
% 11.61/11.77 tff(5175,plain,
% 11.61/11.77 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s1) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s1)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s1) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s1)))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5176,plain,
% 11.61/11.77 (((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s1)) | until2p29(s1)) <=> (until2p29(s1) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s1)))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5177,plain,
% 11.61/11.77 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s1)) | until2p29(s1))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s1) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s1))))),
% 11.61/11.77 inference(monotonicity,[status(thm)],[5176])).
% 11.61/11.77 tff(5178,plain,
% 11.61/11.77 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s1)) | until2p29(s1))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s1) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s1)))),
% 11.61/11.77 inference(transitivity,[status(thm)],[5177, 5175])).
% 11.61/11.77 tff(5179,plain,
% 11.61/11.77 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s1)) | until2p29(s1))),
% 11.61/11.77 inference(quant_inst,[status(thm)],[])).
% 11.61/11.77 tff(5180,plain,
% 11.61/11.77 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s1) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s1))),
% 11.61/11.77 inference(modus_ponens,[status(thm)],[5179, 5178])).
% 11.61/11.77 tff(5181,plain,
% 11.61/11.77 ($false),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5180, 5019, 5174, 5068, 5173, 5079])).
% 11.61/11.77 tff(5182,plain,((~trans(s9, s1)) | until2p29(s1) | (~xuntil28(s9))), inference(lemma,lemma(discharge,[]))).
% 11.61/11.77 tff(5183,plain,
% 11.61/11.77 (~trans(s9, s1)),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5182, 5172, 5009])).
% 11.61/11.77 tff(5184,assumption,(~until2p29(s9)), introduced(assumption)).
% 11.61/11.77 tff(5185,assumption,(trans(s9, s9)), introduced(assumption)).
% 11.61/11.77 tff(5186,plain,
% 11.61/11.77 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s9) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s9)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s9) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s9)))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5187,plain,
% 11.61/11.77 (((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s9)) | until2p29(s9)) <=> (until2p29(s9) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s9)))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5188,plain,
% 11.61/11.77 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s9)) | until2p29(s9))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s9) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s9))))),
% 11.61/11.77 inference(monotonicity,[status(thm)],[5187])).
% 11.61/11.77 tff(5189,plain,
% 11.61/11.77 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s9)) | until2p29(s9))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s9) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s9)))),
% 11.61/11.77 inference(transitivity,[status(thm)],[5188, 5186])).
% 11.61/11.77 tff(5190,plain,
% 11.61/11.77 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s9)) | until2p29(s9))),
% 11.61/11.77 inference(quant_inst,[status(thm)],[])).
% 11.61/11.77 tff(5191,plain,
% 11.61/11.77 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s9) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s9))),
% 11.61/11.77 inference(modus_ponens,[status(thm)],[5190, 5189])).
% 11.61/11.77 tff(5192,plain,
% 11.61/11.77 ($false),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5191, 5019, 5185, 5068, 5184, 5079])).
% 11.61/11.77 tff(5193,plain,((~trans(s9, s9)) | until2p29(s9) | (~xuntil28(s9))), inference(lemma,lemma(discharge,[]))).
% 11.61/11.77 tff(5194,plain,
% 11.61/11.77 (~trans(s9, s9)),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5193, 5038, 5009])).
% 11.61/11.77 tff(5195,assumption,(~until2p29(s5)), introduced(assumption)).
% 11.61/11.77 tff(5196,assumption,(trans(s9, s5)), introduced(assumption)).
% 11.61/11.77 tff(5197,plain,
% 11.61/11.77 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s5) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s5)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s5) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s5)))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5198,plain,
% 11.61/11.77 (((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s5)) | until2p29(s5)) <=> (until2p29(s5) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s5)))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5199,plain,
% 11.61/11.77 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s5)) | until2p29(s5))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s5) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s5))))),
% 11.61/11.77 inference(monotonicity,[status(thm)],[5198])).
% 11.61/11.77 tff(5200,plain,
% 11.61/11.77 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s5)) | until2p29(s5))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s5) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s5)))),
% 11.61/11.77 inference(transitivity,[status(thm)],[5199, 5197])).
% 11.61/11.77 tff(5201,plain,
% 11.61/11.77 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s5)) | until2p29(s5))),
% 11.61/11.77 inference(quant_inst,[status(thm)],[])).
% 11.61/11.77 tff(5202,plain,
% 11.61/11.77 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s5) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s5))),
% 11.61/11.77 inference(modus_ponens,[status(thm)],[5201, 5200])).
% 11.61/11.77 tff(5203,plain,
% 11.61/11.77 ($false),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5202, 5019, 5196, 5068, 5195, 5079])).
% 11.61/11.77 tff(5204,plain,((~trans(s9, s5)) | until2p29(s5) | (~xuntil28(s9))), inference(lemma,lemma(discharge,[]))).
% 11.61/11.77 tff(5205,plain,
% 11.61/11.77 (~trans(s9, s5)),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5204, 5121, 5009])).
% 11.61/11.77 tff(5206,assumption,(~until2p29(s4)), introduced(assumption)).
% 11.61/11.77 tff(5207,assumption,(trans(s9, s4)), introduced(assumption)).
% 11.61/11.77 tff(5208,plain,
% 11.61/11.77 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s4) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s4)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s4) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s4)))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5209,plain,
% 11.61/11.77 (((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s4)) | until2p29(s4)) <=> (until2p29(s4) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s4)))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5210,plain,
% 11.61/11.77 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s4)) | until2p29(s4))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s4) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s4))))),
% 11.61/11.77 inference(monotonicity,[status(thm)],[5209])).
% 11.61/11.77 tff(5211,plain,
% 11.61/11.77 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s4)) | until2p29(s4))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s4) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s4)))),
% 11.61/11.77 inference(transitivity,[status(thm)],[5210, 5208])).
% 11.61/11.77 tff(5212,plain,
% 11.61/11.77 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s4)) | until2p29(s4))),
% 11.61/11.77 inference(quant_inst,[status(thm)],[])).
% 11.61/11.77 tff(5213,plain,
% 11.61/11.77 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s4) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s4))),
% 11.61/11.77 inference(modus_ponens,[status(thm)],[5212, 5211])).
% 11.61/11.77 tff(5214,plain,
% 11.61/11.77 ($false),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5213, 5019, 5207, 5068, 5206, 5079])).
% 11.61/11.77 tff(5215,plain,((~trans(s9, s4)) | until2p29(s4) | (~xuntil28(s9))), inference(lemma,lemma(discharge,[]))).
% 11.61/11.77 tff(5216,plain,
% 11.61/11.77 (~trans(s9, s4)),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5215, 5131, 5009])).
% 11.61/11.77 tff(5217,assumption,(~until2p29(s3)), introduced(assumption)).
% 11.61/11.77 tff(5218,assumption,(trans(s9, s3)), introduced(assumption)).
% 11.61/11.77 tff(5219,plain,
% 11.61/11.77 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s3) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s3)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s3) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s3)))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5220,plain,
% 11.61/11.77 (((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s3)) | until2p29(s3)) <=> (until2p29(s3) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s3)))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5221,plain,
% 11.61/11.77 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s3)) | until2p29(s3))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s3) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s3))))),
% 11.61/11.77 inference(monotonicity,[status(thm)],[5220])).
% 11.61/11.77 tff(5222,plain,
% 11.61/11.77 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s3)) | until2p29(s3))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s3) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s3)))),
% 11.61/11.77 inference(transitivity,[status(thm)],[5221, 5219])).
% 11.61/11.77 tff(5223,plain,
% 11.61/11.77 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s3)) | until2p29(s3))),
% 11.61/11.77 inference(quant_inst,[status(thm)],[])).
% 11.61/11.77 tff(5224,plain,
% 11.61/11.77 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s3) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s3))),
% 11.61/11.77 inference(modus_ponens,[status(thm)],[5223, 5222])).
% 11.61/11.77 tff(5225,plain,
% 11.61/11.77 ($false),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5224, 5019, 5218, 5068, 5217, 5079])).
% 11.61/11.77 tff(5226,plain,((~trans(s9, s3)) | until2p29(s3) | (~xuntil28(s9))), inference(lemma,lemma(discharge,[]))).
% 11.61/11.77 tff(5227,plain,
% 11.61/11.77 (~trans(s9, s3)),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5226, 5141, 5009])).
% 11.61/11.77 tff(5228,plain,
% 11.61/11.77 (^[X: $i] : refl((loop | (~last(X)) | (~xuntil28(X))) <=> (loop | (~last(X)) | (~xuntil28(X))))),
% 11.61/11.77 inference(bind,[status(th)],[])).
% 11.61/11.77 tff(5229,plain,
% 11.61/11.77 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 11.61/11.77 inference(quant_intro,[status(thm)],[5228])).
% 11.61/11.77 tff(5230,plain,
% 11.61/11.77 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5231,plain,
% 11.61/11.77 (^[X: $i] : rewrite(((loop | (~last(X))) | (~xuntil28(X))) <=> (loop | (~last(X)) | (~xuntil28(X))))),
% 11.61/11.77 inference(bind,[status(th)],[])).
% 11.61/11.77 tff(5232,plain,
% 11.61/11.77 (![X: $i] : ((loop | (~last(X))) | (~xuntil28(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 11.61/11.77 inference(quant_intro,[status(thm)],[5231])).
% 11.61/11.77 tff(5233,axiom,(![X: $i] : ((loop | (~last(X))) | (~xuntil28(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty10')).
% 11.61/11.77 tff(5234,plain,
% 11.61/11.77 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 11.61/11.77 inference(modus_ponens,[status(thm)],[5233, 5232])).
% 11.61/11.77 tff(5235,plain,
% 11.61/11.77 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 11.61/11.77 inference(modus_ponens,[status(thm)],[5234, 5230])).
% 11.61/11.77 tff(5236,plain,(
% 11.61/11.77 ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 11.61/11.77 inference(skolemize,[status(sab)],[5235])).
% 11.61/11.77 tff(5237,plain,
% 11.61/11.77 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 11.61/11.77 inference(modus_ponens,[status(thm)],[5236, 5229])).
% 11.61/11.77 tff(5238,plain,
% 11.61/11.77 (((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | (loop | (~last(s9)) | (~xuntil28(s9)))) <=> ((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | loop | (~last(s9)) | (~xuntil28(s9)))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5239,plain,
% 11.61/11.77 ((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | (loop | (~last(s9)) | (~xuntil28(s9)))),
% 11.61/11.77 inference(quant_inst,[status(thm)],[])).
% 11.61/11.77 tff(5240,plain,
% 11.61/11.77 ((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | loop | (~last(s9)) | (~xuntil28(s9))),
% 11.61/11.77 inference(modus_ponens,[status(thm)],[5239, 5238])).
% 11.61/11.77 tff(5241,plain,
% 11.61/11.77 (loop | (~xuntil28(s9))),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5240, 5019, 5237])).
% 11.61/11.77 tff(5242,plain,
% 11.61/11.77 (loop),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5241, 5009])).
% 11.61/11.77 tff(5243,plain,
% 11.61/11.77 (((~![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)))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5244,plain,
% 11.61/11.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s0, s1)) | until2p29(s1) | (~xuntil2p30(s0)))),
% 11.61/11.77 inference(quant_inst,[status(thm)],[])).
% 11.61/11.77 tff(5245,plain,
% 11.61/11.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s0, s1)) | until2p29(s1) | (~xuntil2p30(s0))),
% 11.61/11.77 inference(modus_ponens,[status(thm)],[5244, 5243])).
% 11.61/11.77 tff(5246,plain,
% 11.61/11.77 (until2p29(s1) | (~xuntil2p30(s0))),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5245, 96, 5048])).
% 11.61/11.77 tff(5247,plain,
% 11.61/11.77 (~xuntil2p30(s0)),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5246, 5172])).
% 11.61/11.77 tff(5248,plain,
% 11.61/11.77 (((~![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)))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5249,plain,
% 11.61/11.77 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s0) | xuntil2p30(s0) | (~until2p29(s0)))),
% 11.61/11.77 inference(quant_inst,[status(thm)],[])).
% 11.61/11.77 tff(5250,plain,
% 11.61/11.77 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s0) | xuntil2p30(s0) | (~until2p29(s0))),
% 11.61/11.77 inference(modus_ponens,[status(thm)],[5249, 5248])).
% 11.61/11.77 tff(5251,plain,
% 11.61/11.77 (xuntil2p30(s0) | (~until2p29(s0))),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5250, 5033, 4857])).
% 11.61/11.77 tff(5252,plain,
% 11.61/11.77 (~until2p29(s0)),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5251, 5247])).
% 11.61/11.77 tff(5253,assumption,(~until2p29(s0)), introduced(assumption)).
% 11.61/11.77 tff(5254,assumption,(trans(s9, s0)), introduced(assumption)).
% 11.61/11.77 tff(5255,plain,
% 11.61/11.77 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | until2p29(s0) | (~trans(s9, s0)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (~last(s9)) | (~xuntil28(s9)) | until2p29(s0) | (~trans(s9, s0)))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5256,plain,
% 11.61/11.77 (((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s0)) | until2p29(s0)) <=> ((~last(s9)) | (~xuntil28(s9)) | until2p29(s0) | (~trans(s9, s0)))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5257,plain,
% 11.61/11.77 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s0)) | until2p29(s0))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | until2p29(s0) | (~trans(s9, s0))))),
% 11.61/11.77 inference(monotonicity,[status(thm)],[5256])).
% 11.61/11.77 tff(5258,plain,
% 11.61/11.77 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s0)) | until2p29(s0))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (~last(s9)) | (~xuntil28(s9)) | until2p29(s0) | (~trans(s9, s0)))),
% 11.61/11.77 inference(transitivity,[status(thm)],[5257, 5255])).
% 11.61/11.77 tff(5259,plain,
% 11.61/11.77 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s0)) | until2p29(s0))),
% 11.61/11.77 inference(quant_inst,[status(thm)],[])).
% 11.61/11.77 tff(5260,plain,
% 11.61/11.77 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (~last(s9)) | (~xuntil28(s9)) | until2p29(s0) | (~trans(s9, s0))),
% 11.61/11.77 inference(modus_ponens,[status(thm)],[5259, 5258])).
% 11.61/11.77 tff(5261,plain,
% 11.61/11.77 ($false),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5260, 5019, 5254, 5068, 5079, 5253])).
% 11.61/11.77 tff(5262,plain,((~trans(s9, s0)) | (~xuntil28(s9)) | until2p29(s0)), inference(lemma,lemma(discharge,[]))).
% 11.61/11.77 tff(5263,plain,
% 11.61/11.77 (~trans(s9, s0)),
% 11.61/11.77 inference(unit_resolution,[status(thm)],[5262, 5009, 5252])).
% 11.61/11.77 tff(5264,plain,
% 11.61/11.77 (((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7) | trans(s9, s8) | trans(s9, s9)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7) | trans(s9, s8) | trans(s9, s9))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5265,plain,
% 11.61/11.77 ((((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7) | trans(s9, s8)) | trans(s9, s9)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7) | trans(s9, s8) | trans(s9, s9))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5266,plain,
% 11.61/11.77 ((((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7)) | trans(s9, s8)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7) | trans(s9, s8))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5267,plain,
% 11.61/11.77 ((((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6)) | trans(s9, s7)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7))),
% 11.61/11.77 inference(rewrite,[status(thm)],[])).
% 11.61/11.77 tff(5268,plain,
% 11.61/11.77 ((((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5)) | trans(s9, s6)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6))),
% 11.61/11.78 inference(rewrite,[status(thm)],[])).
% 11.61/11.78 tff(5269,plain,
% 11.61/11.78 ((((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4)) | trans(s9, s5)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5))),
% 11.61/11.78 inference(rewrite,[status(thm)],[])).
% 11.61/11.78 tff(5270,plain,
% 11.61/11.78 ((((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3)) | trans(s9, s4)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4))),
% 11.61/11.78 inference(rewrite,[status(thm)],[])).
% 11.61/11.78 tff(5271,plain,
% 11.61/11.78 ((((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2)) | trans(s9, s3)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3))),
% 11.61/11.78 inference(rewrite,[status(thm)],[])).
% 11.61/11.78 tff(5272,plain,
% 11.61/11.78 ((((~loop) | trans(s9, s0) | trans(s9, s1)) | trans(s9, s2)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2))),
% 11.61/11.78 inference(rewrite,[status(thm)],[])).
% 11.61/11.78 tff(5273,plain,
% 11.61/11.78 ((((~loop) | trans(s9, s0)) | trans(s9, s1)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1))),
% 11.61/11.78 inference(rewrite,[status(thm)],[])).
% 11.61/11.78 tff(5274,plain,
% 11.61/11.78 (((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) <=> (((~loop) | trans(s9, s0) | trans(s9, s1)) | trans(s9, s2))),
% 11.61/11.78 inference(monotonicity,[status(thm)],[5273])).
% 11.61/11.78 tff(5275,plain,
% 11.61/11.78 (((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2))),
% 11.61/11.78 inference(transitivity,[status(thm)],[5274, 5272])).
% 11.61/11.78 tff(5276,plain,
% 11.61/11.78 ((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) <=> (((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2)) | trans(s9, s3))),
% 11.61/11.78 inference(monotonicity,[status(thm)],[5275])).
% 11.61/11.78 tff(5277,plain,
% 11.61/11.78 ((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3))),
% 11.61/11.78 inference(transitivity,[status(thm)],[5276, 5271])).
% 11.61/11.78 tff(5278,plain,
% 11.61/11.78 (((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) <=> (((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3)) | trans(s9, s4))),
% 11.61/11.78 inference(monotonicity,[status(thm)],[5277])).
% 11.61/11.78 tff(5279,plain,
% 11.61/11.78 (((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4))),
% 11.61/11.78 inference(transitivity,[status(thm)],[5278, 5270])).
% 11.61/11.78 tff(5280,plain,
% 11.61/11.78 ((((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) | trans(s9, s5)) <=> (((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4)) | trans(s9, s5))),
% 11.61/11.78 inference(monotonicity,[status(thm)],[5279])).
% 11.61/11.78 tff(5281,plain,
% 11.61/11.78 ((((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) | trans(s9, s5)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5))),
% 11.61/11.78 inference(transitivity,[status(thm)],[5280, 5269])).
% 11.61/11.78 tff(5282,plain,
% 11.61/11.78 (((((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) | trans(s9, s5)) | trans(s9, s6)) <=> (((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5)) | trans(s9, s6))),
% 11.61/11.78 inference(monotonicity,[status(thm)],[5281])).
% 11.61/11.78 tff(5283,plain,
% 11.61/11.78 (((((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) | trans(s9, s5)) | trans(s9, s6)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6))),
% 11.61/11.78 inference(transitivity,[status(thm)],[5282, 5268])).
% 11.61/11.78 tff(5284,plain,
% 11.61/11.78 ((((((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) | trans(s9, s5)) | trans(s9, s6)) | trans(s9, s7)) <=> (((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6)) | trans(s9, s7))),
% 11.61/11.78 inference(monotonicity,[status(thm)],[5283])).
% 11.61/11.78 tff(5285,plain,
% 11.61/11.78 ((((((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) | trans(s9, s5)) | trans(s9, s6)) | trans(s9, s7)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7))),
% 11.61/11.78 inference(transitivity,[status(thm)],[5284, 5267])).
% 11.61/11.78 tff(5286,plain,
% 11.61/11.78 (((((((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) | trans(s9, s5)) | trans(s9, s6)) | trans(s9, s7)) | trans(s9, s8)) <=> (((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7)) | trans(s9, s8))),
% 11.61/11.78 inference(monotonicity,[status(thm)],[5285])).
% 11.61/11.78 tff(5287,plain,
% 11.61/11.78 (((((((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) | trans(s9, s5)) | trans(s9, s6)) | trans(s9, s7)) | trans(s9, s8)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7) | trans(s9, s8))),
% 11.61/11.78 inference(transitivity,[status(thm)],[5286, 5266])).
% 11.61/11.78 tff(5288,plain,
% 11.61/11.78 ((((((((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) | trans(s9, s5)) | trans(s9, s6)) | trans(s9, s7)) | trans(s9, s8)) | trans(s9, s9)) <=> (((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7) | trans(s9, s8)) | trans(s9, s9))),
% 11.61/11.78 inference(monotonicity,[status(thm)],[5287])).
% 11.61/11.78 tff(5289,plain,
% 11.61/11.78 ((((((((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) | trans(s9, s5)) | trans(s9, s6)) | trans(s9, s7)) | trans(s9, s8)) | trans(s9, s9)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7) | trans(s9, s8) | trans(s9, s9))),
% 11.61/11.78 inference(transitivity,[status(thm)],[5288, 5265])).
% 11.61/11.78 tff(5290,axiom,(((((((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) | trans(s9, s5)) | trans(s9, s6)) | trans(s9, s7)) | trans(s9, s8)) | trans(s9, s9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound12')).
% 11.61/11.78 tff(5291,plain,
% 11.61/11.78 ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7) | trans(s9, s8) | trans(s9, s9)),
% 11.61/11.78 inference(modus_ponens,[status(thm)],[5290, 5289])).
% 11.61/11.78 tff(5292,plain,
% 11.61/11.78 ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7) | trans(s9, s8) | trans(s9, s9)),
% 11.61/11.78 inference(modus_ponens,[status(thm)],[5291, 5264])).
% 11.61/11.78 tff(5293,plain,
% 11.61/11.78 (trans(s9, s8)),
% 11.61/11.78 inference(unit_resolution,[status(thm)],[5292, 5263, 5242, 5227, 5216, 5205, 5194, 5183, 5162, 5111, 5090])).
% 11.61/11.78 tff(5294,plain,
% 11.61/11.78 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s8) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s8)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s8) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s8)))),
% 11.61/11.78 inference(rewrite,[status(thm)],[])).
% 11.61/11.78 tff(5295,plain,
% 11.61/11.78 (((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s8)) | until2p29(s8)) <=> (until2p29(s8) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s8)))),
% 11.61/11.78 inference(rewrite,[status(thm)],[])).
% 11.61/11.78 tff(5296,plain,
% 11.61/11.78 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s8)) | until2p29(s8))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s8) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s8))))),
% 11.63/11.78 inference(monotonicity,[status(thm)],[5295])).
% 11.63/11.78 tff(5297,plain,
% 11.63/11.78 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s8)) | until2p29(s8))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s8) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s8)))),
% 11.63/11.78 inference(transitivity,[status(thm)],[5296, 5294])).
% 11.63/11.78 tff(5298,plain,
% 11.63/11.78 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s8)) | until2p29(s8))),
% 11.63/11.78 inference(quant_inst,[status(thm)],[])).
% 11.63/11.78 tff(5299,plain,
% 11.63/11.78 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s8) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s8))),
% 11.63/11.78 inference(modus_ponens,[status(thm)],[5298, 5297])).
% 11.63/11.78 tff(5300,plain,
% 11.63/11.78 ($false),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5299, 5019, 5293, 5068, 5058, 5009])).
% 11.63/11.78 tff(5301,plain,(node26(s9) | node26(s2) | node26(s3) | node26(s4) | node26(s5) | node26(s6) | node26(s7) | node26(s8)), inference(lemma,lemma(discharge,[]))).
% 11.63/11.78 tff(5302,plain,
% 11.63/11.78 ($false),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5301, 4740, 4728, 4640, 4653, 4639, 4652, 4704, 4703])).
% 11.63/11.78 tff(5303,plain,(m_user_v_ack(c_e_h_1, c_u, s2) | node26(s9) | node26(s8) | node26(s6) | node26(s7) | node26(s4) | node26(s5) | node23(s3) | node25(s3) | m_and_h_gate_v_out(c_e_h_1, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 11.63/11.78 tff(5304,plain,
% 11.63/11.78 (m_user_v_ack(c_e_h_1, c_u, s2) | node26(s9) | node26(s8) | node26(s6) | node26(s7) | node26(s4) | node26(s5) | node23(s3) | m_and_h_gate_v_out(c_e_h_1, c_r, s3)),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5303, 4702])).
% 11.63/11.78 tff(5305,plain,
% 11.63/11.78 ($false),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5304, 4694, 4681, 4653, 4329, 4652, 4651, 4640, 4639, 4638])).
% 11.63/11.78 tff(5306,plain,(m_and_h_gate_v_out(c_e_h_1, c_r, s4) | node26(s8) | m_and_h_gate_v_out(c_e_h_1, c_r, s3) | node26(s7) | node26(s9) | node26(s6) | m_user_v_ack(c_e_h_1, c_u, s2) | node23(s5) | node25(s5)), inference(lemma,lemma(discharge,[]))).
% 11.63/11.78 tff(5307,plain,
% 11.63/11.78 (m_and_h_gate_v_out(c_e_h_1, c_r, s4) | node26(s8) | m_and_h_gate_v_out(c_e_h_1, c_r, s3) | node26(s7) | node26(s9) | node26(s6) | m_user_v_ack(c_e_h_1, c_u, s2) | node23(s5)),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5306, 4637])).
% 11.63/11.78 tff(5308,plain,
% 11.63/11.78 (node26(s8) | node26(s9)),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5307, 4629, 4304, 4335, 4622, 4594, 4586])).
% 11.63/11.78 tff(5309,plain,
% 11.63/11.78 (node26(s9)),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5308, 4558])).
% 11.63/11.78 tff(5310,assumption,(~node23(s9)), introduced(assumption)).
% 11.63/11.78 tff(5311,assumption,(~node24(s9)), introduced(assumption)).
% 11.63/11.78 tff(5312,plain,
% 11.63/11.78 (((~![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)))),
% 11.63/11.78 inference(rewrite,[status(thm)],[])).
% 11.63/11.78 tff(5313,plain,
% 11.63/11.78 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s9) | node24(s9) | node25(s9) | (~node26(s9)))),
% 11.63/11.78 inference(quant_inst,[status(thm)],[])).
% 11.63/11.78 tff(5314,plain,
% 11.63/11.78 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s9) | node24(s9) | node25(s9) | (~node26(s9))),
% 11.63/11.78 inference(modus_ponens,[status(thm)],[5313, 5312])).
% 11.63/11.78 tff(5315,plain,
% 11.63/11.78 (node25(s9) | (~node26(s9))),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5314, 4553, 5311, 5310])).
% 11.63/11.78 tff(5316,plain,
% 11.63/11.78 (node25(s9)),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5315, 5309])).
% 11.63/11.78 tff(5317,plain,
% 11.63/11.78 (((~![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)))),
% 11.63/11.78 inference(rewrite,[status(thm)],[])).
% 11.63/11.78 tff(5318,plain,
% 11.63/11.78 ((~![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)))),
% 11.63/11.78 inference(quant_inst,[status(thm)],[])).
% 11.63/11.78 tff(5319,plain,
% 11.63/11.78 ((~![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))),
% 11.63/11.78 inference(modus_ponens,[status(thm)],[5318, 5317])).
% 11.63/11.78 tff(5320,plain,
% 11.63/11.78 (m_user_v_ack(c_e_h_3, c_u, s9)),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5319, 4538, 5316])).
% 11.63/11.78 tff(5321,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s9)), introduced(assumption)).
% 11.63/11.78 tff(5322,assumption,(m_user_v_ack(c_e_h_3, c_u, s9)), introduced(assumption)).
% 11.63/11.78 tff(5323,plain,
% 11.63/11.78 (((~![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))),
% 11.63/11.78 inference(rewrite,[status(thm)],[])).
% 11.63/11.78 tff(5324,plain,
% 11.63/11.78 ((~![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))),
% 11.63/11.78 inference(quant_inst,[status(thm)],[])).
% 11.63/11.78 tff(5325,plain,
% 11.63/11.78 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s9)) | m_and_h_gate_v_out(c_e_h_3, c_r, s9)),
% 11.63/11.78 inference(modus_ponens,[status(thm)],[5324, 5323])).
% 11.63/11.78 tff(5326,plain,
% 11.63/11.78 ($false),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5325, 4458, 5322, 5321])).
% 11.63/11.78 tff(5327,plain,((~m_user_v_ack(c_e_h_3, c_u, s9)) | m_and_h_gate_v_out(c_e_h_3, c_r, s9)), inference(lemma,lemma(discharge,[]))).
% 11.63/11.78 tff(5328,plain,
% 11.63/11.78 (m_and_h_gate_v_out(c_e_h_3, c_r, s9)),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5327, 5320])).
% 11.63/11.78 tff(5329,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s9)), introduced(assumption)).
% 11.63/11.78 tff(5330,assumption,(node22(c_e_h_3, c_r, s8, s9)), introduced(assumption)).
% 11.63/11.78 tff(5331,plain,
% 11.63/11.78 (((~![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_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))),
% 11.63/11.78 inference(rewrite,[status(thm)],[])).
% 11.63/11.78 tff(5332,plain,
% 11.63/11.78 ((~![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_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))),
% 11.63/11.78 inference(quant_inst,[status(thm)],[])).
% 11.63/11.78 tff(5333,plain,
% 11.63/11.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s9)) | (~node22(c_e_h_3, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_r, s8)),
% 11.63/11.78 inference(modus_ponens,[status(thm)],[5332, 5331])).
% 11.63/11.78 tff(5334,plain,
% 11.63/11.78 ($false),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5333, 273, 4480, 5329, 5330])).
% 11.63/11.78 tff(5335,plain,((~node22(c_e_h_3, c_r, s8, s9)) | 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, s9))), inference(lemma,lemma(discharge,[]))).
% 11.63/11.78 tff(5336,plain,
% 11.63/11.78 (~node22(c_e_h_3, c_r, s8, s9)),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5335, 5329, 4480])).
% 11.63/11.78 tff(5337,assumption,(~node20(c_e_h_3, c_r, s8)), introduced(assumption)).
% 11.63/11.78 tff(5338,assumption,(node21(c_e_h_3, c_r, s8, s9)), introduced(assumption)).
% 11.63/11.78 tff(5339,plain,
% 11.63/11.78 (((~![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_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) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s9)) | (~node21(c_e_h_3, c_r, s8, s9)))),
% 11.63/11.78 inference(rewrite,[status(thm)],[])).
% 11.63/11.78 tff(5340,plain,
% 11.63/11.78 ((~![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_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)))),
% 11.63/11.78 inference(quant_inst,[status(thm)],[])).
% 11.63/11.78 tff(5341,plain,
% 11.63/11.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s9)) | (~node21(c_e_h_3, c_r, s8, s9))),
% 11.63/11.78 inference(modus_ponens,[status(thm)],[5340, 5339])).
% 11.63/11.78 tff(5342,plain,
% 11.63/11.78 ($false),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5341, 228, 5329, 5337, 5338])).
% 11.63/11.78 tff(5343,plain,((~node21(c_e_h_3, c_r, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s9)) | node20(c_e_h_3, c_r, s8)), inference(lemma,lemma(discharge,[]))).
% 11.63/11.78 tff(5344,plain,
% 11.63/11.78 (~node21(c_e_h_3, c_r, s8, s9)),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5343, 5329, 5337])).
% 11.63/11.78 tff(5345,plain,
% 11.63/11.78 (((~![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))),
% 11.63/11.78 inference(rewrite,[status(thm)],[])).
% 11.63/11.78 tff(5346,plain,
% 11.63/11.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s8, s9)) | trans(s8, s9))),
% 11.63/11.78 inference(quant_inst,[status(thm)],[])).
% 11.63/11.78 tff(5347,plain,
% 11.63/11.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s8, s9)) | trans(s8, s9)),
% 11.63/11.78 inference(modus_ponens,[status(thm)],[5346, 5345])).
% 11.63/11.78 tff(5348,plain,
% 11.63/11.78 (trans(s8, s9)),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5347, 4996, 93])).
% 11.63/11.78 tff(5349,plain,
% 11.63/11.78 (((~![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))),
% 11.63/11.78 inference(rewrite,[status(thm)],[])).
% 11.63/11.78 tff(5350,plain,
% 11.63/11.78 ((~![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))),
% 11.63/11.78 inference(quant_inst,[status(thm)],[])).
% 11.63/11.78 tff(5351,plain,
% 11.63/11.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_3, c_r, s8, s9) | node22(c_e_h_3, c_r, s8, s9)),
% 11.63/11.78 inference(modus_ponens,[status(thm)],[5350, 5349])).
% 11.63/11.78 tff(5352,plain,
% 11.63/11.78 (node21(c_e_h_3, c_r, s8, s9) | node22(c_e_h_3, c_r, s8, s9)),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5351, 247, 5348])).
% 11.63/11.78 tff(5353,plain,
% 11.63/11.78 ($false),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5352, 5344, 5336])).
% 11.63/11.78 tff(5354,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s9)) | node20(c_e_h_3, c_r, s8) | m_and_h_gate_v_out(c_e_h_3, c_r, s8)), inference(lemma,lemma(discharge,[]))).
% 11.63/11.78 tff(5355,plain,
% 11.63/11.78 (node20(c_e_h_3, c_r, s8)),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5354, 5328, 4530])).
% 11.63/11.78 tff(5356,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_r, s8)), introduced(assumption)).
% 11.63/11.78 tff(5357,assumption,(node20(c_e_h_3, c_r, s8)), introduced(assumption)).
% 11.63/11.78 tff(5358,plain,
% 11.63/11.78 (((~![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))),
% 11.63/11.78 inference(rewrite,[status(thm)],[])).
% 11.63/11.78 tff(5359,plain,
% 11.63/11.78 ((~![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))),
% 11.63/11.78 inference(quant_inst,[status(thm)],[])).
% 11.63/11.78 tff(5360,plain,
% 11.63/11.78 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s8)),
% 11.63/11.78 inference(modus_ponens,[status(thm)],[5359, 5358])).
% 11.63/11.78 tff(5361,plain,
% 11.63/11.78 ($false),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5360, 213, 5357, 5356])).
% 11.63/11.78 tff(5362,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,[]))).
% 11.63/11.78 tff(5363,plain,
% 11.63/11.78 (m_and_h_gate_v_in1(c_e_h_3, c_r, s8)),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5362, 5355])).
% 11.63/11.78 tff(5364,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_r, s8)), introduced(assumption)).
% 11.63/11.78 tff(5365,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s8)), introduced(assumption)).
% 11.63/11.78 tff(5366,plain,
% 11.63/11.78 (((~![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))),
% 11.63/11.78 inference(rewrite,[status(thm)],[])).
% 11.63/11.78 tff(5367,plain,
% 11.63/11.78 ((~![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))),
% 11.63/11.78 inference(quant_inst,[status(thm)],[])).
% 11.63/11.78 tff(5368,plain,
% 11.63/11.78 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s8)),
% 11.63/11.78 inference(modus_ponens,[status(thm)],[5367, 5366])).
% 11.63/11.78 tff(5369,plain,
% 11.63/11.78 ($false),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5368, 2431, 5365, 5364])).
% 11.63/11.78 tff(5370,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,[]))).
% 11.63/11.78 tff(5371,plain,
% 11.63/11.78 (m_c_h_element_v_out(c_e_h_3, c_e, s8)),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5370, 5363])).
% 11.63/11.78 tff(5372,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_e, s7)), introduced(assumption)).
% 11.63/11.78 tff(5373,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s8)), introduced(assumption)).
% 11.63/11.78 tff(5374,assumption,(~node16(c_e_h_3, c_e, s7)), introduced(assumption)).
% 11.63/11.78 tff(5375,assumption,(node15(c_e_h_3, c_e, s7, s8)), introduced(assumption)).
% 11.63/11.78 tff(5376,plain,
% 11.63/11.78 (((~![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_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))),
% 11.63/11.78 inference(rewrite,[status(thm)],[])).
% 11.63/11.78 tff(5377,plain,
% 11.63/11.78 ((~![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_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))),
% 11.63/11.78 inference(quant_inst,[status(thm)],[])).
% 11.63/11.78 tff(5378,plain,
% 11.63/11.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | (~node15(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s7)),
% 11.63/11.78 inference(modus_ponens,[status(thm)],[5377, 5376])).
% 11.63/11.78 tff(5379,plain,
% 11.63/11.78 ($false),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5378, 393, 5373, 2690, 5375])).
% 11.63/11.78 tff(5380,plain,((~node15(c_e_h_3, c_e, s7, s8)) | (~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)), inference(lemma,lemma(discharge,[]))).
% 11.63/11.78 tff(5381,plain,
% 11.63/11.78 (~node15(c_e_h_3, c_e, s7, s8)),
% 11.63/11.78 inference(unit_resolution,[status(thm)],[5380, 5373, 2690])).
% 11.63/11.78 tff(5382,plain,
% 11.63/11.78 (((~![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))),
% 11.63/11.79 inference(rewrite,[status(thm)],[])).
% 11.63/11.79 tff(5383,plain,
% 11.63/11.79 ((~![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))),
% 11.63/11.79 inference(quant_inst,[status(thm)],[])).
% 11.63/11.79 tff(5384,plain,
% 11.63/11.79 ((~![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)),
% 11.63/11.79 inference(modus_ponens,[status(thm)],[5383, 5382])).
% 11.63/11.79 tff(5385,plain,
% 11.63/11.79 (node19(c_e_h_3, c_e, s7, s8)),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5384, 312, 2669])).
% 11.63/11.79 tff(5386,plain,
% 11.63/11.79 (((~![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_3, c_e, s7, s8)) | 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))) <=> ((~![Y: $i, I0: $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, s7, s8)) | 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))),
% 11.63/11.79 inference(rewrite,[status(thm)],[])).
% 11.63/11.79 tff(5387,plain,
% 11.63/11.79 ((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))) <=> ((~node19(c_e_h_3, c_e, s7, s8)) | 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))),
% 11.63/11.79 inference(rewrite,[status(thm)],[])).
% 11.63/11.79 tff(5388,plain,
% 11.63/11.79 (((~![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_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)))) | ((~node19(c_e_h_3, c_e, s7, s8)) | 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)))),
% 11.63/11.79 inference(monotonicity,[status(thm)],[5387])).
% 11.63/11.79 tff(5389,plain,
% 11.63/11.79 (((~![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_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)))) | (~node19(c_e_h_3, c_e, s7, s8)) | 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))),
% 11.63/11.79 inference(transitivity,[status(thm)],[5388, 5386])).
% 11.63/11.79 tff(5390,plain,
% 11.63/11.79 ((~![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_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)))),
% 11.63/11.79 inference(quant_inst,[status(thm)],[])).
% 11.63/11.79 tff(5391,plain,
% 11.63/11.79 ((~![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_3, c_e, s7, s8)) | 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)),
% 11.63/11.79 inference(modus_ponens,[status(thm)],[5390, 5389])).
% 11.63/11.79 tff(5392,plain,
% 11.63/11.79 (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)),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5391, 409, 5385])).
% 11.63/11.79 tff(5393,plain,
% 11.63/11.79 (node14(c_e_h_3, c_e, s7, s8)),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5392, 5381, 5374])).
% 11.63/11.79 tff(5394,plain,
% 11.63/11.79 (((~![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_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)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, 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, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7) | (~node14(c_e_h_3, c_e, s7, s8)))),
% 11.63/11.79 inference(rewrite,[status(thm)],[])).
% 11.63/11.79 tff(5395,plain,
% 11.63/11.79 (((~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_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)))),
% 11.63/11.79 inference(rewrite,[status(thm)],[])).
% 11.63/11.79 tff(5396,plain,
% 11.63/11.79 (((~![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_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_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))))),
% 11.63/11.79 inference(monotonicity,[status(thm)],[5395])).
% 11.63/11.79 tff(5397,plain,
% 11.63/11.79 (((~![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_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_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)))),
% 11.63/11.79 inference(transitivity,[status(thm)],[5396, 5394])).
% 11.63/11.79 tff(5398,plain,
% 11.63/11.79 ((~![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_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)))),
% 11.63/11.79 inference(quant_inst,[status(thm)],[])).
% 11.63/11.79 tff(5399,plain,
% 11.63/11.79 ((~![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_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))),
% 11.63/11.79 inference(modus_ponens,[status(thm)],[5398, 5397])).
% 11.63/11.79 tff(5400,plain,
% 11.63/11.79 (m_c_h_element_v_in1(c_e_h_3, c_e, s7)),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5399, 427, 5373, 5393])).
% 11.63/11.79 tff(5401,plain,
% 11.63/11.79 (((~![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_3, c_e, s7) | (~m_c_h_element_v_in1(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) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s7)) | (~node17(c_e_h_3, c_e, s7)))),
% 11.63/11.79 inference(rewrite,[status(thm)],[])).
% 11.63/11.79 tff(5402,plain,
% 11.63/11.79 (((~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) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s7)) | (~node17(c_e_h_3, c_e, s7)))),
% 11.63/11.79 inference(rewrite,[status(thm)],[])).
% 11.63/11.79 tff(5403,plain,
% 11.63/11.79 (((~![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_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) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s7)) | (~node17(c_e_h_3, c_e, s7))))),
% 11.63/11.79 inference(monotonicity,[status(thm)],[5402])).
% 11.63/11.79 tff(5404,plain,
% 11.63/11.79 (((~![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_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) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s7)) | (~node17(c_e_h_3, c_e, s7)))),
% 11.63/11.79 inference(transitivity,[status(thm)],[5403, 5401])).
% 11.63/11.79 tff(5405,plain,
% 11.63/11.79 ((~![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_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)))),
% 11.63/11.79 inference(quant_inst,[status(thm)],[])).
% 11.63/11.79 tff(5406,plain,
% 11.63/11.79 ((~![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_3, c_e, s7) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s7)) | (~node17(c_e_h_3, c_e, s7))),
% 11.63/11.79 inference(modus_ponens,[status(thm)],[5405, 5404])).
% 11.63/11.79 tff(5407,plain,
% 11.63/11.79 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s7)) | (~node17(c_e_h_3, c_e, s7))),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5406, 359, 5372])).
% 11.63/11.79 tff(5408,plain,
% 11.63/11.79 (~node17(c_e_h_3, c_e, s7)),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5407, 5400])).
% 11.63/11.79 tff(5409,plain,
% 11.63/11.79 (((~![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_3, c_e, s7, s8)) | node17(c_e_h_3, c_e, s7) | 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)))) | (~node19(c_e_h_3, c_e, s7, s8)) | node17(c_e_h_3, c_e, s7) | node18(c_e_h_3, c_e, s7, s8))),
% 11.63/11.79 inference(rewrite,[status(thm)],[])).
% 11.63/11.79 tff(5410,plain,
% 11.63/11.79 ((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))) <=> ((~node19(c_e_h_3, c_e, s7, s8)) | node17(c_e_h_3, c_e, s7) | node18(c_e_h_3, c_e, s7, s8))),
% 11.63/11.79 inference(rewrite,[status(thm)],[])).
% 11.63/11.79 tff(5411,plain,
% 11.63/11.79 (((~![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_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)))) | ((~node19(c_e_h_3, c_e, s7, s8)) | node17(c_e_h_3, c_e, s7) | node18(c_e_h_3, c_e, s7, s8)))),
% 11.63/11.79 inference(monotonicity,[status(thm)],[5410])).
% 11.63/11.79 tff(5412,plain,
% 11.63/11.79 (((~![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_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)))) | (~node19(c_e_h_3, c_e, s7, s8)) | node17(c_e_h_3, c_e, s7) | node18(c_e_h_3, c_e, s7, s8))),
% 11.63/11.79 inference(transitivity,[status(thm)],[5411, 5409])).
% 11.63/11.79 tff(5413,plain,
% 11.63/11.79 ((~![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_3, c_e, s7) | node18(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)))),
% 11.63/11.79 inference(quant_inst,[status(thm)],[])).
% 11.63/11.79 tff(5414,plain,
% 11.63/11.79 ((~![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_3, c_e, s7, s8)) | node17(c_e_h_3, c_e, s7) | node18(c_e_h_3, c_e, s7, s8)),
% 11.63/11.79 inference(modus_ponens,[status(thm)],[5413, 5412])).
% 11.63/11.79 tff(5415,plain,
% 11.63/11.79 (node17(c_e_h_3, c_e, s7) | node18(c_e_h_3, c_e, s7, s8)),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5414, 326, 5385])).
% 11.63/11.79 tff(5416,plain,
% 11.63/11.79 (node18(c_e_h_3, c_e, s7, s8)),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5415, 5408])).
% 11.63/11.79 tff(5417,plain,
% 11.63/11.79 (((~![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_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, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~node18(c_e_h_3, c_e, s7, s8)))),
% 11.63/11.79 inference(rewrite,[status(thm)],[])).
% 11.63/11.79 tff(5418,plain,
% 11.63/11.79 ((~![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_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)))),
% 11.63/11.79 inference(quant_inst,[status(thm)],[])).
% 11.63/11.79 tff(5419,plain,
% 11.63/11.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~node18(c_e_h_3, c_e, s7, s8))),
% 11.63/11.79 inference(modus_ponens,[status(thm)],[5418, 5417])).
% 11.63/11.79 tff(5420,plain,
% 11.63/11.79 ($false),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5419, 296, 5373, 2690, 5416])).
% 11.63/11.79 tff(5421,plain,((~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) | m_c_h_element_v_in2(c_e_h_3, c_e, s7) | node16(c_e_h_3, c_e, s7)), inference(lemma,lemma(discharge,[]))).
% 11.63/11.79 tff(5422,plain,
% 11.63/11.79 (node16(c_e_h_3, c_e, s7)),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5421, 5373, 5372, 2690])).
% 11.63/11.79 tff(5423,plain,
% 11.63/11.79 (((~![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_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))),
% 11.63/11.79 inference(rewrite,[status(thm)],[])).
% 11.63/11.79 tff(5424,plain,
% 11.63/11.79 ((~![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_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))),
% 11.63/11.79 inference(quant_inst,[status(thm)],[])).
% 11.63/11.79 tff(5425,plain,
% 11.63/11.79 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7) | m_c_h_element_v_in2(c_e_h_3, c_e, s7)),
% 11.63/11.79 inference(modus_ponens,[status(thm)],[5424, 5423])).
% 11.63/11.79 tff(5426,plain,
% 11.63/11.79 ((~node16(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7)),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5425, 377, 5372])).
% 11.63/11.79 tff(5427,plain,
% 11.63/11.79 (m_c_h_element_v_in1(c_e_h_3, c_e, s7)),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5426, 5422])).
% 11.63/11.79 tff(5428,plain,
% 11.63/11.79 (~node17(c_e_h_3, c_e, s7)),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5407, 5427])).
% 11.63/11.79 tff(5429,plain,
% 11.63/11.79 (node18(c_e_h_3, c_e, s7, s8)),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5415, 5428])).
% 11.63/11.79 tff(5430,plain,
% 11.63/11.79 ($false),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5419, 296, 5373, 2690, 5429])).
% 11.63/11.79 tff(5431,plain,((~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) | m_c_h_element_v_in2(c_e_h_3, c_e, s7)), inference(lemma,lemma(discharge,[]))).
% 11.63/11.79 tff(5432,plain,
% 11.63/11.79 (m_c_h_element_v_in2(c_e_h_3, c_e, s7)),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5431, 5371, 4521])).
% 11.63/11.79 tff(5433,assumption,(m_c_h_element_v_in2(c_e_h_3, c_e, s7)), introduced(assumption)).
% 11.63/11.79 tff(5434,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s7)), introduced(assumption)).
% 11.63/11.79 tff(5435,plain,
% 11.63/11.79 (((~![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))),
% 11.63/11.79 inference(rewrite,[status(thm)],[])).
% 11.63/11.79 tff(5436,plain,
% 11.63/11.79 ((~![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))),
% 11.63/11.79 inference(quant_inst,[status(thm)],[])).
% 11.63/11.79 tff(5437,plain,
% 11.63/11.79 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7)),
% 11.63/11.79 inference(modus_ponens,[status(thm)],[5436, 5435])).
% 11.63/11.79 tff(5438,plain,
% 11.63/11.79 ($false),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5437, 1965, 5434, 5433])).
% 11.63/11.79 tff(5439,plain,(m_and_h_gate_v_out(c_e_h_3, c_i, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s7))), inference(lemma,lemma(discharge,[]))).
% 11.63/11.79 tff(5440,plain,
% 11.63/11.79 (m_and_h_gate_v_out(c_e_h_3, c_i, s7)),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5439, 5432])).
% 11.63/11.79 tff(5441,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s7)), introduced(assumption)).
% 11.63/11.79 tff(5442,assumption,(node22(c_e_h_3, c_i, s6, s7)), introduced(assumption)).
% 11.63/11.79 tff(5443,plain,
% 11.63/11.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, 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))),
% 11.63/11.79 inference(rewrite,[status(thm)],[])).
% 11.63/11.79 tff(5444,plain,
% 11.63/11.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, 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))),
% 11.63/11.79 inference(quant_inst,[status(thm)],[])).
% 11.63/11.79 tff(5445,plain,
% 11.63/11.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | (~node22(c_e_h_3, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6)),
% 11.63/11.79 inference(modus_ponens,[status(thm)],[5444, 5443])).
% 11.63/11.79 tff(5446,plain,
% 11.63/11.79 ($false),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5445, 273, 5442, 2768, 5441])).
% 11.63/11.79 tff(5447,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,[]))).
% 11.63/11.79 tff(5448,plain,
% 11.63/11.79 (~node22(c_e_h_3, c_i, s6, s7)),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5447, 5441, 2768])).
% 11.63/11.79 tff(5449,assumption,(~node20(c_e_h_3, c_i, s6)), introduced(assumption)).
% 11.63/11.79 tff(5450,assumption,(node21(c_e_h_3, c_i, s6, s7)), introduced(assumption)).
% 11.63/11.79 tff(5451,plain,
% 11.63/11.79 (((~![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)))) | ((~node21(c_e_h_3, c_i, s6, s7)) | node20(c_e_h_3, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_i, 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)))) | (~node21(c_e_h_3, c_i, s6, s7)) | node20(c_e_h_3, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)))),
% 11.63/11.79 inference(rewrite,[status(thm)],[])).
% 11.63/11.79 tff(5452,plain,
% 11.63/11.79 ((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))) <=> ((~node21(c_e_h_3, c_i, s6, s7)) | node20(c_e_h_3, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)))),
% 11.63/11.79 inference(rewrite,[status(thm)],[])).
% 11.63/11.79 tff(5453,plain,
% 11.63/11.79 (((~![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_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)))) | ((~node21(c_e_h_3, c_i, s6, s7)) | node20(c_e_h_3, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7))))),
% 11.63/11.79 inference(monotonicity,[status(thm)],[5452])).
% 11.63/11.79 tff(5454,plain,
% 11.63/11.79 (((~![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_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)))) | (~node21(c_e_h_3, c_i, s6, s7)) | node20(c_e_h_3, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)))),
% 11.63/11.79 inference(transitivity,[status(thm)],[5453, 5451])).
% 11.63/11.79 tff(5455,plain,
% 11.63/11.79 ((~![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_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)))),
% 11.63/11.79 inference(quant_inst,[status(thm)],[])).
% 11.63/11.79 tff(5456,plain,
% 11.63/11.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_3, c_i, s6, s7)) | node20(c_e_h_3, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7))),
% 11.63/11.79 inference(modus_ponens,[status(thm)],[5455, 5454])).
% 11.63/11.79 tff(5457,plain,
% 11.63/11.79 ($false),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5456, 228, 5450, 5441, 5449])).
% 11.63/11.79 tff(5458,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,[]))).
% 11.63/11.79 tff(5459,plain,
% 11.63/11.79 (~node21(c_e_h_3, c_i, s6, s7)),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5458, 5441, 5449])).
% 11.63/11.79 tff(5460,plain,
% 11.63/11.79 (((~![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))),
% 11.63/11.79 inference(rewrite,[status(thm)],[])).
% 11.63/11.79 tff(5461,plain,
% 11.63/11.79 ((~![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))),
% 11.63/11.79 inference(quant_inst,[status(thm)],[])).
% 11.63/11.79 tff(5462,plain,
% 11.63/11.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_3, c_i, s6, s7) | node22(c_e_h_3, c_i, s6, s7)),
% 11.63/11.79 inference(modus_ponens,[status(thm)],[5461, 5460])).
% 11.63/11.79 tff(5463,plain,
% 11.63/11.79 (node21(c_e_h_3, c_i, s6, s7) | node22(c_e_h_3, c_i, s6, s7)),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5462, 247, 2649])).
% 11.63/11.79 tff(5464,plain,
% 11.63/11.79 ($false),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5463, 5459, 5448])).
% 11.63/11.79 tff(5465,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,[]))).
% 11.63/11.79 tff(5466,plain,
% 11.63/11.79 (node20(c_e_h_3, c_i, s6)),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5465, 5440, 4516])).
% 11.63/11.79 tff(5467,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_i, s6)), introduced(assumption)).
% 11.63/11.79 tff(5468,assumption,(node20(c_e_h_3, c_i, s6)), introduced(assumption)).
% 11.63/11.79 tff(5469,plain,
% 11.63/11.79 (((~![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))),
% 11.63/11.79 inference(rewrite,[status(thm)],[])).
% 11.63/11.79 tff(5470,plain,
% 11.63/11.79 ((~![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))),
% 11.63/11.79 inference(quant_inst,[status(thm)],[])).
% 11.63/11.79 tff(5471,plain,
% 11.63/11.79 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s6)),
% 11.63/11.79 inference(modus_ponens,[status(thm)],[5470, 5469])).
% 11.63/11.79 tff(5472,plain,
% 11.63/11.79 ($false),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5471, 213, 5468, 5467])).
% 11.63/11.79 tff(5473,plain,((~node20(c_e_h_3, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s6)), inference(lemma,lemma(discharge,[]))).
% 11.63/11.79 tff(5474,plain,
% 11.63/11.79 (m_and_h_gate_v_in1(c_e_h_3, c_i, s6)),
% 11.63/11.79 inference(unit_resolution,[status(thm)],[5473, 5466])).
% 11.63/11.80 tff(5475,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_i, s6)), introduced(assumption)).
% 11.63/11.80 tff(5476,assumption,(~m_c_h_element_v_out(c_e_h_3, c_h, s6)), introduced(assumption)).
% 11.63/11.80 tff(5477,plain,
% 11.63/11.80 (((~![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))),
% 11.63/11.80 inference(rewrite,[status(thm)],[])).
% 11.63/11.80 tff(5478,plain,
% 11.63/11.80 ((~![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))),
% 11.63/11.80 inference(quant_inst,[status(thm)],[])).
% 11.63/11.80 tff(5479,plain,
% 11.63/11.80 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s6)),
% 11.63/11.80 inference(modus_ponens,[status(thm)],[5478, 5477])).
% 11.63/11.80 tff(5480,plain,
% 11.63/11.80 ($false),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5479, 503, 5476, 5475])).
% 11.63/11.80 tff(5481,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 11.63/11.80 tff(5482,plain,
% 11.63/11.80 (m_c_h_element_v_out(c_e_h_3, c_h, s6)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5481, 5474])).
% 11.63/11.80 tff(5483,assumption,(node18(c_e_h_3, c_h, s5, s6)), introduced(assumption)).
% 11.63/11.80 tff(5484,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s6)), introduced(assumption)).
% 11.63/11.80 tff(5485,plain,
% 11.63/11.80 (((~![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)))) | ((~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)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $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_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)))),
% 11.63/11.80 inference(rewrite,[status(thm)],[])).
% 11.63/11.80 tff(5486,plain,
% 11.63/11.80 (((~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))) <=> ((~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)))),
% 11.63/11.80 inference(rewrite,[status(thm)],[])).
% 11.63/11.80 tff(5487,plain,
% 11.63/11.80 (((~![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_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)))) | ((~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))))),
% 11.63/11.80 inference(monotonicity,[status(thm)],[5486])).
% 11.63/11.80 tff(5488,plain,
% 11.63/11.80 (((~![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_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)))) | (~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)))),
% 11.63/11.80 inference(transitivity,[status(thm)],[5487, 5485])).
% 11.63/11.80 tff(5489,plain,
% 11.63/11.80 ((~![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_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)))),
% 11.63/11.80 inference(quant_inst,[status(thm)],[])).
% 11.63/11.80 tff(5490,plain,
% 11.63/11.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_3, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6))),
% 11.63/11.80 inference(modus_ponens,[status(thm)],[5489, 5488])).
% 11.63/11.80 tff(5491,plain,
% 11.63/11.80 ($false),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5490, 296, 4474, 5484, 5483])).
% 11.63/11.80 tff(5492,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,[]))).
% 11.63/11.80 tff(5493,plain,
% 11.63/11.80 (~node18(c_e_h_3, c_h, s5, s6)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5492, 5482, 4474])).
% 11.63/11.80 tff(5494,assumption,(~node19(c_e_h_3, c_h, s5, s6)), introduced(assumption)).
% 11.63/11.80 tff(5495,plain,
% 11.63/11.80 (((~![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))),
% 11.63/11.80 inference(rewrite,[status(thm)],[])).
% 11.63/11.80 tff(5496,plain,
% 11.63/11.80 ((~![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))),
% 11.63/11.80 inference(quant_inst,[status(thm)],[])).
% 11.63/11.80 tff(5497,plain,
% 11.63/11.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_3, c_h, s5, s6)),
% 11.63/11.80 inference(modus_ponens,[status(thm)],[5496, 5495])).
% 11.63/11.80 tff(5498,plain,
% 11.63/11.80 ($false),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5497, 312, 2348, 5494])).
% 11.63/11.80 tff(5499,plain,(node19(c_e_h_3, c_h, s5, s6)), inference(lemma,lemma(discharge,[]))).
% 11.63/11.80 tff(5500,plain,
% 11.63/11.80 (((~![Y: $i, 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) | node18(c_e_h_3, c_h, s5, s6) | (~node19(c_e_h_3, c_h, s5, s6)))),
% 11.63/11.80 inference(rewrite,[status(thm)],[])).
% 11.63/11.80 tff(5501,plain,
% 11.63/11.80 ((~![Y: $i, 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)))),
% 11.63/11.80 inference(quant_inst,[status(thm)],[])).
% 11.63/11.80 tff(5502,plain,
% 11.63/11.80 ((~![Y: $i, 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))),
% 11.63/11.80 inference(modus_ponens,[status(thm)],[5501, 5500])).
% 11.63/11.80 tff(5503,plain,
% 11.63/11.80 (node17(c_e_h_3, c_h, s5) | node18(c_e_h_3, c_h, s5, s6)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5502, 326, 5499])).
% 11.63/11.80 tff(5504,plain,
% 11.63/11.80 (node17(c_e_h_3, c_h, s5)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5503, 5493])).
% 11.63/11.80 tff(5505,assumption,(node15(c_e_h_3, c_h, s5, s6)), introduced(assumption)).
% 11.63/11.80 tff(5506,plain,
% 11.63/11.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 11.63/11.80 inference(rewrite,[status(thm)],[])).
% 11.63/11.80 tff(5507,plain,
% 11.63/11.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 11.63/11.80 inference(quant_inst,[status(thm)],[])).
% 11.63/11.80 tff(5508,plain,
% 11.63/11.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node15(c_e_h_3, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s5)),
% 11.63/11.80 inference(modus_ponens,[status(thm)],[5507, 5506])).
% 11.63/11.80 tff(5509,plain,
% 11.63/11.80 ($false),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5508, 393, 4474, 5484, 5505])).
% 11.63/11.80 tff(5510,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,[]))).
% 11.63/11.80 tff(5511,plain,
% 11.63/11.80 (~node15(c_e_h_3, c_h, s5, s6)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5510, 5482, 4474])).
% 11.63/11.80 tff(5512,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_h, s5)), introduced(assumption)).
% 11.63/11.80 tff(5513,assumption,(node14(c_e_h_3, c_h, s5, s6)), introduced(assumption)).
% 11.63/11.80 tff(5514,plain,
% 11.63/11.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_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)))),
% 11.63/11.80 inference(rewrite,[status(thm)],[])).
% 11.63/11.80 tff(5515,plain,
% 11.63/11.80 (((~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)))),
% 11.63/11.80 inference(rewrite,[status(thm)],[])).
% 11.63/11.80 tff(5516,plain,
% 11.63/11.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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))))),
% 11.63/11.80 inference(monotonicity,[status(thm)],[5515])).
% 11.63/11.80 tff(5517,plain,
% 11.63/11.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))),
% 11.63/11.80 inference(transitivity,[status(thm)],[5516, 5514])).
% 11.63/11.80 tff(5518,plain,
% 11.63/11.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))),
% 11.63/11.80 inference(quant_inst,[status(thm)],[])).
% 11.63/11.80 tff(5519,plain,
% 11.63/11.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node14(c_e_h_3, c_h, s5, s6))),
% 11.63/11.80 inference(modus_ponens,[status(thm)],[5518, 5517])).
% 11.63/11.80 tff(5520,plain,
% 11.63/11.80 ($false),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5519, 427, 5484, 5512, 5513])).
% 11.63/11.80 tff(5521,plain,((~node14(c_e_h_3, c_h, s5, s6)) | (~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,[]))).
% 11.63/11.80 tff(5522,plain,
% 11.63/11.80 (~node14(c_e_h_3, c_h, s5, s6)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5521, 5482, 5512])).
% 11.63/11.80 tff(5523,plain,
% 11.63/11.80 (((~![Y: $i, I0: $i, X: $i, I1: $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) | 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)))),
% 11.63/11.80 inference(rewrite,[status(thm)],[])).
% 11.63/11.80 tff(5524,plain,
% 11.63/11.80 ((~![Y: $i, I0: $i, X: $i, I1: $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)))),
% 11.63/11.80 inference(quant_inst,[status(thm)],[])).
% 11.63/11.80 tff(5525,plain,
% 11.63/11.80 ((~![Y: $i, I0: $i, X: $i, I1: $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))),
% 11.63/11.80 inference(modus_ponens,[status(thm)],[5524, 5523])).
% 11.63/11.80 tff(5526,plain,
% 11.63/11.80 (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)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5525, 409, 5499])).
% 11.63/11.80 tff(5527,plain,
% 11.63/11.80 (node16(c_e_h_3, c_h, s5)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5526, 5522, 5511])).
% 11.63/11.80 tff(5528,assumption,(node17(c_e_h_3, c_h, s5)), introduced(assumption)).
% 11.63/11.80 tff(5529,assumption,(node16(c_e_h_3, c_h, s5)), introduced(assumption)).
% 11.63/11.80 tff(5530,plain,
% 11.63/11.80 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, 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_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)))),
% 11.63/11.80 inference(rewrite,[status(thm)],[])).
% 11.63/11.80 tff(5531,plain,
% 11.63/11.80 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, 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)))),
% 11.63/11.80 inference(quant_inst,[status(thm)],[])).
% 11.63/11.80 tff(5532,plain,
% 11.63/11.80 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, 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))),
% 11.63/11.80 inference(modus_ponens,[status(thm)],[5531, 5530])).
% 11.63/11.80 tff(5533,plain,
% 11.63/11.80 (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))),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5532, 2125, 5528])).
% 11.63/11.80 tff(5534,plain,
% 11.63/11.80 (~m_c_h_element_v_in2(c_e_h_3, c_h, s5)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5533, 5512])).
% 11.63/11.80 tff(5535,plain,
% 11.63/11.80 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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))),
% 11.63/11.80 inference(rewrite,[status(thm)],[])).
% 11.63/11.80 tff(5536,plain,
% 11.63/11.80 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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))),
% 11.63/11.80 inference(quant_inst,[status(thm)],[])).
% 11.63/11.80 tff(5537,plain,
% 11.63/11.80 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | m_c_h_element_v_in2(c_e_h_3, c_h, s5)),
% 11.63/11.80 inference(modus_ponens,[status(thm)],[5536, 5535])).
% 11.63/11.80 tff(5538,plain,
% 11.63/11.80 (m_c_h_element_v_in1(c_e_h_3, c_h, s5) | m_c_h_element_v_in2(c_e_h_3, c_h, s5)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5537, 377, 5529])).
% 11.63/11.80 tff(5539,plain,
% 11.63/11.80 ($false),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5538, 5534, 5512])).
% 11.63/11.80 tff(5540,plain,(m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~node16(c_e_h_3, c_h, s5)) | (~node17(c_e_h_3, c_h, s5))), inference(lemma,lemma(discharge,[]))).
% 11.63/11.80 tff(5541,plain,
% 11.63/11.80 (m_c_h_element_v_in1(c_e_h_3, c_h, s5)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5540, 5529, 5528])).
% 11.63/11.80 tff(5542,plain,
% 11.63/11.80 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, 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_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)))),
% 11.63/11.80 inference(rewrite,[status(thm)],[])).
% 11.63/11.80 tff(5543,plain,
% 11.63/11.80 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, 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)))),
% 11.63/11.80 inference(quant_inst,[status(thm)],[])).
% 11.63/11.80 tff(5544,plain,
% 11.63/11.80 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, 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))),
% 11.63/11.80 inference(modus_ponens,[status(thm)],[5543, 5542])).
% 11.63/11.80 tff(5545,plain,
% 11.63/11.80 ((~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)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5544, 359, 5528])).
% 11.63/11.80 tff(5546,plain,
% 11.63/11.80 (m_c_h_element_v_in2(c_e_h_3, c_h, s5)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5545, 5541])).
% 11.63/11.80 tff(5547,plain,
% 11.63/11.80 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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)))),
% 11.63/11.80 inference(rewrite,[status(thm)],[])).
% 11.63/11.80 tff(5548,plain,
% 11.63/11.80 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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)))),
% 11.63/11.80 inference(quant_inst,[status(thm)],[])).
% 11.63/11.80 tff(5549,plain,
% 11.63/11.80 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_3, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s5)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s5))),
% 11.63/11.80 inference(modus_ponens,[status(thm)],[5548, 5547])).
% 11.63/11.80 tff(5550,plain,
% 11.63/11.80 ((~m_c_h_element_v_in1(c_e_h_3, c_h, s5)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s5))),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5549, 2142, 5529])).
% 11.63/11.80 tff(5551,plain,
% 11.63/11.80 ($false),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5550, 5546, 5541])).
% 11.63/11.80 tff(5552,plain,((~node16(c_e_h_3, c_h, s5)) | (~node17(c_e_h_3, c_h, s5))), inference(lemma,lemma(discharge,[]))).
% 11.63/11.80 tff(5553,plain,
% 11.63/11.80 ($false),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5552, 5527, 5504])).
% 11.63/11.80 tff(5554,plain,(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, s5) | node24(s9) | node23(s9) | node23(s8) | node24(s8)), inference(lemma,lemma(discharge,[]))).
% 11.63/11.80 tff(5555,plain,
% 11.63/11.80 (m_c_h_element_v_in1(c_e_h_3, c_h, s5)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5554, 4509, 4474, 4498, 4479, 4478])).
% 11.63/11.80 tff(5556,plain,
% 11.63/11.80 ((~m_c_h_element_v_in1(c_e_h_3, c_h, s5)) | (~node17(c_e_h_3, c_h, s5))),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5544, 359, 1556])).
% 11.63/11.80 tff(5557,plain,
% 11.63/11.80 (~node17(c_e_h_3, c_h, s5)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5556, 5555])).
% 11.63/11.80 tff(5558,plain,
% 11.63/11.80 (node18(c_e_h_3, c_h, s5, s6)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5503, 5557])).
% 11.63/11.80 tff(5559,plain,
% 11.63/11.80 (~m_c_h_element_v_out(c_e_h_3, c_h, s6)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5492, 5558, 4474])).
% 11.63/11.80 tff(5560,plain,
% 11.63/11.80 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s6)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5481, 5559])).
% 11.63/11.80 tff(5561,plain,
% 11.63/11.80 (~m_and_h_gate_v_out(c_e_h_3, c_r, s9)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5354, 4480, 5337])).
% 11.63/11.80 tff(5562,plain,
% 11.63/11.80 (~m_user_v_ack(c_e_h_3, c_u, s9)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5327, 5561])).
% 11.63/11.80 tff(5563,plain,
% 11.63/11.80 (~node25(s9)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5319, 4538, 5562])).
% 11.63/11.80 tff(5564,plain,
% 11.63/11.80 (~node26(s9)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5315, 5563])).
% 11.63/11.80 tff(5565,plain,
% 11.63/11.80 (~node25(s8)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[4541, 4538, 4484])).
% 11.63/11.80 tff(5566,plain,
% 11.63/11.80 (~node26(s8)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[4557, 5565])).
% 11.63/11.80 tff(5567,plain,
% 11.63/11.80 ($false),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5308, 5566, 5564])).
% 11.63/11.80 tff(5568,plain,(m_and_h_gate_v_out(c_e_h_3, c_r, s8) | node23(s8) | node24(s8) | node24(s9) | node23(s9) | node20(c_e_h_3, c_r, s8)), inference(lemma,lemma(discharge,[]))).
% 11.63/11.80 tff(5569,plain,
% 11.63/11.80 (node20(c_e_h_3, c_r, s8)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5568, 4478, 4480, 4479, 4509, 4498])).
% 11.63/11.80 tff(5570,plain,
% 11.63/11.80 (m_and_h_gate_v_in1(c_e_h_3, c_r, s8)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5362, 5569])).
% 11.63/11.80 tff(5571,plain,
% 11.63/11.80 (m_c_h_element_v_out(c_e_h_3, c_e, s8)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5370, 5570])).
% 11.63/11.80 tff(5572,plain,
% 11.63/11.80 (m_c_h_element_v_in2(c_e_h_3, c_e, s7)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5431, 5571, 4521])).
% 11.63/11.80 tff(5573,plain,
% 11.63/11.80 (m_and_h_gate_v_out(c_e_h_3, c_i, s7)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5439, 5572])).
% 11.63/11.80 tff(5574,plain,
% 11.63/11.80 (node20(c_e_h_3, c_i, s6)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5465, 5573, 4516])).
% 11.63/11.80 tff(5575,plain,
% 11.63/11.80 ($false),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5473, 5574, 5560])).
% 11.63/11.80 tff(5576,plain,(m_user_v_ack(c_e_h_1, c_u, s9) | m_c_h_element_v_out(c_e_h_3, c_h, s5) | m_c_h_element_v_in2(c_e_h_3, c_h, s5) | node23(s8) | m_and_h_gate_v_out(c_e_h_3, c_r, s8)), inference(lemma,lemma(discharge,[]))).
% 11.63/11.80 tff(5577,plain,
% 11.63/11.80 (m_user_v_ack(c_e_h_1, c_u, s9) | m_c_h_element_v_out(c_e_h_3, c_h, s5) | m_c_h_element_v_in2(c_e_h_3, c_h, s5) | m_and_h_gate_v_out(c_e_h_3, c_r, s8)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5576, 4473])).
% 11.63/11.80 tff(5578,plain,
% 11.63/11.80 ($false),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5577, 2883, 2875, 1557, 1556])).
% 11.63/11.80 tff(5579,plain,(m_c_h_element_v_in2(c_e_h_3, c_h, s4) | m_user_v_ack(c_e_h_1, c_u, s9) | m_c_h_element_v_in2(c_e_h_3, c_h, s5)), inference(lemma,lemma(discharge,[]))).
% 11.63/11.80 tff(5580,plain,
% 11.63/11.80 (m_user_v_ack(c_e_h_1, c_u, s9)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5579, 1555, 1123])).
% 11.63/11.80 tff(5581,plain,
% 11.63/11.80 (((~![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))),
% 11.63/11.80 inference(rewrite,[status(thm)],[])).
% 11.63/11.80 tff(5582,plain,
% 11.63/11.80 ((~![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))),
% 11.63/11.80 inference(quant_inst,[status(thm)],[])).
% 11.63/11.80 tff(5583,plain,
% 11.63/11.80 ((~![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)),
% 11.63/11.80 inference(modus_ponens,[status(thm)],[5582, 5581])).
% 11.63/11.80 tff(5584,plain,
% 11.63/11.80 (m_and_h_gate_v_out(c_e_h_1, c_r, s9)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5583, 4458, 5580])).
% 11.63/11.80 tff(5585,assumption,(~node20(c_e_h_1, c_r, s8)), introduced(assumption)).
% 11.63/11.80 tff(5586,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s9)), introduced(assumption)).
% 11.63/11.80 tff(5587,assumption,(node21(c_e_h_1, c_r, s8, s9)), introduced(assumption)).
% 11.63/11.80 tff(5588,plain,
% 11.63/11.80 (((~![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, 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)))) | 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)))),
% 11.63/11.80 inference(rewrite,[status(thm)],[])).
% 11.63/11.80 tff(5589,plain,
% 11.63/11.80 ((~![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, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | (~node21(c_e_h_1, c_r, s8, s9)))),
% 11.63/11.80 inference(quant_inst,[status(thm)],[])).
% 11.63/11.80 tff(5590,plain,
% 11.63/11.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | (~node21(c_e_h_1, c_r, s8, s9))),
% 11.63/11.80 inference(modus_ponens,[status(thm)],[5589, 5588])).
% 11.63/11.80 tff(5591,plain,
% 11.63/11.80 ($false),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5590, 228, 5586, 5587, 5585])).
% 11.63/11.80 tff(5592,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,[]))).
% 11.63/11.80 tff(5593,plain,
% 11.63/11.80 (~node21(c_e_h_1, c_r, s8, s9)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5592, 5586, 5585])).
% 11.63/11.80 tff(5594,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s8)), introduced(assumption)).
% 11.63/11.80 tff(5595,assumption,(node22(c_e_h_1, c_r, s8, s9)), introduced(assumption)).
% 11.63/11.80 tff(5596,plain,
% 11.63/11.80 (((~![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, 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))),
% 11.63/11.80 inference(rewrite,[status(thm)],[])).
% 11.63/11.80 tff(5597,plain,
% 11.63/11.80 ((~![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, s9)) | (~node22(c_e_h_1, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_r, s8))),
% 11.63/11.80 inference(quant_inst,[status(thm)],[])).
% 11.63/11.80 tff(5598,plain,
% 11.63/11.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | (~node22(c_e_h_1, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_r, s8)),
% 11.63/11.80 inference(modus_ponens,[status(thm)],[5597, 5596])).
% 11.63/11.80 tff(5599,plain,
% 11.63/11.80 ($false),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5598, 273, 5594, 5586, 5595])).
% 11.63/11.80 tff(5600,plain,((~node22(c_e_h_1, c_r, s8, s9)) | 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, s9))), inference(lemma,lemma(discharge,[]))).
% 11.63/11.80 tff(5601,plain,
% 11.63/11.80 (~node22(c_e_h_1, c_r, s8, s9)),
% 11.63/11.80 inference(unit_resolution,[status(thm)],[5600, 5586, 5594])).
% 11.63/11.80 tff(5602,plain,
% 11.63/11.80 (((~![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))),
% 11.63/11.80 inference(rewrite,[status(thm)],[])).
% 11.63/11.80 tff(5603,plain,
% 11.63/11.80 ((~![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))),
% 11.63/11.80 inference(quant_inst,[status(thm)],[])).
% 11.63/11.80 tff(5604,plain,
% 11.63/11.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_1, c_r, s8, s9) | node22(c_e_h_1, c_r, s8, s9)),
% 11.63/11.81 inference(modus_ponens,[status(thm)],[5603, 5602])).
% 11.63/11.81 tff(5605,plain,
% 11.63/11.81 (node21(c_e_h_1, c_r, s8, s9) | node22(c_e_h_1, c_r, s8, s9)),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5604, 247, 5348])).
% 11.63/11.81 tff(5606,plain,
% 11.63/11.81 ($false),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5605, 5601, 5593])).
% 11.63/11.81 tff(5607,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) | node20(c_e_h_1, c_r, s8)), inference(lemma,lemma(discharge,[]))).
% 11.63/11.81 tff(5608,plain,
% 11.63/11.81 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | node20(c_e_h_1, c_r, s8)),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5607, 4451])).
% 11.63/11.81 tff(5609,plain,
% 11.63/11.81 (node20(c_e_h_1, c_r, s8)),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5608, 5584])).
% 11.63/11.81 tff(5610,plain,
% 11.63/11.81 (((~![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))),
% 11.63/11.81 inference(rewrite,[status(thm)],[])).
% 11.63/11.81 tff(5611,plain,
% 11.63/11.81 ((~![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))),
% 11.63/11.81 inference(quant_inst,[status(thm)],[])).
% 11.63/11.81 tff(5612,plain,
% 11.63/11.81 ((~![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)),
% 11.63/11.81 inference(modus_ponens,[status(thm)],[5611, 5610])).
% 11.63/11.81 tff(5613,plain,
% 11.63/11.81 (m_and_h_gate_v_in2(c_e_h_1, c_r, s8)),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5612, 173, 5609])).
% 11.63/11.81 tff(5614,plain,
% 11.63/11.81 (((~![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))),
% 11.63/11.81 inference(rewrite,[status(thm)],[])).
% 11.63/11.81 tff(5615,plain,
% 11.63/11.81 ((~![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))),
% 11.63/11.81 inference(quant_inst,[status(thm)],[])).
% 11.63/11.81 tff(5616,plain,
% 11.63/11.81 ((~![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)),
% 11.63/11.81 inference(modus_ponens,[status(thm)],[5615, 5614])).
% 11.63/11.81 tff(5617,plain,
% 11.63/11.81 (m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5616, 4211, 5613])).
% 11.63/11.81 tff(5618,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)), introduced(assumption)).
% 11.63/11.81 tff(5619,assumption,(node11(c_e_h_1, c_m, s7, s8)), introduced(assumption)).
% 11.63/11.81 tff(5620,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)), introduced(assumption)).
% 11.63/11.81 tff(5621,plain,
% 11.63/11.81 (((~![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_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))),
% 11.63/11.81 inference(rewrite,[status(thm)],[])).
% 11.63/11.81 tff(5622,plain,
% 11.63/11.81 ((~![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_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))),
% 11.63/11.81 inference(quant_inst,[status(thm)],[])).
% 11.63/11.81 tff(5623,plain,
% 11.63/11.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | (~node11(c_e_h_1, c_m, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)),
% 11.63/11.81 inference(modus_ponens,[status(thm)],[5622, 5621])).
% 11.63/11.81 tff(5624,plain,
% 11.63/11.81 ($false),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5623, 147, 5620, 5619, 5618])).
% 11.63/11.81 tff(5625,plain,((~node11(c_e_h_1, c_m, s7, s8)) | 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, s8))), inference(lemma,lemma(discharge,[]))).
% 11.63/11.81 tff(5626,plain,
% 11.63/11.81 ((~node11(c_e_h_1, c_m, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5625, 4204])).
% 11.63/11.81 tff(5627,plain,
% 11.63/11.81 (~node11(c_e_h_1, c_m, s7, s8)),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5626, 5617])).
% 11.63/11.81 tff(5628,plain,
% 11.63/11.81 (((~![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))),
% 11.63/11.81 inference(rewrite,[status(thm)],[])).
% 11.63/11.81 tff(5629,plain,
% 11.63/11.81 ((~![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))),
% 11.63/11.81 inference(quant_inst,[status(thm)],[])).
% 11.63/11.81 tff(5630,plain,
% 11.63/11.81 ((~![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)),
% 11.63/11.81 inference(modus_ponens,[status(thm)],[5629, 5628])).
% 11.63/11.81 tff(5631,plain,
% 11.63/11.81 (node10(c_e_h_1, c_m, s7, s8) | node11(c_e_h_1, c_m, s7, s8)),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5630, 110, 2669])).
% 11.63/11.81 tff(5632,plain,
% 11.63/11.81 (node10(c_e_h_1, c_m, s7, s8)),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5631, 5627])).
% 11.63/11.81 tff(5633,plain,
% 11.63/11.81 (((~![Y: $i, I0: $i, 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, s8)) | node9(c_e_h_1, c_m, s7) | (~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)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | node9(c_e_h_1, c_m, s7) | (~node10(c_e_h_1, c_m, s7, s8)))),
% 11.63/11.81 inference(rewrite,[status(thm)],[])).
% 11.63/11.81 tff(5634,plain,
% 11.63/11.81 ((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))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | node9(c_e_h_1, c_m, s7) | (~node10(c_e_h_1, c_m, s7, s8)))),
% 11.63/11.81 inference(rewrite,[status(thm)],[])).
% 11.63/11.81 tff(5635,plain,
% 11.63/11.81 (((~![Y: $i, I0: $i, 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)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | node9(c_e_h_1, c_m, s7) | (~node10(c_e_h_1, c_m, s7, s8))))),
% 11.63/11.81 inference(monotonicity,[status(thm)],[5634])).
% 11.63/11.81 tff(5636,plain,
% 11.63/11.81 (((~![Y: $i, I0: $i, 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)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | node9(c_e_h_1, c_m, s7) | (~node10(c_e_h_1, c_m, s7, s8)))),
% 11.63/11.81 inference(transitivity,[status(thm)],[5635, 5633])).
% 11.63/11.81 tff(5637,plain,
% 11.63/11.81 ((~![Y: $i, I0: $i, 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)))),
% 11.63/11.81 inference(quant_inst,[status(thm)],[])).
% 11.63/11.81 tff(5638,plain,
% 11.63/11.81 ((~![Y: $i, I0: $i, 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, s8)) | node9(c_e_h_1, c_m, s7) | (~node10(c_e_h_1, c_m, s7, s8))),
% 11.63/11.81 inference(modus_ponens,[status(thm)],[5637, 5636])).
% 11.63/11.81 tff(5639,plain,
% 11.63/11.81 (node9(c_e_h_1, c_m, s7)),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5638, 77, 5632, 5617])).
% 11.63/11.81 tff(5640,plain,
% 11.63/11.81 (((~![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))),
% 11.63/11.81 inference(rewrite,[status(thm)],[])).
% 11.63/11.81 tff(5641,plain,
% 11.63/11.81 ((~![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))),
% 11.63/11.81 inference(quant_inst,[status(thm)],[])).
% 11.63/11.81 tff(5642,plain,
% 11.63/11.81 ((~![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)),
% 11.63/11.81 inference(modus_ponens,[status(thm)],[5641, 5640])).
% 11.63/11.81 tff(5643,plain,
% 11.63/11.81 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s7)),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5642, 63, 5639])).
% 11.63/11.81 tff(5644,plain,
% 11.63/11.81 (((~![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)))),
% 11.63/11.81 inference(rewrite,[status(thm)],[])).
% 11.63/11.81 tff(5645,plain,
% 11.63/11.81 ((~![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)))),
% 11.63/11.81 inference(quant_inst,[status(thm)],[])).
% 11.63/11.81 tff(5646,plain,
% 11.63/11.81 ((~![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))),
% 11.63/11.81 inference(modus_ponens,[status(thm)],[5645, 5644])).
% 11.63/11.81 tff(5647,plain,
% 11.63/11.81 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5646, 49, 5643])).
% 11.63/11.81 tff(5648,plain,
% 11.63/11.81 (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))),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[4140, 4078])).
% 11.63/11.81 tff(5649,plain,
% 11.63/11.81 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5648, 3770])).
% 11.63/11.81 tff(5650,plain,
% 11.63/11.81 (((~![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, 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))),
% 11.63/11.81 inference(rewrite,[status(thm)],[])).
% 11.63/11.81 tff(5651,plain,
% 11.63/11.81 ((~![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, s6) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))),
% 11.63/11.81 inference(quant_inst,[status(thm)],[])).
% 11.63/11.81 tff(5652,plain,
% 11.63/11.81 ((~![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, s6) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)),
% 11.63/11.81 inference(modus_ponens,[status(thm)],[5651, 5650])).
% 11.63/11.81 tff(5653,plain,
% 11.63/11.81 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5652, 3794, 4400])).
% 11.63/11.81 tff(5654,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)), introduced(assumption)).
% 11.63/11.81 tff(5655,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)), introduced(assumption)).
% 11.63/11.81 tff(5656,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)), introduced(assumption)).
% 11.63/11.81 tff(5657,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)), introduced(assumption)).
% 11.63/11.81 tff(5658,assumption,(node11(c_e_h_1, c_n, s6, s7)), introduced(assumption)).
% 11.63/11.81 tff(5659,plain,
% 11.63/11.81 (((~![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, 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) | (~node11(c_e_h_1, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)))),
% 11.63/11.81 inference(rewrite,[status(thm)],[])).
% 11.63/11.81 tff(5660,plain,
% 11.63/11.81 ((~![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, 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)))),
% 11.63/11.81 inference(quant_inst,[status(thm)],[])).
% 11.63/11.81 tff(5661,plain,
% 11.63/11.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~node11(c_e_h_1, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6))),
% 11.63/11.81 inference(modus_ponens,[status(thm)],[5660, 5659])).
% 11.63/11.81 tff(5662,plain,
% 11.63/11.81 ($false),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5661, 3810, 5656, 5657, 5658])).
% 11.63/11.81 tff(5663,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,[]))).
% 11.63/11.81 tff(5664,plain,
% 11.63/11.81 (~node11(c_e_h_1, c_n, s6, s7)),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5663, 5657, 5656])).
% 11.63/11.81 tff(5665,plain,
% 11.63/11.81 (((~![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))),
% 11.63/11.81 inference(rewrite,[status(thm)],[])).
% 11.63/11.81 tff(5666,plain,
% 11.63/11.81 ((~![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))),
% 11.63/11.81 inference(quant_inst,[status(thm)],[])).
% 11.63/11.81 tff(5667,plain,
% 11.63/11.81 ((~![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)),
% 11.63/11.81 inference(modus_ponens,[status(thm)],[5666, 5665])).
% 11.63/11.81 tff(5668,plain,
% 11.63/11.81 (node10(c_e_h_1, c_n, s6, s7) | node11(c_e_h_1, c_n, s6, s7)),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5667, 110, 2649])).
% 11.63/11.81 tff(5669,plain,
% 11.63/11.81 (node10(c_e_h_1, c_n, s6, s7)),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5668, 5664])).
% 11.63/11.81 tff(5670,plain,
% 11.63/11.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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)))),
% 11.63/11.81 inference(rewrite,[status(thm)],[])).
% 11.63/11.81 tff(5671,plain,
% 11.63/11.81 (((~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)))),
% 11.63/11.81 inference(rewrite,[status(thm)],[])).
% 11.63/11.81 tff(5672,plain,
% 11.63/11.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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))))),
% 11.63/11.81 inference(monotonicity,[status(thm)],[5671])).
% 11.63/11.81 tff(5673,plain,
% 11.63/11.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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)))),
% 11.63/11.81 inference(transitivity,[status(thm)],[5672, 5670])).
% 11.63/11.81 tff(5674,plain,
% 11.63/11.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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))),
% 11.63/11.81 inference(quant_inst,[status(thm)],[])).
% 11.63/11.81 tff(5675,plain,
% 11.63/11.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)) | (~node10(c_e_h_1, c_n, s6, s7))),
% 11.63/11.81 inference(modus_ponens,[status(thm)],[5674, 5673])).
% 11.63/11.81 tff(5676,plain,
% 11.63/11.81 ($false),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5675, 3834, 5657, 5669, 5655, 5654])).
% 11.63/11.81 tff(5677,plain,(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, 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, s6))), inference(lemma,lemma(discharge,[]))).
% 11.63/11.81 tff(5678,plain,
% 11.63/11.81 (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_out(c_e_h_1, c_n, s6))),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5677, 5653])).
% 11.63/11.81 tff(5679,plain,
% 11.63/11.81 (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))),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5678, 5649])).
% 11.63/11.81 tff(5680,plain,
% 11.63/11.81 (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5679, 5647])).
% 11.63/11.81 tff(5681,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)), introduced(assumption)).
% 11.63/11.81 tff(5682,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s6)), introduced(assumption)).
% 11.63/11.81 tff(5683,plain,
% 11.63/11.81 (((~![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, 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))),
% 11.63/11.81 inference(rewrite,[status(thm)],[])).
% 11.63/11.81 tff(5684,plain,
% 11.63/11.81 ((~![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, s6) | m_c_h_element_v_out(c_e_h_1, c_e, s6))),
% 11.63/11.81 inference(quant_inst,[status(thm)],[])).
% 11.63/11.81 tff(5685,plain,
% 11.63/11.81 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6) | m_c_h_element_v_out(c_e_h_1, c_e, s6)),
% 11.63/11.81 inference(modus_ponens,[status(thm)],[5684, 5683])).
% 11.63/11.81 tff(5686,plain,
% 11.63/11.81 ($false),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5685, 3764, 5682, 5681])).
% 11.63/11.81 tff(5687,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,[]))).
% 11.63/11.81 tff(5688,plain,
% 11.63/11.81 (m_c_h_element_v_out(c_e_h_1, c_e, s6)),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5687, 5680])).
% 11.63/11.81 tff(5689,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s6)), introduced(assumption)).
% 11.63/11.81 tff(5690,assumption,(node18(c_e_h_1, c_e, s5, s6)), introduced(assumption)).
% 11.63/11.81 tff(5691,plain,
% 11.63/11.81 (((~![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_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, 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) | (~node18(c_e_h_1, c_e, s5, s6)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)))),
% 11.63/11.81 inference(rewrite,[status(thm)],[])).
% 11.63/11.81 tff(5692,plain,
% 11.63/11.81 (((~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) | (~node18(c_e_h_1, c_e, s5, s6)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)))),
% 11.63/11.81 inference(rewrite,[status(thm)],[])).
% 11.63/11.81 tff(5693,plain,
% 11.63/11.81 (((~![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_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) | (~node18(c_e_h_1, c_e, s5, s6)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6))))),
% 11.63/11.81 inference(monotonicity,[status(thm)],[5692])).
% 11.63/11.81 tff(5694,plain,
% 11.63/11.81 (((~![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_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) | (~node18(c_e_h_1, c_e, s5, s6)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)))),
% 11.63/11.81 inference(transitivity,[status(thm)],[5693, 5691])).
% 11.63/11.81 tff(5695,plain,
% 11.63/11.81 ((~![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_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)))),
% 11.63/11.81 inference(quant_inst,[status(thm)],[])).
% 11.63/11.81 tff(5696,plain,
% 11.63/11.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~node18(c_e_h_1, c_e, s5, s6)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6))),
% 11.63/11.81 inference(modus_ponens,[status(thm)],[5695, 5694])).
% 11.63/11.81 tff(5697,plain,
% 11.63/11.81 ($false),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5696, 296, 3757, 5690, 5689])).
% 11.63/11.81 tff(5698,plain,((~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))), inference(lemma,lemma(discharge,[]))).
% 11.63/11.81 tff(5699,plain,
% 11.63/11.81 (~node18(c_e_h_1, c_e, s5, s6)),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5698, 5689, 3757])).
% 11.63/11.81 tff(5700,plain,
% 11.63/11.81 (((~![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))),
% 11.63/11.81 inference(rewrite,[status(thm)],[])).
% 11.63/11.81 tff(5701,plain,
% 11.63/11.81 ((~![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))),
% 11.63/11.81 inference(quant_inst,[status(thm)],[])).
% 11.63/11.81 tff(5702,plain,
% 11.63/11.81 ((~![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)),
% 11.63/11.81 inference(modus_ponens,[status(thm)],[5701, 5700])).
% 11.63/11.81 tff(5703,plain,
% 11.63/11.81 (node19(c_e_h_1, c_e, s5, s6)),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5702, 312, 2348])).
% 11.63/11.81 tff(5704,plain,
% 11.63/11.81 (((~![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)))),
% 11.63/11.81 inference(rewrite,[status(thm)],[])).
% 11.63/11.81 tff(5705,plain,
% 11.63/11.81 ((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)))),
% 11.63/11.81 inference(rewrite,[status(thm)],[])).
% 11.63/11.81 tff(5706,plain,
% 11.63/11.81 (((~![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, 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))))),
% 11.63/11.81 inference(monotonicity,[status(thm)],[5705])).
% 11.63/11.81 tff(5707,plain,
% 11.63/11.81 (((~![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, 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)))),
% 11.63/11.81 inference(transitivity,[status(thm)],[5706, 5704])).
% 11.63/11.81 tff(5708,plain,
% 11.63/11.81 ((~![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, s5) | node18(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)))),
% 11.63/11.81 inference(quant_inst,[status(thm)],[])).
% 11.63/11.81 tff(5709,plain,
% 11.63/11.81 ((~![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))),
% 11.63/11.81 inference(modus_ponens,[status(thm)],[5708, 5707])).
% 11.63/11.81 tff(5710,plain,
% 11.63/11.81 (node18(c_e_h_1, c_e, s5, s6) | node17(c_e_h_1, c_e, s5)),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5709, 326, 5703])).
% 11.63/11.81 tff(5711,plain,
% 11.63/11.81 (node17(c_e_h_1, c_e, s5)),
% 11.63/11.81 inference(unit_resolution,[status(thm)],[5710, 5699])).
% 11.63/11.82 tff(5712,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s5)), introduced(assumption)).
% 11.63/11.82 tff(5713,plain,
% 11.63/11.82 (((~![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, 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)))),
% 11.63/11.82 inference(rewrite,[status(thm)],[])).
% 11.63/11.82 tff(5714,plain,
% 11.63/11.82 (((~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)))),
% 11.63/11.82 inference(rewrite,[status(thm)],[])).
% 11.63/11.82 tff(5715,plain,
% 11.63/11.82 (((~![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, 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))))),
% 11.63/11.82 inference(monotonicity,[status(thm)],[5714])).
% 11.63/11.82 tff(5716,plain,
% 11.63/11.82 (((~![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, 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)))),
% 11.63/11.82 inference(transitivity,[status(thm)],[5715, 5713])).
% 11.63/11.82 tff(5717,plain,
% 11.63/11.82 ((~![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, s5)) | m_c_h_element_v_in2(c_e_h_1, c_e, s5) | (~node17(c_e_h_1, c_e, s5)))),
% 11.63/11.82 inference(quant_inst,[status(thm)],[])).
% 11.63/11.82 tff(5718,plain,
% 11.63/11.82 ((~![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, s5) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5))),
% 11.63/11.82 inference(modus_ponens,[status(thm)],[5717, 5716])).
% 11.63/11.82 tff(5719,plain,
% 11.63/11.82 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5))),
% 11.63/11.82 inference(unit_resolution,[status(thm)],[5718, 359, 5712])).
% 11.63/11.82 tff(5720,plain,
% 11.63/11.82 (~m_c_h_element_v_in1(c_e_h_1, c_e, s5)),
% 11.63/11.82 inference(unit_resolution,[status(thm)],[5719, 5711])).
% 11.63/11.82 tff(5721,assumption,(node15(c_e_h_1, c_e, s5, s6)), introduced(assumption)).
% 11.63/11.82 tff(5722,plain,
% 11.63/11.82 (((~![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, 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))),
% 11.63/11.82 inference(rewrite,[status(thm)],[])).
% 11.63/11.82 tff(5723,plain,
% 11.63/11.82 ((~![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, s6)) | (~node15(c_e_h_1, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5))),
% 11.63/11.82 inference(quant_inst,[status(thm)],[])).
% 11.63/11.82 tff(5724,plain,
% 11.63/11.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node15(c_e_h_1, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5)),
% 11.63/11.82 inference(modus_ponens,[status(thm)],[5723, 5722])).
% 11.63/11.82 tff(5725,plain,
% 11.63/11.82 ($false),
% 11.63/11.82 inference(unit_resolution,[status(thm)],[5724, 393, 3757, 5721, 5689])).
% 11.63/11.82 tff(5726,plain,((~node15(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))), inference(lemma,lemma(discharge,[]))).
% 11.63/11.82 tff(5727,plain,
% 11.63/11.82 (~node15(c_e_h_1, c_e, s5, s6)),
% 11.63/11.82 inference(unit_resolution,[status(thm)],[5726, 5689, 3757])).
% 11.63/11.82 tff(5728,assumption,(node17(c_e_h_1, c_e, s5)), introduced(assumption)).
% 11.63/11.82 tff(5729,assumption,(node16(c_e_h_1, c_e, s5)), introduced(assumption)).
% 11.63/11.82 tff(5730,plain,
% 11.63/11.82 (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))),
% 11.63/11.82 inference(unit_resolution,[status(thm)],[5718, 359, 5728])).
% 11.63/11.82 tff(5731,plain,
% 11.63/11.82 (~m_c_h_element_v_in1(c_e_h_1, c_e, s5)),
% 11.63/11.82 inference(unit_resolution,[status(thm)],[5730, 5712])).
% 11.63/11.82 tff(5732,plain,
% 11.63/11.82 (((~![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_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))),
% 11.63/11.82 inference(rewrite,[status(thm)],[])).
% 11.63/11.82 tff(5733,plain,
% 11.63/11.82 ((~![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_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))),
% 11.63/11.82 inference(quant_inst,[status(thm)],[])).
% 11.63/11.82 tff(5734,plain,
% 11.63/11.82 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | m_c_h_element_v_in2(c_e_h_1, c_e, s5)),
% 11.63/11.82 inference(modus_ponens,[status(thm)],[5733, 5732])).
% 11.63/11.82 tff(5735,plain,
% 11.63/11.82 (m_c_h_element_v_in1(c_e_h_1, c_e, s5) | m_c_h_element_v_in2(c_e_h_1, c_e, s5)),
% 11.63/11.82 inference(unit_resolution,[status(thm)],[5734, 377, 5729])).
% 11.63/11.82 tff(5736,plain,
% 11.63/11.82 ($false),
% 11.63/11.82 inference(unit_resolution,[status(thm)],[5735, 5731, 5712])).
% 11.63/11.82 tff(5737,plain,(m_c_h_element_v_in2(c_e_h_1, c_e, s5) | (~node16(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5))), inference(lemma,lemma(discharge,[]))).
% 11.63/11.82 tff(5738,plain,
% 11.63/11.82 (m_c_h_element_v_in2(c_e_h_1, c_e, s5)),
% 11.63/11.82 inference(unit_resolution,[status(thm)],[5737, 5729, 5728])).
% 11.63/11.82 tff(5739,plain,
% 11.63/11.82 (((~![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, 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)))),
% 11.63/11.82 inference(rewrite,[status(thm)],[])).
% 11.63/11.82 tff(5740,plain,
% 11.63/11.82 ((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)))),
% 11.63/11.82 inference(rewrite,[status(thm)],[])).
% 11.63/11.82 tff(5741,plain,
% 11.63/11.82 (((~![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, 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))))),
% 11.63/11.82 inference(monotonicity,[status(thm)],[5740])).
% 11.63/11.82 tff(5742,plain,
% 11.63/11.82 (((~![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, 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)))),
% 11.63/11.82 inference(transitivity,[status(thm)],[5741, 5739])).
% 11.63/11.82 tff(5743,plain,
% 11.63/11.82 ((~![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, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5)))),
% 11.63/11.82 inference(quant_inst,[status(thm)],[])).
% 11.63/11.82 tff(5744,plain,
% 11.63/11.82 ((~![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, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~node17(c_e_h_1, c_e, s5))),
% 11.63/11.82 inference(modus_ponens,[status(thm)],[5743, 5742])).
% 11.63/11.82 tff(5745,plain,
% 11.63/11.82 ((~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)),
% 11.63/11.82 inference(unit_resolution,[status(thm)],[5744, 2125, 5728])).
% 11.63/11.82 tff(5746,plain,
% 11.63/11.82 (m_c_h_element_v_in1(c_e_h_1, c_e, s5)),
% 11.63/11.82 inference(unit_resolution,[status(thm)],[5745, 5738])).
% 11.63/11.82 tff(5747,plain,
% 11.63/11.82 (((~![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)))) | ((~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)))) <=> ((~![I0: $i, X: $i, 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, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~node16(c_e_h_1, c_e, s5)))),
% 11.63/11.82 inference(rewrite,[status(thm)],[])).
% 11.63/11.82 tff(5748,plain,
% 11.63/11.82 (((~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_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)))),
% 11.63/11.82 inference(rewrite,[status(thm)],[])).
% 11.63/11.82 tff(5749,plain,
% 11.63/11.82 (((~![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_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_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))))),
% 11.63/11.82 inference(monotonicity,[status(thm)],[5748])).
% 11.63/11.82 tff(5750,plain,
% 11.63/11.82 (((~![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_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_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)))),
% 11.63/11.82 inference(transitivity,[status(thm)],[5749, 5747])).
% 11.63/11.82 tff(5751,plain,
% 11.63/11.82 ((~![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_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)))),
% 11.63/11.82 inference(quant_inst,[status(thm)],[])).
% 11.63/11.82 tff(5752,plain,
% 11.63/11.82 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~node16(c_e_h_1, c_e, s5))),
% 11.63/11.82 inference(modus_ponens,[status(thm)],[5751, 5750])).
% 11.68/11.82 tff(5753,plain,
% 11.68/11.82 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s5))),
% 11.68/11.82 inference(unit_resolution,[status(thm)],[5752, 2142, 5729])).
% 11.68/11.82 tff(5754,plain,
% 11.68/11.82 ($false),
% 11.68/11.82 inference(unit_resolution,[status(thm)],[5753, 5746, 5738])).
% 11.68/11.82 tff(5755,plain,((~node16(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5))), inference(lemma,lemma(discharge,[]))).
% 11.68/11.82 tff(5756,plain,
% 11.68/11.82 (~node16(c_e_h_1, c_e, s5)),
% 11.68/11.82 inference(unit_resolution,[status(thm)],[5755, 5711])).
% 11.68/11.82 tff(5757,plain,
% 11.68/11.82 (((~![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)))) | (node15(c_e_h_1, c_e, s5, s6) | node16(c_e_h_1, c_e, s5) | (~node19(c_e_h_1, c_e, s5, s6)) | node14(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) | node16(c_e_h_1, c_e, s5) | (~node19(c_e_h_1, c_e, s5, s6)) | node14(c_e_h_1, c_e, s5, s6))),
% 11.68/11.82 inference(rewrite,[status(thm)],[])).
% 11.68/11.82 tff(5758,plain,
% 11.68/11.82 ((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) | node16(c_e_h_1, c_e, s5) | (~node19(c_e_h_1, c_e, s5, s6)) | node14(c_e_h_1, c_e, s5, s6))),
% 11.68/11.82 inference(rewrite,[status(thm)],[])).
% 11.68/11.82 tff(5759,plain,
% 11.68/11.82 (((~![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_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) | node16(c_e_h_1, c_e, s5) | (~node19(c_e_h_1, c_e, s5, s6)) | node14(c_e_h_1, c_e, s5, s6)))),
% 11.68/11.82 inference(monotonicity,[status(thm)],[5758])).
% 11.68/11.82 tff(5760,plain,
% 11.68/11.82 (((~![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_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) | node16(c_e_h_1, c_e, s5) | (~node19(c_e_h_1, c_e, s5, s6)) | node14(c_e_h_1, c_e, s5, s6))),
% 11.68/11.82 inference(transitivity,[status(thm)],[5759, 5757])).
% 11.68/11.82 tff(5761,plain,
% 11.68/11.82 ((~![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_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)))),
% 11.68/11.82 inference(quant_inst,[status(thm)],[])).
% 11.68/11.82 tff(5762,plain,
% 11.68/11.82 ((~![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)))) | node15(c_e_h_1, c_e, s5, s6) | node16(c_e_h_1, c_e, s5) | (~node19(c_e_h_1, c_e, s5, s6)) | node14(c_e_h_1, c_e, s5, s6)),
% 11.68/11.82 inference(modus_ponens,[status(thm)],[5761, 5760])).
% 11.68/11.82 tff(5763,plain,
% 11.68/11.82 (node15(c_e_h_1, c_e, s5, s6) | node16(c_e_h_1, c_e, s5) | node14(c_e_h_1, c_e, s5, s6)),
% 11.68/11.82 inference(unit_resolution,[status(thm)],[5762, 409, 5703])).
% 11.68/11.82 tff(5764,plain,
% 11.68/11.82 (node14(c_e_h_1, c_e, s5, s6)),
% 11.68/11.82 inference(unit_resolution,[status(thm)],[5763, 5756, 5727])).
% 11.68/11.82 tff(5765,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s5)), introduced(assumption)).
% 11.68/11.82 tff(5766,assumption,(node14(c_e_h_1, c_e, s5, s6)), introduced(assumption)).
% 11.68/11.82 tff(5767,plain,
% 11.68/11.82 (((~![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_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)))),
% 11.68/11.82 inference(rewrite,[status(thm)],[])).
% 11.68/11.82 tff(5768,plain,
% 11.68/11.82 (((~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)))),
% 11.68/11.82 inference(rewrite,[status(thm)],[])).
% 11.68/11.82 tff(5769,plain,
% 11.68/11.82 (((~![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_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))))),
% 11.68/11.82 inference(monotonicity,[status(thm)],[5768])).
% 11.68/11.82 tff(5770,plain,
% 11.68/11.82 (((~![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_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)))),
% 11.68/11.82 inference(transitivity,[status(thm)],[5769, 5767])).
% 11.68/11.82 tff(5771,plain,
% 11.68/11.82 ((~![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_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)))),
% 11.68/11.82 inference(quant_inst,[status(thm)],[])).
% 11.68/11.82 tff(5772,plain,
% 11.68/11.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node14(c_e_h_1, c_e, s5, s6))),
% 11.68/11.82 inference(modus_ponens,[status(thm)],[5771, 5770])).
% 11.68/11.82 tff(5773,plain,
% 11.68/11.82 ($false),
% 11.68/11.82 inference(unit_resolution,[status(thm)],[5772, 427, 5766, 5689, 5765])).
% 11.68/11.82 tff(5774,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,[]))).
% 11.68/11.82 tff(5775,plain,
% 11.68/11.82 ($false),
% 11.68/11.82 inference(unit_resolution,[status(thm)],[5774, 5764, 5720, 5689])).
% 11.68/11.82 tff(5776,plain,((~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) | m_c_h_element_v_out(c_e_h_1, c_e, s5)), inference(lemma,lemma(discharge,[]))).
% 11.68/11.82 tff(5777,plain,
% 11.68/11.82 ((~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)),
% 11.68/11.82 inference(unit_resolution,[status(thm)],[5776, 3755])).
% 11.68/11.82 tff(5778,plain,
% 11.68/11.82 (m_c_h_element_v_in2(c_e_h_1, c_e, s5)),
% 11.68/11.82 inference(unit_resolution,[status(thm)],[5777, 5688])).
% 11.68/11.82 tff(5779,plain,
% 11.68/11.82 (((~![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, 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))),
% 11.68/11.82 inference(rewrite,[status(thm)],[])).
% 11.68/11.82 tff(5780,plain,
% 11.68/11.82 ((~![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, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5))),
% 11.68/11.82 inference(quant_inst,[status(thm)],[])).
% 11.68/11.82 tff(5781,plain,
% 11.68/11.82 ((~![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, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5)),
% 11.68/11.82 inference(modus_ponens,[status(thm)],[5780, 5779])).
% 11.68/11.82 tff(5782,plain,
% 11.68/11.82 (m_and_h_gate_v_out(c_e_h_1, c_i, s5)),
% 11.68/11.82 inference(unit_resolution,[status(thm)],[5781, 1965, 5778])).
% 11.68/11.82 tff(5783,assumption,(~node20(c_e_h_1, c_i, s4)), introduced(assumption)).
% 11.68/11.82 tff(5784,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s5)), introduced(assumption)).
% 11.68/11.82 tff(5785,plain,
% 11.68/11.82 (((~![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_i, s5)) | node20(c_e_h_1, c_i, s4) | (~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)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | node20(c_e_h_1, c_i, s4) | (~node21(c_e_h_1, c_i, s4, s5)))),
% 11.68/11.82 inference(rewrite,[status(thm)],[])).
% 11.68/11.82 tff(5786,plain,
% 11.68/11.82 ((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))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | node20(c_e_h_1, c_i, s4) | (~node21(c_e_h_1, c_i, s4, s5)))),
% 11.68/11.82 inference(rewrite,[status(thm)],[])).
% 11.68/11.82 tff(5787,plain,
% 11.68/11.82 (((~![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_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)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | node20(c_e_h_1, c_i, s4) | (~node21(c_e_h_1, c_i, s4, s5))))),
% 11.68/11.82 inference(monotonicity,[status(thm)],[5786])).
% 11.68/11.82 tff(5788,plain,
% 11.68/11.82 (((~![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_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)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | node20(c_e_h_1, c_i, s4) | (~node21(c_e_h_1, c_i, s4, s5)))),
% 11.68/11.82 inference(transitivity,[status(thm)],[5787, 5785])).
% 11.68/11.82 tff(5789,plain,
% 11.68/11.82 ((~![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_i, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | (~node21(c_e_h_1, c_i, s4, s5)))),
% 11.68/11.82 inference(quant_inst,[status(thm)],[])).
% 11.68/11.82 tff(5790,plain,
% 11.68/11.82 ((~![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_i, s5)) | node20(c_e_h_1, c_i, s4) | (~node21(c_e_h_1, c_i, s4, s5))),
% 11.68/11.82 inference(modus_ponens,[status(thm)],[5789, 5788])).
% 11.68/11.82 tff(5791,plain,
% 11.68/11.82 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | node20(c_e_h_1, c_i, s4) | (~node21(c_e_h_1, c_i, s4, s5))),
% 11.68/11.82 inference(unit_resolution,[status(thm)],[5790, 228])).
% 11.68/11.82 tff(5792,plain,
% 11.68/11.82 (~node21(c_e_h_1, c_i, s4, s5)),
% 11.68/11.82 inference(unit_resolution,[status(thm)],[5791, 5784, 5783])).
% 11.68/11.82 tff(5793,plain,
% 11.68/11.82 (((~![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_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))),
% 11.68/11.82 inference(rewrite,[status(thm)],[])).
% 11.68/11.82 tff(5794,plain,
% 11.68/11.82 ((~![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_i, s4, s5) | node22(c_e_h_1, c_i, s4, s5))),
% 11.68/11.82 inference(quant_inst,[status(thm)],[])).
% 11.68/11.82 tff(5795,plain,
% 11.68/11.82 ((~![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_i, s4, s5) | node22(c_e_h_1, c_i, s4, s5)),
% 11.68/11.82 inference(modus_ponens,[status(thm)],[5794, 5793])).
% 11.68/11.82 tff(5796,plain,
% 11.68/11.82 (node22(c_e_h_1, c_i, s4, s5)),
% 11.68/11.82 inference(unit_resolution,[status(thm)],[5795, 247, 1542, 5792])).
% 11.68/11.82 tff(5797,plain,
% 11.68/11.82 (((~![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_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))),
% 11.68/11.83 inference(rewrite,[status(thm)],[])).
% 11.68/11.83 tff(5798,plain,
% 11.68/11.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, 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))),
% 11.68/11.83 inference(quant_inst,[status(thm)],[])).
% 11.68/11.83 tff(5799,plain,
% 11.68/11.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | (~node22(c_e_h_1, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4)),
% 11.68/11.83 inference(modus_ponens,[status(thm)],[5798, 5797])).
% 11.68/11.83 tff(5800,plain,
% 11.68/11.83 ($false),
% 11.68/11.83 inference(unit_resolution,[status(thm)],[5799, 273, 3422, 5784, 5796])).
% 11.68/11.83 tff(5801,plain,((~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) | node20(c_e_h_1, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 11.68/11.83 tff(5802,plain,
% 11.68/11.83 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | node20(c_e_h_1, c_i, s4)),
% 11.68/11.83 inference(unit_resolution,[status(thm)],[5801, 3420])).
% 11.68/11.83 tff(5803,plain,
% 11.68/11.83 (node20(c_e_h_1, c_i, s4)),
% 11.68/11.83 inference(unit_resolution,[status(thm)],[5802, 5782])).
% 11.68/11.83 tff(5804,plain,
% 11.68/11.83 (((~![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))),
% 11.68/11.83 inference(rewrite,[status(thm)],[])).
% 11.68/11.83 tff(5805,plain,
% 11.68/11.83 ((~![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))),
% 11.68/11.83 inference(quant_inst,[status(thm)],[])).
% 11.68/11.83 tff(5806,plain,
% 11.68/11.83 ((~![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)),
% 11.68/11.83 inference(modus_ponens,[status(thm)],[5805, 5804])).
% 11.68/11.83 tff(5807,plain,
% 11.68/11.83 (m_and_h_gate_v_in1(c_e_h_1, c_i, s4)),
% 11.68/11.83 inference(unit_resolution,[status(thm)],[5806, 213, 5803])).
% 11.68/11.83 tff(5808,plain,
% 11.68/11.83 (((~![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))),
% 11.68/11.83 inference(rewrite,[status(thm)],[])).
% 11.68/11.83 tff(5809,plain,
% 11.68/11.83 ((~![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))),
% 11.68/11.83 inference(quant_inst,[status(thm)],[])).
% 11.68/11.83 tff(5810,plain,
% 11.68/11.83 ((~![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)),
% 11.68/11.83 inference(modus_ponens,[status(thm)],[5809, 5808])).
% 11.68/11.83 tff(5811,plain,
% 11.68/11.83 (m_c_h_element_v_out(c_e_h_1, c_h, s4)),
% 11.68/11.83 inference(unit_resolution,[status(thm)],[5810, 503, 5807])).
% 11.68/11.83 tff(5812,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s3)), introduced(assumption)).
% 11.68/11.83 tff(5813,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s4)), introduced(assumption)).
% 11.68/11.83 tff(5814,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s3)), introduced(assumption)).
% 11.68/11.83 tff(5815,plain,
% 11.68/11.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 11.68/11.83 inference(rewrite,[status(thm)],[])).
% 11.68/11.83 tff(5816,plain,
% 11.68/11.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 11.68/11.83 inference(quant_inst,[status(thm)],[])).
% 11.68/11.83 tff(5817,plain,
% 11.68/11.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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)),
% 11.68/11.83 inference(modus_ponens,[status(thm)],[5816, 5815])).
% 11.68/11.83 tff(5818,plain,
% 11.68/11.83 ((~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)),
% 11.68/11.83 inference(unit_resolution,[status(thm)],[5817, 393])).
% 11.68/11.83 tff(5819,plain,
% 11.68/11.83 (~node15(c_e_h_1, c_h, s3, s4)),
% 11.68/11.83 inference(unit_resolution,[status(thm)],[5818, 5814, 5813])).
% 11.68/11.83 tff(5820,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s3)), introduced(assumption)).
% 11.68/11.83 tff(5821,assumption,(~node15(c_e_h_1, c_h, s3, s4)), introduced(assumption)).
% 11.68/11.83 tff(5822,plain,
% 11.68/11.83 (((~![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, 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))),
% 11.68/11.83 inference(rewrite,[status(thm)],[])).
% 11.68/11.83 tff(5823,plain,
% 11.68/11.83 ((~![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, 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))),
% 11.68/11.83 inference(quant_inst,[status(thm)],[])).
% 11.68/11.83 tff(5824,plain,
% 11.68/11.83 ((~![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, 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)),
% 11.68/11.83 inference(modus_ponens,[status(thm)],[5823, 5822])).
% 11.68/11.83 tff(5825,plain,
% 11.68/11.83 ((~node16(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3)),
% 11.68/11.83 inference(unit_resolution,[status(thm)],[5824, 377, 5812])).
% 11.68/11.83 tff(5826,plain,
% 11.68/11.83 (~node16(c_e_h_1, c_h, s3)),
% 11.68/11.83 inference(unit_resolution,[status(thm)],[5825, 5820])).
% 11.68/11.83 tff(5827,assumption,(~node19(c_e_h_1, c_h, s3, s4)), introduced(assumption)).
% 11.68/11.83 tff(5828,plain,
% 11.68/11.83 (((~![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))),
% 11.68/11.83 inference(rewrite,[status(thm)],[])).
% 11.68/11.83 tff(5829,plain,
% 11.68/11.83 ((~![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))),
% 11.68/11.83 inference(quant_inst,[status(thm)],[])).
% 11.68/11.83 tff(5830,plain,
% 11.68/11.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_1, c_h, s3, s4)),
% 11.68/11.83 inference(modus_ponens,[status(thm)],[5829, 5828])).
% 11.68/11.83 tff(5831,plain,
% 11.68/11.83 ($false),
% 11.68/11.83 inference(unit_resolution,[status(thm)],[5830, 312, 1092, 5827])).
% 11.68/11.83 tff(5832,plain,(node19(c_e_h_1, c_h, s3, s4)), inference(lemma,lemma(discharge,[]))).
% 11.68/11.83 tff(5833,plain,
% 11.68/11.83 (((~![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, s3) | (~node19(c_e_h_1, c_h, s3, s4)) | node15(c_e_h_1, c_h, s3, s4) | node14(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) | (~node19(c_e_h_1, c_h, s3, s4)) | node15(c_e_h_1, c_h, s3, s4) | node14(c_e_h_1, c_h, s3, s4))),
% 11.68/11.83 inference(rewrite,[status(thm)],[])).
% 11.68/11.83 tff(5834,plain,
% 11.68/11.83 ((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))) <=> (node16(c_e_h_1, c_h, s3) | (~node19(c_e_h_1, c_h, s3, s4)) | node15(c_e_h_1, c_h, s3, s4) | node14(c_e_h_1, c_h, s3, s4))),
% 11.68/11.83 inference(rewrite,[status(thm)],[])).
% 11.68/11.83 tff(5835,plain,
% 11.68/11.83 (((~![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, 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) | (~node19(c_e_h_1, c_h, s3, s4)) | node15(c_e_h_1, c_h, s3, s4) | node14(c_e_h_1, c_h, s3, s4)))),
% 11.68/11.83 inference(monotonicity,[status(thm)],[5834])).
% 11.68/11.83 tff(5836,plain,
% 11.68/11.83 (((~![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, 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) | (~node19(c_e_h_1, c_h, s3, s4)) | node15(c_e_h_1, c_h, s3, s4) | node14(c_e_h_1, c_h, s3, s4))),
% 11.68/11.83 inference(transitivity,[status(thm)],[5835, 5833])).
% 11.68/11.83 tff(5837,plain,
% 11.68/11.83 ((~![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, 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)))),
% 11.68/11.83 inference(quant_inst,[status(thm)],[])).
% 11.68/11.83 tff(5838,plain,
% 11.68/11.83 ((~![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, s3) | (~node19(c_e_h_1, c_h, s3, s4)) | node15(c_e_h_1, c_h, s3, s4) | node14(c_e_h_1, c_h, s3, s4)),
% 11.68/11.83 inference(modus_ponens,[status(thm)],[5837, 5836])).
% 11.68/11.83 tff(5839,plain,
% 11.68/11.83 (node16(c_e_h_1, c_h, s3) | node15(c_e_h_1, c_h, s3, s4) | node14(c_e_h_1, c_h, s3, s4)),
% 11.68/11.83 inference(unit_resolution,[status(thm)],[5838, 409, 5832])).
% 11.68/11.83 tff(5840,plain,
% 11.68/11.83 (node14(c_e_h_1, c_h, s3, s4)),
% 11.68/11.83 inference(unit_resolution,[status(thm)],[5839, 5826, 5821])).
% 11.68/11.83 tff(5841,plain,
% 11.68/11.83 (((~![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_in1(c_e_h_1, c_h, s3) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | (~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_in1(c_e_h_1, c_h, s3) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | (~node14(c_e_h_1, c_h, s3, s4)))),
% 11.68/11.83 inference(rewrite,[status(thm)],[])).
% 11.68/11.83 tff(5842,plain,
% 11.68/11.83 (((~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_in1(c_e_h_1, c_h, s3) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | (~node14(c_e_h_1, c_h, s3, s4)))),
% 11.68/11.83 inference(rewrite,[status(thm)],[])).
% 11.68/11.83 tff(5843,plain,
% 11.68/11.83 (((~![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_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_in1(c_e_h_1, c_h, s3) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | (~node14(c_e_h_1, c_h, s3, s4))))),
% 11.68/11.83 inference(monotonicity,[status(thm)],[5842])).
% 11.68/11.83 tff(5844,plain,
% 11.68/11.83 (((~![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_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_in1(c_e_h_1, c_h, s3) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | (~node14(c_e_h_1, c_h, s3, s4)))),
% 11.68/11.83 inference(transitivity,[status(thm)],[5843, 5841])).
% 11.68/11.83 tff(5845,plain,
% 11.68/11.83 ((~![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_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)))),
% 11.68/11.83 inference(quant_inst,[status(thm)],[])).
% 11.68/11.83 tff(5846,plain,
% 11.68/11.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | (~node14(c_e_h_1, c_h, s3, s4))),
% 11.68/11.83 inference(modus_ponens,[status(thm)],[5845, 5844])).
% 11.68/11.83 tff(5847,plain,
% 11.68/11.83 ($false),
% 11.68/11.83 inference(unit_resolution,[status(thm)],[5846, 427, 5813, 5840, 5820])).
% 11.68/11.83 tff(5848,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,[]))).
% 11.68/11.83 tff(5849,plain,
% 11.68/11.83 (m_c_h_element_v_in1(c_e_h_1, c_h, s3)),
% 11.68/11.83 inference(unit_resolution,[status(thm)],[5848, 5819, 5813, 5812])).
% 11.68/11.83 tff(5850,plain,
% 11.68/11.83 (((~![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_h, s3)) | 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)))) <=> ((~![I0: $i, X: $i, 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, s3)) | 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)))),
% 11.68/11.83 inference(rewrite,[status(thm)],[])).
% 11.68/11.83 tff(5851,plain,
% 11.68/11.83 (((~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))) <=> ((~node17(c_e_h_1, c_h, s3)) | 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)))),
% 11.68/11.83 inference(rewrite,[status(thm)],[])).
% 11.68/11.83 tff(5852,plain,
% 11.68/11.83 (((~![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, 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)))) | ((~node17(c_e_h_1, c_h, s3)) | 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))))),
% 11.68/11.83 inference(monotonicity,[status(thm)],[5851])).
% 11.68/11.83 tff(5853,plain,
% 11.68/11.83 (((~![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, 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)))) | (~node17(c_e_h_1, c_h, s3)) | 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)))),
% 11.68/11.83 inference(transitivity,[status(thm)],[5852, 5850])).
% 11.68/11.83 tff(5854,plain,
% 11.68/11.83 ((~![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, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3) | (~node17(c_e_h_1, c_h, s3)))),
% 11.68/11.83 inference(quant_inst,[status(thm)],[])).
% 11.68/11.83 tff(5855,plain,
% 11.68/11.83 ((~![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_h, s3)) | 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))),
% 11.68/11.83 inference(modus_ponens,[status(thm)],[5854, 5853])).
% 11.68/11.83 tff(5856,plain,
% 11.68/11.83 ((~node17(c_e_h_1, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s3))),
% 11.68/11.83 inference(unit_resolution,[status(thm)],[5855, 359, 5812])).
% 11.68/11.83 tff(5857,plain,
% 11.68/11.83 (~node17(c_e_h_1, c_h, s3)),
% 11.68/11.83 inference(unit_resolution,[status(thm)],[5856, 5849])).
% 11.68/11.83 tff(5858,plain,
% 11.68/11.83 (((~![Y: $i, 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) | (~node19(c_e_h_1, c_h, s3, s4)) | node18(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) | (~node19(c_e_h_1, c_h, s3, s4)) | node18(c_e_h_1, c_h, s3, s4))),
% 11.68/11.83 inference(rewrite,[status(thm)],[])).
% 11.68/11.83 tff(5859,plain,
% 11.68/11.83 ((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))) <=> (node17(c_e_h_1, c_h, s3) | (~node19(c_e_h_1, c_h, s3, s4)) | node18(c_e_h_1, c_h, s3, s4))),
% 11.68/11.83 inference(rewrite,[status(thm)],[])).
% 11.68/11.83 tff(5860,plain,
% 11.68/11.83 (((~![Y: $i, 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) | (~node19(c_e_h_1, c_h, s3, s4)) | node18(c_e_h_1, c_h, s3, s4)))),
% 11.68/11.83 inference(monotonicity,[status(thm)],[5859])).
% 11.68/11.83 tff(5861,plain,
% 11.68/11.83 (((~![Y: $i, 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) | (~node19(c_e_h_1, c_h, s3, s4)) | node18(c_e_h_1, c_h, s3, s4))),
% 11.68/11.83 inference(transitivity,[status(thm)],[5860, 5858])).
% 11.68/11.83 tff(5862,plain,
% 11.68/11.83 ((~![Y: $i, 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)))),
% 11.68/11.83 inference(quant_inst,[status(thm)],[])).
% 11.68/11.83 tff(5863,plain,
% 11.68/11.83 ((~![Y: $i, 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) | (~node19(c_e_h_1, c_h, s3, s4)) | node18(c_e_h_1, c_h, s3, s4)),
% 11.68/11.83 inference(modus_ponens,[status(thm)],[5862, 5861])).
% 11.68/11.83 tff(5864,plain,
% 11.68/11.83 (node17(c_e_h_1, c_h, s3) | node18(c_e_h_1, c_h, s3, s4)),
% 11.68/11.83 inference(unit_resolution,[status(thm)],[5863, 326, 5832])).
% 11.68/11.83 tff(5865,plain,
% 11.68/11.83 (node18(c_e_h_1, c_h, s3, s4)),
% 11.68/11.83 inference(unit_resolution,[status(thm)],[5864, 5857])).
% 11.68/11.83 tff(5866,plain,
% 11.68/11.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_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, s4)) | (~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, s3) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | (~node18(c_e_h_1, c_h, s3, s4)))),
% 11.68/11.83 inference(rewrite,[status(thm)],[])).
% 11.68/11.83 tff(5867,plain,
% 11.68/11.83 (((~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))) <=> (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, s4)) | (~node18(c_e_h_1, c_h, s3, s4)))),
% 11.68/11.83 inference(rewrite,[status(thm)],[])).
% 11.68/11.83 tff(5868,plain,
% 11.68/11.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_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, s3) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | (~node18(c_e_h_1, c_h, s3, s4))))),
% 11.68/11.83 inference(monotonicity,[status(thm)],[5867])).
% 11.68/11.83 tff(5869,plain,
% 11.68/11.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_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, s3) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | (~node18(c_e_h_1, c_h, s3, s4)))),
% 11.68/11.83 inference(transitivity,[status(thm)],[5868, 5866])).
% 11.68/11.83 tff(5870,plain,
% 11.68/11.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_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)))),
% 11.68/11.83 inference(quant_inst,[status(thm)],[])).
% 11.68/11.83 tff(5871,plain,
% 11.68/11.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s3) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | (~node18(c_e_h_1, c_h, s3, s4))),
% 11.68/11.83 inference(modus_ponens,[status(thm)],[5870, 5869])).
% 11.68/11.83 tff(5872,plain,
% 11.68/11.83 ($false),
% 11.68/11.83 inference(unit_resolution,[status(thm)],[5871, 296, 5813, 5814, 5865])).
% 11.68/11.83 tff(5873,plain,(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, s4)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 11.68/11.83 tff(5874,plain,
% 11.68/11.83 ((~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)),
% 11.68/11.83 inference(unit_resolution,[status(thm)],[5873, 3300])).
% 11.68/11.83 tff(5875,plain,
% 11.68/11.83 (m_c_h_element_v_in2(c_e_h_1, c_h, s3)),
% 11.68/11.83 inference(unit_resolution,[status(thm)],[5874, 5811])).
% 11.68/11.83 tff(5876,assumption,(m_c_h_element_v_in2(c_e_h_1, c_h, s3)), introduced(assumption)).
% 11.68/11.83 tff(5877,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s3)), introduced(assumption)).
% 11.68/11.83 tff(5878,plain,
% 11.68/11.83 (((~![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))),
% 11.68/11.83 inference(rewrite,[status(thm)],[])).
% 11.68/11.83 tff(5879,plain,
% 11.68/11.83 ((~![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))),
% 11.68/11.83 inference(quant_inst,[status(thm)],[])).
% 11.68/11.83 tff(5880,plain,
% 11.68/11.83 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s3)),
% 11.68/11.83 inference(modus_ponens,[status(thm)],[5879, 5878])).
% 11.68/11.83 tff(5881,plain,
% 11.68/11.83 ($false),
% 11.68/11.83 inference(unit_resolution,[status(thm)],[5880, 1117, 5877, 5876])).
% 11.68/11.83 tff(5882,plain,(m_or_h_gate_v_out(c_e_h_1, c_j, s3) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3))), inference(lemma,lemma(discharge,[]))).
% 11.68/11.83 tff(5883,plain,
% 11.68/11.83 (m_or_h_gate_v_out(c_e_h_1, c_j, s3)),
% 11.68/11.83 inference(unit_resolution,[status(thm)],[5882, 5875])).
% 11.68/11.83 tff(5884,assumption,(node6(c_e_h_1, c_j, s2, s3)), introduced(assumption)).
% 11.68/11.83 tff(5885,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s2)), introduced(assumption)).
% 11.68/11.83 tff(5886,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s3)), introduced(assumption)).
% 11.68/11.83 tff(5887,plain,
% 11.68/11.83 (((~![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_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)))),
% 11.68/11.84 inference(rewrite,[status(thm)],[])).
% 11.68/11.84 tff(5888,plain,
% 11.68/11.84 (((~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)))),
% 11.68/11.84 inference(rewrite,[status(thm)],[])).
% 11.68/11.84 tff(5889,plain,
% 11.68/11.84 (((~![Y: $i, I0: $i, X: $i, I1: $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))))),
% 11.68/11.84 inference(monotonicity,[status(thm)],[5888])).
% 11.68/11.84 tff(5890,plain,
% 11.68/11.84 (((~![Y: $i, I0: $i, X: $i, I1: $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)))),
% 11.68/11.84 inference(transitivity,[status(thm)],[5889, 5887])).
% 11.68/11.84 tff(5891,plain,
% 11.68/11.84 ((~![Y: $i, I0: $i, X: $i, I1: $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))),
% 11.68/11.84 inference(quant_inst,[status(thm)],[])).
% 11.68/11.84 tff(5892,plain,
% 11.68/11.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s2) | (~node6(c_e_h_1, c_j, s2, s3))),
% 11.68/11.84 inference(modus_ponens,[status(thm)],[5891, 5890])).
% 11.68/11.84 tff(5893,plain,
% 11.68/11.84 ($false),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5892, 742, 5886, 5885, 5884])).
% 11.68/11.84 tff(5894,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,[]))).
% 11.68/11.84 tff(5895,plain,
% 11.68/11.84 ((~node6(c_e_h_1, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3))),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5894, 3079])).
% 11.68/11.84 tff(5896,plain,
% 11.68/11.84 (~node6(c_e_h_1, c_j, s2, s3)),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5895, 5883])).
% 11.68/11.84 tff(5897,plain,
% 11.68/11.84 (((~![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_1, c_j, s2, s3) | node5(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)) | node6(c_e_h_1, c_j, s2, s3) | node5(c_e_h_1, c_j, s2, s3))),
% 11.68/11.84 inference(rewrite,[status(thm)],[])).
% 11.68/11.84 tff(5898,plain,
% 11.68/11.84 ((node6(c_e_h_1, c_j, s2, s3) | node5(c_e_h_1, c_j, s2, s3) | (~trans(s2, s3))) <=> ((~trans(s2, s3)) | node6(c_e_h_1, c_j, s2, s3) | node5(c_e_h_1, c_j, s2, s3))),
% 11.68/11.84 inference(rewrite,[status(thm)],[])).
% 11.68/11.84 tff(5899,plain,
% 11.68/11.84 (((~![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)) | node6(c_e_h_1, c_j, s2, s3) | node5(c_e_h_1, c_j, s2, s3)))),
% 11.68/11.84 inference(monotonicity,[status(thm)],[5898])).
% 11.68/11.84 tff(5900,plain,
% 11.68/11.84 (((~![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)) | node6(c_e_h_1, c_j, s2, s3) | node5(c_e_h_1, c_j, s2, s3))),
% 11.68/11.84 inference(transitivity,[status(thm)],[5899, 5897])).
% 11.68/11.84 tff(5901,plain,
% 11.68/11.84 ((~![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)))),
% 11.68/11.84 inference(quant_inst,[status(thm)],[])).
% 11.68/11.84 tff(5902,plain,
% 11.68/11.84 ((~![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_1, c_j, s2, s3) | node5(c_e_h_1, c_j, s2, s3)),
% 11.68/11.84 inference(modus_ponens,[status(thm)],[5901, 5900])).
% 11.68/11.84 tff(5903,plain,
% 11.68/11.84 (node6(c_e_h_1, c_j, s2, s3) | node5(c_e_h_1, c_j, s2, s3)),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5902, 724, 604])).
% 11.68/11.84 tff(5904,plain,
% 11.68/11.84 (node5(c_e_h_1, c_j, s2, s3)),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5903, 5896])).
% 11.68/11.84 tff(5905,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s2)), introduced(assumption)).
% 11.68/11.84 tff(5906,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s2)), introduced(assumption)).
% 11.68/11.84 tff(5907,assumption,(node21(c_e_h_3, c_q, s1, s2)), introduced(assumption)).
% 11.68/11.84 tff(5908,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)), introduced(assumption)).
% 11.68/11.84 tff(5909,assumption,(node11(c_e_h_3, c_n, s0, s1)), introduced(assumption)).
% 11.68/11.84 tff(5910,plain,
% 11.68/11.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, 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))),
% 11.68/11.84 inference(rewrite,[status(thm)],[])).
% 11.68/11.84 tff(5911,plain,
% 11.68/11.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, 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))),
% 11.68/11.84 inference(quant_inst,[status(thm)],[])).
% 11.68/11.84 tff(5912,plain,
% 11.68/11.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)) | (~node11(c_e_h_3, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0)),
% 11.68/11.84 inference(modus_ponens,[status(thm)],[5911, 5910])).
% 11.68/11.84 tff(5913,plain,
% 11.68/11.84 ($false),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5912, 147, 5908, 3014, 5909])).
% 11.68/11.84 tff(5914,plain,((~node11(c_e_h_3, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1))), inference(lemma,lemma(discharge,[]))).
% 11.68/11.84 tff(5915,plain,
% 11.68/11.84 (~node11(c_e_h_3, c_n, s0, s1)),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5914, 5908])).
% 11.68/11.84 tff(5916,plain,
% 11.68/11.84 (((~![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))),
% 11.68/11.84 inference(rewrite,[status(thm)],[])).
% 11.68/11.84 tff(5917,plain,
% 11.68/11.84 ((~![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))),
% 11.68/11.84 inference(quant_inst,[status(thm)],[])).
% 11.68/11.84 tff(5918,plain,
% 11.68/11.84 ((~![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)),
% 11.68/11.84 inference(modus_ponens,[status(thm)],[5917, 5916])).
% 11.68/11.84 tff(5919,plain,
% 11.68/11.84 (node10(c_e_h_3, c_n, s0, s1) | node11(c_e_h_3, c_n, s0, s1)),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5918, 110, 100])).
% 11.68/11.84 tff(5920,plain,
% 11.68/11.84 (node10(c_e_h_3, c_n, s0, s1)),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5919, 5915])).
% 11.68/11.84 tff(5921,plain,
% 11.68/11.84 (^[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)))),
% 11.68/11.84 inference(bind,[status(th)],[])).
% 11.68/11.84 tff(5922,plain,
% 11.68/11.84 (![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))),
% 11.68/11.84 inference(quant_intro,[status(thm)],[5921])).
% 11.68/11.84 tff(5923,plain,
% 11.68/11.84 (![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))),
% 11.68/11.84 inference(rewrite,[status(thm)],[])).
% 11.68/11.84 tff(5924,plain,
% 11.68/11.84 (^[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)))),
% 11.68/11.84 inference(bind,[status(th)],[])).
% 11.68/11.84 tff(5925,plain,
% 11.68/11.84 (![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))),
% 11.68/11.84 inference(quant_intro,[status(thm)],[5924])).
% 11.68/11.84 tff(5926,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')).
% 11.68/11.84 tff(5927,plain,
% 11.68/11.84 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))),
% 11.68/11.84 inference(modus_ponens,[status(thm)],[5926, 5925])).
% 11.68/11.84 tff(5928,plain,
% 11.68/11.84 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))),
% 11.68/11.84 inference(modus_ponens,[status(thm)],[5927, 5923])).
% 11.68/11.84 tff(5929,plain,(
% 11.68/11.84 ![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))),
% 11.68/11.84 inference(skolemize,[status(sab)],[5928])).
% 11.68/11.84 tff(5930,plain,
% 11.68/11.84 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))),
% 11.68/11.84 inference(modus_ponens,[status(thm)],[5929, 5922])).
% 11.68/11.84 tff(5931,plain,
% 11.68/11.84 (((~![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))),
% 11.68/11.84 inference(rewrite,[status(thm)],[])).
% 11.68/11.84 tff(5932,plain,
% 11.68/11.84 ((~![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))),
% 11.68/11.84 inference(quant_inst,[status(thm)],[])).
% 11.68/11.84 tff(5933,plain,
% 11.68/11.84 ((~![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)),
% 11.68/11.84 inference(modus_ponens,[status(thm)],[5932, 5931])).
% 11.68/11.84 tff(5934,plain,
% 11.68/11.84 (m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_m, s0)),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5933, 5930, 2996])).
% 11.68/11.84 tff(5935,plain,
% 11.68/11.84 (((~![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))),
% 11.68/11.84 inference(rewrite,[status(thm)],[])).
% 11.68/11.84 tff(5936,plain,
% 11.68/11.84 ((~![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))),
% 11.68/11.84 inference(quant_inst,[status(thm)],[])).
% 11.68/11.84 tff(5937,plain,
% 11.68/11.84 ((~![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)),
% 11.68/11.84 inference(modus_ponens,[status(thm)],[5936, 5935])).
% 11.68/11.84 tff(5938,plain,
% 11.68/11.84 ((~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)),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5937, 38])).
% 11.68/11.84 tff(5939,plain,
% 11.68/11.84 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5938, 5934])).
% 11.68/11.84 tff(5940,plain,
% 11.68/11.84 (^[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))))),
% 11.68/11.84 inference(bind,[status(th)],[])).
% 11.68/11.84 tff(5941,plain,
% 11.68/11.84 (![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)))),
% 11.68/11.84 inference(quant_intro,[status(thm)],[5940])).
% 11.68/11.84 tff(5942,plain,
% 11.68/11.84 (![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)))),
% 11.68/11.84 inference(rewrite,[status(thm)],[])).
% 11.68/11.84 tff(5943,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')).
% 11.68/11.84 tff(5944,plain,
% 11.68/11.84 (![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)))),
% 11.68/11.84 inference(modus_ponens,[status(thm)],[5943, 5942])).
% 11.68/11.84 tff(5945,plain,(
% 11.68/11.84 ![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)))),
% 11.68/11.84 inference(skolemize,[status(sab)],[5944])).
% 11.68/11.84 tff(5946,plain,
% 11.68/11.84 (![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)))),
% 11.68/11.84 inference(modus_ponens,[status(thm)],[5945, 5941])).
% 11.68/11.84 tff(5947,plain,
% 11.68/11.84 (((~![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)))),
% 11.68/11.84 inference(rewrite,[status(thm)],[])).
% 11.68/11.84 tff(5948,plain,
% 11.68/11.84 ((~![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)))),
% 11.68/11.84 inference(quant_inst,[status(thm)],[])).
% 11.68/11.84 tff(5949,plain,
% 11.68/11.84 ((~![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))),
% 11.68/11.84 inference(modus_ponens,[status(thm)],[5948, 5947])).
% 11.68/11.84 tff(5950,plain,
% 11.68/11.84 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s0)),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5949, 5946, 5939])).
% 11.68/11.84 tff(5951,plain,
% 11.68/11.84 (((~![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))),
% 11.68/11.84 inference(rewrite,[status(thm)],[])).
% 11.68/11.84 tff(5952,plain,
% 11.68/11.84 ((~![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))),
% 11.68/11.84 inference(quant_inst,[status(thm)],[])).
% 11.68/11.84 tff(5953,plain,
% 11.68/11.84 ((~![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)),
% 11.68/11.84 inference(modus_ponens,[status(thm)],[5952, 5951])).
% 11.68/11.84 tff(5954,plain,
% 11.68/11.84 (~node9(c_e_h_3, c_n, s0)),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5953, 63, 5950])).
% 11.68/11.84 tff(5955,plain,
% 11.68/11.84 (((~![Y: $i, I0: $i, 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, s1)) | node9(c_e_h_3, c_n, s0) | (~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)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)) | node9(c_e_h_3, c_n, s0) | (~node10(c_e_h_3, c_n, s0, s1)))),
% 11.68/11.84 inference(rewrite,[status(thm)],[])).
% 11.68/11.84 tff(5956,plain,
% 11.68/11.84 ((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))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)) | node9(c_e_h_3, c_n, s0) | (~node10(c_e_h_3, c_n, s0, s1)))),
% 11.68/11.84 inference(rewrite,[status(thm)],[])).
% 11.68/11.84 tff(5957,plain,
% 11.68/11.84 (((~![Y: $i, I0: $i, 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)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)) | node9(c_e_h_3, c_n, s0) | (~node10(c_e_h_3, c_n, s0, s1))))),
% 11.68/11.84 inference(monotonicity,[status(thm)],[5956])).
% 11.68/11.84 tff(5958,plain,
% 11.68/11.84 (((~![Y: $i, I0: $i, 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)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)) | node9(c_e_h_3, c_n, s0) | (~node10(c_e_h_3, c_n, s0, s1)))),
% 11.68/11.84 inference(transitivity,[status(thm)],[5957, 5955])).
% 11.68/11.84 tff(5959,plain,
% 11.68/11.84 ((~![Y: $i, I0: $i, 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)))),
% 11.68/11.84 inference(quant_inst,[status(thm)],[])).
% 11.68/11.84 tff(5960,plain,
% 11.68/11.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)) | node9(c_e_h_3, c_n, s0) | (~node10(c_e_h_3, c_n, s0, s1))),
% 11.68/11.84 inference(modus_ponens,[status(thm)],[5959, 5958])).
% 11.68/11.84 tff(5961,plain,
% 11.68/11.84 ($false),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5960, 77, 5908, 5954, 5920])).
% 11.68/11.84 tff(5962,plain,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)), inference(lemma,lemma(discharge,[]))).
% 11.68/11.84 tff(5963,plain,
% 11.68/11.84 (((~![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, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1))) <=> ((~![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, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1))),
% 11.68/11.84 inference(rewrite,[status(thm)],[])).
% 11.68/11.84 tff(5964,plain,
% 11.68/11.84 ((~![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, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1))),
% 11.68/11.84 inference(quant_inst,[status(thm)],[])).
% 11.68/11.84 tff(5965,plain,
% 11.68/11.84 ((~![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, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)),
% 11.68/11.84 inference(modus_ponens,[status(thm)],[5964, 5963])).
% 11.68/11.84 tff(5966,plain,
% 11.68/11.84 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s1)),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5965, 3021, 5962])).
% 11.68/11.84 tff(5967,plain,
% 11.68/11.84 (((~![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, s1)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s1))) <=> ((~![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, s1)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s1))),
% 11.68/11.84 inference(rewrite,[status(thm)],[])).
% 11.68/11.84 tff(5968,plain,
% 11.68/11.84 ((~![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, s1)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s1))),
% 11.68/11.84 inference(quant_inst,[status(thm)],[])).
% 11.68/11.84 tff(5969,plain,
% 11.68/11.84 ((~![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, s1)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s1)),
% 11.68/11.84 inference(modus_ponens,[status(thm)],[5968, 5967])).
% 11.68/11.84 tff(5970,plain,
% 11.68/11.84 (~node20(c_e_h_3, c_q, s1)),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5969, 173, 5966])).
% 11.68/11.84 tff(5971,plain,
% 11.68/11.84 (((~![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_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)))),
% 11.68/11.84 inference(rewrite,[status(thm)],[])).
% 11.68/11.84 tff(5972,plain,
% 11.68/11.84 ((~![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_q, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s2)) | (~node21(c_e_h_3, c_q, s1, s2)))),
% 11.68/11.84 inference(quant_inst,[status(thm)],[])).
% 11.68/11.84 tff(5973,plain,
% 11.68/11.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s2)) | (~node21(c_e_h_3, c_q, s1, s2))),
% 11.68/11.84 inference(modus_ponens,[status(thm)],[5972, 5971])).
% 11.68/11.84 tff(5974,plain,
% 11.68/11.84 ($false),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5973, 228, 5906, 5970, 5907])).
% 11.68/11.84 tff(5975,plain,((~node21(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,[]))).
% 11.68/11.84 tff(5976,plain,
% 11.68/11.84 (~node21(c_e_h_3, c_q, s1, s2)),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5975, 5906])).
% 11.68/11.84 tff(5977,plain,
% 11.68/11.84 (((~![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_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))),
% 11.68/11.84 inference(rewrite,[status(thm)],[])).
% 11.68/11.84 tff(5978,plain,
% 11.68/11.84 ((~![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_q, s1, s2) | node22(c_e_h_3, c_q, s1, s2))),
% 11.68/11.84 inference(quant_inst,[status(thm)],[])).
% 11.68/11.84 tff(5979,plain,
% 11.68/11.84 ((~![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_q, s1, s2) | node22(c_e_h_3, c_q, s1, s2)),
% 11.68/11.84 inference(modus_ponens,[status(thm)],[5978, 5977])).
% 11.68/11.84 tff(5980,plain,
% 11.68/11.84 (node21(c_e_h_3, c_q, s1, s2) | node22(c_e_h_3, c_q, s1, s2)),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5979, 247, 470])).
% 11.68/11.84 tff(5981,plain,
% 11.68/11.84 (node22(c_e_h_3, c_q, s1, s2)),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5980, 5976])).
% 11.68/11.84 tff(5982,plain,
% 11.68/11.84 (((~![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_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))),
% 11.68/11.84 inference(rewrite,[status(thm)],[])).
% 11.68/11.84 tff(5983,plain,
% 11.68/11.84 ((~![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_q, s2)) | (~node22(c_e_h_3, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_q, s1))),
% 11.68/11.84 inference(quant_inst,[status(thm)],[])).
% 11.68/11.84 tff(5984,plain,
% 11.68/11.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s2)) | (~node22(c_e_h_3, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_q, s1)),
% 11.68/11.84 inference(modus_ponens,[status(thm)],[5983, 5982])).
% 11.68/11.84 tff(5985,plain,
% 11.68/11.84 ($false),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5984, 273, 3045, 5906, 5981])).
% 11.68/11.84 tff(5986,plain,(~m_and_h_gate_v_out(c_e_h_3, c_q, s2)), inference(lemma,lemma(discharge,[]))).
% 11.68/11.84 tff(5987,assumption,(~node3(c_e_h_3, c_e_h_1, s2)), introduced(assumption)).
% 11.68/11.84 tff(5988,plain,
% 11.68/11.84 (((~![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))),
% 11.68/11.84 inference(rewrite,[status(thm)],[])).
% 11.68/11.84 tff(5989,plain,
% 11.68/11.84 ((~![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))),
% 11.68/11.84 inference(quant_inst,[status(thm)],[])).
% 11.68/11.84 tff(5990,plain,
% 11.68/11.84 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s2)),
% 11.68/11.84 inference(modus_ponens,[status(thm)],[5989, 5988])).
% 11.68/11.84 tff(5991,plain,
% 11.68/11.84 ($false),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5990, 2923, 616, 5987])).
% 11.68/11.84 tff(5992,plain,(node3(c_e_h_3, c_e_h_1, s2)), inference(lemma,lemma(discharge,[]))).
% 11.68/11.84 tff(5993,plain,
% 11.68/11.84 (((~![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))),
% 11.68/11.84 inference(rewrite,[status(thm)],[])).
% 11.68/11.84 tff(5994,plain,
% 11.68/11.84 ((~![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))),
% 11.68/11.84 inference(quant_inst,[status(thm)],[])).
% 11.68/11.84 tff(5995,plain,
% 11.68/11.84 ((~![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)),
% 11.68/11.84 inference(modus_ponens,[status(thm)],[5994, 5993])).
% 11.68/11.84 tff(5996,plain,
% 11.68/11.84 ((~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)),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5995, 633])).
% 11.68/11.84 tff(5997,plain,
% 11.68/11.84 ((~m_cell_v_ack(c_e_h_1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_q, s2)),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5996, 5992])).
% 11.68/11.84 tff(5998,plain,
% 11.68/11.84 (~m_cell_v_ack(c_e_h_1, s2)),
% 11.68/11.84 inference(unit_resolution,[status(thm)],[5997, 5986])).
% 11.68/11.84 tff(5999,plain,
% 11.68/11.84 (((~![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))),
% 11.68/11.85 inference(rewrite,[status(thm)],[])).
% 11.68/11.85 tff(6000,plain,
% 11.68/11.85 ((~![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_1, c_j, s2)) | m_cell_v_ack(c_e_h_1, s2))),
% 11.68/11.85 inference(quant_inst,[status(thm)],[])).
% 11.68/11.85 tff(6001,plain,
% 11.68/11.85 ((~![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_1, c_j, s2)) | m_cell_v_ack(c_e_h_1, s2)),
% 11.68/11.85 inference(modus_ponens,[status(thm)],[6000, 5999])).
% 11.68/11.85 tff(6002,plain,
% 11.68/11.85 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s2)),
% 11.68/11.85 inference(unit_resolution,[status(thm)],[6001, 645, 5998])).
% 11.68/11.85 tff(6003,assumption,(node5(c_e_h_1, c_j, s2, s3)), introduced(assumption)).
% 11.68/11.85 tff(6004,plain,
% 11.68/11.85 (((~![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_1, c_j, s3)) | 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_in1(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_in2(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s2))),
% 11.68/11.85 inference(rewrite,[status(thm)],[])).
% 11.68/11.85 tff(6005,plain,
% 11.68/11.85 ((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_in2(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s2))),
% 11.68/11.85 inference(rewrite,[status(thm)],[])).
% 11.68/11.85 tff(6006,plain,
% 11.68/11.85 (((~![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_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_in2(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s2)))),
% 11.68/11.85 inference(monotonicity,[status(thm)],[6005])).
% 11.68/11.85 tff(6007,plain,
% 11.68/11.85 (((~![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_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_in2(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s2))),
% 11.68/11.85 inference(transitivity,[status(thm)],[6006, 6004])).
% 11.68/11.85 tff(6008,plain,
% 11.68/11.85 ((~![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_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)))),
% 11.68/11.85 inference(quant_inst,[status(thm)],[])).
% 11.68/11.85 tff(6009,plain,
% 11.68/11.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s2)),
% 11.68/11.85 inference(modus_ponens,[status(thm)],[6008, 6007])).
% 11.68/11.85 tff(6010,plain,
% 11.68/11.85 ($false),
% 11.68/11.85 inference(unit_resolution,[status(thm)],[6009, 705, 5886, 6003, 6002, 5905])).
% 11.68/11.85 tff(6011,plain,((~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_in1(c_e_h_1, c_j, s2)), inference(lemma,lemma(discharge,[]))).
% 11.68/11.85 tff(6012,plain,
% 11.68/11.85 (m_or_h_gate_v_in1(c_e_h_1, c_j, s2)),
% 11.68/11.85 inference(unit_resolution,[status(thm)],[6011, 5904, 5883])).
% 11.68/11.85 tff(6013,assumption,(m_or_h_gate_v_in1(c_e_h_1, c_j, s2)), introduced(assumption)).
% 11.68/11.85 tff(6014,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_l, s2)), introduced(assumption)).
% 11.68/11.85 tff(6015,plain,
% 11.68/11.85 (((~![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))),
% 11.68/11.85 inference(rewrite,[status(thm)],[])).
% 11.68/11.85 tff(6016,plain,
% 11.68/11.85 ((~![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))),
% 11.68/11.85 inference(quant_inst,[status(thm)],[])).
% 11.68/11.85 tff(6017,plain,
% 11.68/11.85 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s2)) | m_and_h_gate_v_out(c_e_h_1, c_l, s2)),
% 11.68/11.85 inference(modus_ponens,[status(thm)],[6016, 6015])).
% 11.68/11.85 tff(6018,plain,
% 11.68/11.85 ($false),
% 11.68/11.85 inference(unit_resolution,[status(thm)],[6017, 920, 6014, 6013])).
% 11.68/11.85 tff(6019,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 11.68/11.85 tff(6020,plain,
% 11.68/11.85 (m_and_h_gate_v_out(c_e_h_1, c_l, s2)),
% 11.68/11.85 inference(unit_resolution,[status(thm)],[6019, 6012])).
% 11.68/11.85 tff(6021,plain,
% 11.68/11.85 (((~![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_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)))),
% 11.68/11.85 inference(rewrite,[status(thm)],[])).
% 11.68/11.85 tff(6022,plain,
% 11.68/11.85 ((~![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_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)))),
% 11.68/11.85 inference(quant_inst,[status(thm)],[])).
% 11.68/11.85 tff(6023,plain,
% 11.68/11.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s2)) | (~node21(c_e_h_1, c_l, s1, s2))),
% 11.68/11.85 inference(modus_ponens,[status(thm)],[6022, 6021])).
% 11.68/11.85 tff(6024,plain,
% 11.68/11.85 ($false),
% 11.68/11.85 inference(unit_resolution,[status(thm)],[6023, 228, 6020, 177, 1])).
% 11.68/11.85 tff(6025,plain,(~node21(c_e_h_1, c_l, s1, s2)), inference(lemma,lemma(discharge,[]))).
% 11.68/11.85 tff(6026,plain,
% 11.68/11.85 (((~![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))),
% 11.68/11.85 inference(rewrite,[status(thm)],[])).
% 11.68/11.85 tff(6027,plain,
% 11.68/11.85 ((~![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))),
% 11.68/11.85 inference(quant_inst,[status(thm)],[])).
% 11.68/11.85 tff(6028,plain,
% 11.68/11.85 ((~![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)),
% 11.68/11.85 inference(modus_ponens,[status(thm)],[6027, 6026])).
% 11.71/11.86 tff(6029,plain,
% 11.71/11.86 (node21(c_e_h_1, c_l, s1, s2) | node22(c_e_h_1, c_l, s1, s2)),
% 11.71/11.86 inference(unit_resolution,[status(thm)],[6028, 247, 470])).
% 11.71/11.86 tff(6030,plain,
% 11.71/11.86 (node22(c_e_h_1, c_l, s1, s2)),
% 11.71/11.86 inference(unit_resolution,[status(thm)],[6029, 6025])).
% 11.71/11.86 tff(6031,plain,
% 11.71/11.86 (((~![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, 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))),
% 11.71/11.86 inference(rewrite,[status(thm)],[])).
% 11.71/11.86 tff(6032,plain,
% 11.71/11.86 ((~![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, s2)) | (~node22(c_e_h_1, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_l, s1))),
% 11.71/11.86 inference(quant_inst,[status(thm)],[])).
% 11.71/11.86 tff(6033,plain,
% 11.71/11.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s2)) | (~node22(c_e_h_1, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_l, s1)),
% 11.71/11.86 inference(modus_ponens,[status(thm)],[6032, 6031])).
% 11.71/11.86 tff(6034,plain,
% 11.71/11.86 ($false),
% 11.71/11.86 inference(unit_resolution,[status(thm)],[6033, 273, 2981, 6020, 6030])).
% 11.71/11.86 % SZS output end Proof
% 11.71/11.86 % E exiting
%------------------------------------------------------------------------------