%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV419-1.005 : TPTP v9.0.0. Released v3.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 1.82s 2.05s
% Output : Proof 1.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV419-1.005 : TPTP v9.0.0. Released v3.5.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n009.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
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 09:47:03 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.82/2.05 % SZS status Unsatisfiable
% 1.82/2.05 % SZS output start Proof
% 1.82/2.05 tff(node25_type, type, (
% 1.82/2.05 node25: $i > $o)).
% 1.82/2.05 tff(s3_type, type, (
% 1.82/2.05 s3: $i)).
% 1.82/2.05 tff(m_user_v_ack_type, type, (
% 1.82/2.05 m_user_v_ack: ( $i * $i * $i ) > $o)).
% 1.82/2.05 tff(c_u_type, type, (
% 1.82/2.05 c_u: $i)).
% 1.82/2.05 tff(c_e_h_2_type, type, (
% 1.82/2.05 c_e_h_2: $i)).
% 1.82/2.05 tff(m_and_h_gate_v_out_type, type, (
% 1.82/2.05 m_and_h_gate_v_out: ( $i * $i * $i ) > $o)).
% 1.82/2.05 tff(c_r_type, type, (
% 1.82/2.05 c_r: $i)).
% 1.82/2.05 tff(s2_type, type, (
% 1.82/2.05 s2: $i)).
% 1.82/2.05 tff(s1_type, type, (
% 1.82/2.05 s1: $i)).
% 1.82/2.05 tff(node22_type, type, (
% 1.82/2.05 node22: ( $i * $i * $i * $i ) > $o)).
% 1.82/2.05 tff(s0_type, type, (
% 1.82/2.05 s0: $i)).
% 1.82/2.05 tff(node21_type, type, (
% 1.82/2.05 node21: ( $i * $i * $i * $i ) > $o)).
% 1.82/2.05 tff(node20_type, type, (
% 1.82/2.05 node20: ( $i * $i * $i ) > $o)).
% 1.82/2.05 tff(m_and_h_gate_v_in2_type, type, (
% 1.82/2.05 m_and_h_gate_v_in2: ( $i * $i * $i ) > $o)).
% 1.82/2.05 tff(m_and_h_gate_h_init_v_out_type, type, (
% 1.82/2.05 m_and_h_gate_h_init_v_out: ( $i * $i * $i ) > $o)).
% 1.82/2.05 tff(c_m_type, type, (
% 1.82/2.05 c_m: $i)).
% 1.82/2.05 tff(m_and_h_gate_h_init_v_init_h_out_type, type, (
% 1.82/2.05 m_and_h_gate_h_init_v_init_h_out: ( $i * $i * $i ) > $o)).
% 1.82/2.05 tff(m_cell_v_token_type, type, (
% 1.82/2.05 m_cell_v_token: ( $i * $i ) > $o)).
% 1.82/2.05 tff(trans_type, type, (
% 1.82/2.05 trans: ( $i * $i ) > $o)).
% 1.82/2.05 tff(succ_type, type, (
% 1.82/2.05 succ: ( $i * $i ) > $o)).
% 1.82/2.05 tff(node11_type, type, (
% 1.82/2.05 node11: ( $i * $i * $i * $i ) > $o)).
% 1.82/2.05 tff(node10_type, type, (
% 1.82/2.05 node10: ( $i * $i * $i * $i ) > $o)).
% 1.82/2.05 tff(node9_type, type, (
% 1.82/2.05 node9: ( $i * $i * $i ) > $o)).
% 1.82/2.05 tff(m_and_h_gate_h_init_v_in2_type, type, (
% 1.82/2.05 m_and_h_gate_h_init_v_in2: ( $i * $i * $i ) > $o)).
% 1.82/2.05 tff(c_n_type, type, (
% 1.82/2.05 c_n: $i)).
% 1.82/2.05 tff(m_and_h_gate_v_in1_type, type, (
% 1.82/2.05 m_and_h_gate_v_in1: ( $i * $i * $i ) > $o)).
% 1.82/2.05 tff(m_c_h_element_v_out_type, type, (
% 1.82/2.05 m_c_h_element_v_out: ( $i * $i * $i ) > $o)).
% 1.82/2.05 tff(c_e_type, type, (
% 1.82/2.05 c_e: $i)).
% 1.82/2.05 tff(node15_type, type, (
% 1.82/2.05 node15: ( $i * $i * $i * $i ) > $o)).
% 1.82/2.05 tff(node16_type, type, (
% 1.82/2.05 node16: ( $i * $i * $i ) > $o)).
% 1.82/2.05 tff(m_c_h_element_v_in1_type, type, (
% 1.82/2.05 m_c_h_element_v_in1: ( $i * $i * $i ) > $o)).
% 1.82/2.05 tff(node17_type, type, (
% 1.82/2.05 node17: ( $i * $i * $i ) > $o)).
% 1.82/2.05 tff(node18_type, type, (
% 1.82/2.05 node18: ( $i * $i * $i * $i ) > $o)).
% 1.82/2.05 tff(node19_type, type, (
% 1.82/2.05 node19: ( $i * $i * $i * $i ) > $o)).
% 1.82/2.05 tff(m_c_h_element_v_in2_type, type, (
% 1.82/2.05 m_c_h_element_v_in2: ( $i * $i * $i ) > $o)).
% 1.82/2.05 tff(c_i_type, type, (
% 1.82/2.05 c_i: $i)).
% 1.82/2.05 tff(node14_type, type, (
% 1.82/2.05 node14: ( $i * $i * $i * $i ) > $o)).
% 1.82/2.05 tff(c_h_type, type, (
% 1.82/2.05 c_h: $i)).
% 1.82/2.05 tff(node24_type, type, (
% 1.82/2.05 node24: $i > $o)).
% 1.82/2.05 tff(s4_type, type, (
% 1.82/2.05 s4: $i)).
% 1.82/2.05 tff(c_e_h_1_type, type, (
% 1.82/2.05 c_e_h_1: $i)).
% 1.82/2.05 tff(m_and_h_gate_h_init_v_in1_type, type, (
% 1.82/2.05 m_and_h_gate_h_init_v_in1: ( $i * $i * $i ) > $o)).
% 1.82/2.05 tff(node26_type, type, (
% 1.82/2.05 node26: $i > $o)).
% 1.82/2.05 tff(node23_type, type, (
% 1.82/2.05 node23: $i > $o)).
% 1.82/2.05 tff(c_e_h_3_type, type, (
% 1.82/2.05 c_e_h_3: $i)).
% 1.82/2.05 tff(xuntil28_type, type, (
% 1.82/2.05 xuntil28: $i > $o)).
% 1.82/2.05 tff(until27_type, type, (
% 1.82/2.05 until27: $i > $o)).
% 1.82/2.05 tff(until2p29_type, type, (
% 1.82/2.05 until2p29: $i > $o)).
% 1.82/2.05 tff(xuntil2p30_type, type, (
% 1.82/2.05 xuntil2p30: $i > $o)).
% 1.82/2.05 tff(last_type, type, (
% 1.82/2.05 last: $i > $o)).
% 1.82/2.05 tff(loop_type, type, (
% 1.82/2.05 loop: $o)).
% 1.82/2.05 tff(1,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s1)), introduced(assumption)).
% 1.82/2.05 tff(2,assumption,(m_cell_v_token(c_e_h_2, s0)), introduced(assumption)).
% 1.82/2.05 tff(3,plain,
% 1.82/2.05 (^[X: $i] : refl((~m_cell_v_token(c_e_h_2, X)) <=> (~m_cell_v_token(c_e_h_2, X)))),
% 1.82/2.05 inference(bind,[status(th)],[])).
% 1.82/2.05 tff(4,plain,
% 1.82/2.05 (![X: $i] : (~m_cell_v_token(c_e_h_2, X)) <=> ![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 1.82/2.05 inference(quant_intro,[status(thm)],[3])).
% 1.82/2.05 tff(5,plain,
% 1.82/2.05 (![X: $i] : (~m_cell_v_token(c_e_h_2, X)) <=> ![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(6,axiom,(![X: $i] : (~m_cell_v_token(c_e_h_2, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_6')).
% 1.82/2.05 tff(7,plain,
% 1.82/2.05 (![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.82/2.05 tff(8,plain,(
% 1.82/2.05 ![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 1.82/2.05 inference(skolemize,[status(sab)],[7])).
% 1.82/2.05 tff(9,plain,
% 1.82/2.05 (![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[8, 4])).
% 1.82/2.05 tff(10,plain,
% 1.82/2.05 ((~![X: $i] : (~m_cell_v_token(c_e_h_2, X))) | (~m_cell_v_token(c_e_h_2, s0))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(11,plain,
% 1.82/2.05 ($false),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 1.82/2.05 tff(12,plain,(~m_cell_v_token(c_e_h_2, s0)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.05 tff(13,plain,
% 1.82/2.05 (^[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)))),
% 1.82/2.05 inference(bind,[status(th)],[])).
% 1.82/2.05 tff(14,plain,
% 1.82/2.05 (![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))),
% 1.82/2.05 inference(quant_intro,[status(thm)],[13])).
% 1.82/2.05 tff(15,plain,
% 1.82/2.05 (![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))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(16,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/sandbox2/benchmark/theBenchmark.p','m_cell_56')).
% 1.82/2.05 tff(17,plain,
% 1.82/2.05 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.82/2.05 tff(18,plain,(
% 1.82/2.05 ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))),
% 1.82/2.05 inference(skolemize,[status(sab)],[17])).
% 1.82/2.05 tff(19,plain,
% 1.82/2.05 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.82/2.05 tff(20,plain,
% 1.82/2.05 (((~![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))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(21,plain,
% 1.82/2.05 ((~![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))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(22,plain,
% 1.82/2.05 ((~![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)),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[21, 20])).
% 1.82/2.05 tff(23,plain,
% 1.82/2.05 (~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_m, s0)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[22, 19, 12])).
% 1.82/2.05 tff(24,plain,
% 1.82/2.05 (^[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)))),
% 1.82/2.05 inference(bind,[status(th)],[])).
% 1.82/2.05 tff(25,plain,
% 1.82/2.05 (![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))),
% 1.82/2.05 inference(quant_intro,[status(thm)],[24])).
% 1.82/2.05 tff(26,plain,
% 1.82/2.05 (![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))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(27,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/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_h_init_2')).
% 1.82/2.05 tff(28,plain,
% 1.82/2.05 (![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))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[27, 26])).
% 1.82/2.05 tff(29,plain,(
% 1.82/2.05 ![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))),
% 1.82/2.05 inference(skolemize,[status(sab)],[28])).
% 1.82/2.05 tff(30,plain,
% 1.82/2.05 (![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))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[29, 25])).
% 1.82/2.05 tff(31,plain,
% 1.82/2.05 (((~![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))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(32,plain,
% 1.82/2.05 ((~![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))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(33,plain,
% 1.82/2.05 ((~![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)),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[32, 31])).
% 1.82/2.05 tff(34,plain,
% 1.82/2.05 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[33, 30, 23])).
% 1.82/2.05 tff(35,plain,
% 1.82/2.05 (^[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)))),
% 1.82/2.05 inference(bind,[status(th)],[])).
% 1.82/2.05 tff(36,plain,
% 1.82/2.05 (![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))),
% 1.82/2.05 inference(quant_intro,[status(thm)],[35])).
% 1.82/2.05 tff(37,plain,
% 1.82/2.05 (![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))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(38,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/sandbox2/benchmark/theBenchmark.p','m_cell_74')).
% 1.82/2.05 tff(39,plain,
% 1.82/2.05 (![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))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[38, 37])).
% 1.82/2.05 tff(40,plain,(
% 1.82/2.05 ![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))),
% 1.82/2.05 inference(skolemize,[status(sab)],[39])).
% 1.82/2.05 tff(41,plain,
% 1.82/2.05 (![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))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[40, 36])).
% 1.82/2.05 tff(42,plain,
% 1.82/2.05 (((~![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))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(43,plain,
% 1.82/2.05 ((~![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))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(44,plain,
% 1.82/2.05 ((~![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)),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[43, 42])).
% 1.82/2.05 tff(45,plain,
% 1.82/2.05 (~m_and_h_gate_v_in2(c_e_h_2, c_r, s0)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[44, 41, 34])).
% 1.82/2.05 tff(46,plain,
% 1.82/2.05 (^[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)))),
% 1.82/2.05 inference(bind,[status(th)],[])).
% 1.82/2.05 tff(47,plain,
% 1.82/2.05 (![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))),
% 1.82/2.05 inference(quant_intro,[status(thm)],[46])).
% 1.82/2.05 tff(48,plain,
% 1.82/2.05 (![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))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(49,plain,
% 1.82/2.05 (^[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)))),
% 1.82/2.05 inference(bind,[status(th)],[])).
% 1.82/2.05 tff(50,plain,
% 1.82/2.05 (![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))),
% 1.82/2.05 inference(quant_intro,[status(thm)],[49])).
% 1.82/2.05 tff(51,axiom,(![I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_in2(I0, I1, X) | (~node20(I0, I1, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_3')).
% 1.82/2.05 tff(52,plain,
% 1.82/2.05 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[51, 50])).
% 1.82/2.05 tff(53,plain,
% 1.82/2.05 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[52, 48])).
% 1.82/2.05 tff(54,plain,(
% 1.82/2.05 ![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 1.82/2.05 inference(skolemize,[status(sab)],[53])).
% 1.82/2.05 tff(55,plain,
% 1.82/2.05 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[54, 47])).
% 1.82/2.05 tff(56,plain,
% 1.82/2.05 (((~![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))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(57,plain,
% 1.82/2.05 ((~![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))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(58,plain,
% 1.82/2.05 ((~![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)),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[57, 56])).
% 1.82/2.05 tff(59,plain,
% 1.82/2.05 (~node20(c_e_h_2, c_r, s0)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[58, 55, 45])).
% 1.82/2.05 tff(60,plain,
% 1.82/2.05 (^[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))))),
% 1.82/2.05 inference(bind,[status(th)],[])).
% 1.82/2.05 tff(61,plain,
% 1.82/2.05 (![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 1.82/2.05 inference(quant_intro,[status(thm)],[60])).
% 1.82/2.05 tff(62,plain,
% 1.82/2.05 (![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(63,plain,
% 1.82/2.05 (^[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))))),
% 1.82/2.05 inference(bind,[status(th)],[])).
% 1.82/2.05 tff(64,plain,
% 1.82/2.05 (![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)))),
% 1.82/2.05 inference(quant_intro,[status(thm)],[63])).
% 1.82/2.05 tff(65,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/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_5')).
% 1.82/2.05 tff(66,plain,
% 1.82/2.05 (![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[65, 64])).
% 1.82/2.05 tff(67,plain,
% 1.82/2.05 (![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[66, 62])).
% 1.82/2.05 tff(68,plain,(
% 1.82/2.05 ![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 1.82/2.05 inference(skolemize,[status(sab)],[67])).
% 1.82/2.05 tff(69,plain,
% 1.82/2.05 (![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[68, 61])).
% 1.82/2.05 tff(70,plain,
% 1.82/2.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | node20(c_e_h_2, c_r, s0) | (~node21(c_e_h_2, c_r, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | node20(c_e_h_2, c_r, s0) | (~node21(c_e_h_2, c_r, s0, s1)))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(71,plain,
% 1.82/2.05 ((node20(c_e_h_2, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | (~node21(c_e_h_2, c_r, s0, s1))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | node20(c_e_h_2, c_r, s0) | (~node21(c_e_h_2, c_r, s0, s1)))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(72,plain,
% 1.82/2.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | (~node21(c_e_h_2, c_r, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | node20(c_e_h_2, c_r, s0) | (~node21(c_e_h_2, c_r, s0, s1))))),
% 1.82/2.05 inference(monotonicity,[status(thm)],[71])).
% 1.82/2.05 tff(73,plain,
% 1.82/2.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | (~node21(c_e_h_2, c_r, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | node20(c_e_h_2, c_r, s0) | (~node21(c_e_h_2, c_r, s0, s1)))),
% 1.82/2.05 inference(transitivity,[status(thm)],[72, 70])).
% 1.82/2.05 tff(74,plain,
% 1.82/2.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_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)))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(75,plain,
% 1.82/2.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | node20(c_e_h_2, c_r, s0) | (~node21(c_e_h_2, c_r, s0, s1))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[74, 73])).
% 1.82/2.05 tff(76,plain,
% 1.82/2.05 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | (~node21(c_e_h_2, c_r, s0, s1))),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[75, 69, 59])).
% 1.82/2.05 tff(77,plain,
% 1.82/2.05 (~node21(c_e_h_2, c_r, s0, s1)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[76, 1])).
% 1.82/2.05 tff(78,plain,
% 1.82/2.05 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | trans(X, Y)) <=> ((~succ(X, Y)) | trans(X, Y)))),
% 1.82/2.05 inference(bind,[status(th)],[])).
% 1.82/2.05 tff(79,plain,
% 1.82/2.05 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 1.82/2.05 inference(quant_intro,[status(thm)],[78])).
% 1.82/2.05 tff(80,plain,
% 1.82/2.05 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(81,axiom,(![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound6')).
% 1.82/2.05 tff(82,plain,
% 1.82/2.05 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[81, 80])).
% 1.82/2.05 tff(83,plain,(
% 1.82/2.05 ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 1.82/2.05 inference(skolemize,[status(sab)],[82])).
% 1.82/2.05 tff(84,plain,
% 1.82/2.05 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[83, 79])).
% 1.82/2.05 tff(85,plain,
% 1.82/2.05 (succ(s0, s1) <=> succ(s0, s1)),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(86,axiom,(succ(s0, s1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound1')).
% 1.82/2.05 tff(87,plain,
% 1.82/2.05 (succ(s0, s1)),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[86, 85])).
% 1.82/2.05 tff(88,plain,
% 1.82/2.05 (((~![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))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(89,plain,
% 1.82/2.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s0, s1)) | trans(s0, s1))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(90,plain,
% 1.82/2.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s0, s1)) | trans(s0, s1)),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[89, 88])).
% 1.82/2.05 tff(91,plain,
% 1.82/2.05 (trans(s0, s1)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[90, 87, 84])).
% 1.82/2.05 tff(92,plain,
% 1.82/2.05 (^[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)))),
% 1.82/2.05 inference(bind,[status(th)],[])).
% 1.82/2.05 tff(93,plain,
% 1.82/2.05 (![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))),
% 1.82/2.05 inference(quant_intro,[status(thm)],[92])).
% 1.82/2.05 tff(94,plain,
% 1.82/2.05 (![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))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(95,plain,
% 1.82/2.05 (^[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)))),
% 1.82/2.05 inference(bind,[status(th)],[])).
% 1.82/2.05 tff(96,plain,
% 1.82/2.05 (![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))),
% 1.82/2.05 inference(quant_intro,[status(thm)],[95])).
% 1.82/2.05 tff(97,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/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_8')).
% 1.82/2.05 tff(98,plain,
% 1.82/2.05 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[97, 96])).
% 1.82/2.05 tff(99,plain,
% 1.82/2.05 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[98, 94])).
% 1.82/2.05 tff(100,plain,(
% 1.82/2.05 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 1.82/2.05 inference(skolemize,[status(sab)],[99])).
% 1.82/2.05 tff(101,plain,
% 1.82/2.05 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[100, 93])).
% 1.82/2.05 tff(102,plain,
% 1.82/2.05 (((~![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))),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(103,plain,
% 1.82/2.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_r, s0, s1) | node22(c_e_h_2, c_r, s0, s1))),
% 1.82/2.06 inference(quant_inst,[status(thm)],[])).
% 1.82/2.06 tff(104,plain,
% 1.82/2.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_r, s0, s1) | node22(c_e_h_2, c_r, s0, s1)),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[103, 102])).
% 1.82/2.06 tff(105,plain,
% 1.82/2.06 (node22(c_e_h_2, c_r, s0, s1)),
% 1.82/2.06 inference(unit_resolution,[status(thm)],[104, 101, 91, 77])).
% 1.82/2.06 tff(106,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s0)), introduced(assumption)).
% 1.82/2.06 tff(107,plain,
% 1.82/2.06 (^[I0: $i, I1: $i] : refl((~m_and_h_gate_v_out(I0, I1, s0)) <=> (~m_and_h_gate_v_out(I0, I1, s0)))),
% 1.82/2.06 inference(bind,[status(th)],[])).
% 1.82/2.06 tff(108,plain,
% 1.82/2.06 (![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))),
% 1.82/2.06 inference(quant_intro,[status(thm)],[107])).
% 1.82/2.06 tff(109,plain,
% 1.82/2.06 (![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))),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(110,axiom,(![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_1')).
% 1.82/2.06 tff(111,plain,
% 1.82/2.06 (![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[110, 109])).
% 1.82/2.06 tff(112,plain,(
% 1.82/2.06 ![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))),
% 1.82/2.06 inference(skolemize,[status(sab)],[111])).
% 1.82/2.06 tff(113,plain,
% 1.82/2.06 (![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[112, 108])).
% 1.82/2.06 tff(114,plain,
% 1.82/2.06 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s0))),
% 1.82/2.06 inference(quant_inst,[status(thm)],[])).
% 1.82/2.06 tff(115,plain,
% 1.82/2.06 ($false),
% 1.82/2.06 inference(unit_resolution,[status(thm)],[114, 113, 106])).
% 1.82/2.06 tff(116,plain,(~m_and_h_gate_v_out(c_e_h_2, c_r, s0)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.06 tff(117,plain,
% 1.82/2.06 (^[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)))),
% 1.82/2.06 inference(bind,[status(th)],[])).
% 1.82/2.06 tff(118,plain,
% 1.82/2.06 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 1.82/2.06 inference(quant_intro,[status(thm)],[117])).
% 1.82/2.06 tff(119,plain,
% 1.82/2.06 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(120,plain,
% 1.82/2.06 (^[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)))),
% 1.82/2.06 inference(bind,[status(th)],[])).
% 1.82/2.06 tff(121,plain,
% 1.82/2.06 (![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))),
% 1.82/2.06 inference(quant_intro,[status(thm)],[120])).
% 1.82/2.06 tff(122,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/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_7')).
% 1.82/2.06 tff(123,plain,
% 1.82/2.06 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[122, 121])).
% 1.82/2.06 tff(124,plain,
% 1.82/2.06 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[123, 119])).
% 1.82/2.06 tff(125,plain,(
% 1.82/2.06 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 1.82/2.06 inference(skolemize,[status(sab)],[124])).
% 1.82/2.06 tff(126,plain,
% 1.82/2.06 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[125, 118])).
% 1.82/2.06 tff(127,plain,
% 1.82/2.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_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))),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(128,plain,
% 1.82/2.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_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))),
% 1.82/2.06 inference(quant_inst,[status(thm)],[])).
% 1.82/2.06 tff(129,plain,
% 1.82/2.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | (~node22(c_e_h_2, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_r, s0)),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[128, 127])).
% 1.82/2.06 tff(130,plain,
% 1.82/2.06 ($false),
% 1.82/2.06 inference(unit_resolution,[status(thm)],[129, 126, 116, 1, 105])).
% 1.82/2.06 tff(131,plain,(~m_and_h_gate_v_out(c_e_h_2, c_r, s1)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.06 tff(132,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)), introduced(assumption)).
% 1.82/2.06 tff(133,assumption,(node10(c_e_h_2, c_m, s0, s1)), introduced(assumption)).
% 1.82/2.06 tff(134,plain,
% 1.82/2.06 (^[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)))),
% 1.82/2.06 inference(bind,[status(th)],[])).
% 1.82/2.06 tff(135,plain,
% 1.82/2.06 (![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))),
% 1.82/2.06 inference(quant_intro,[status(thm)],[134])).
% 1.82/2.06 tff(136,plain,
% 1.82/2.06 (![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))),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(137,plain,
% 1.82/2.06 (^[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)))),
% 1.82/2.06 inference(bind,[status(th)],[])).
% 1.82/2.06 tff(138,plain,
% 1.82/2.06 (![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))),
% 1.82/2.06 inference(quant_intro,[status(thm)],[137])).
% 1.82/2.06 tff(139,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/sandbox2/benchmark/theBenchmark.p','m_cell_61')).
% 1.82/2.06 tff(140,plain,
% 1.82/2.06 (![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[139, 138])).
% 1.82/2.06 tff(141,plain,
% 1.82/2.06 (![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[140, 136])).
% 1.82/2.06 tff(142,plain,(
% 1.82/2.06 ![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 1.82/2.06 inference(skolemize,[status(sab)],[141])).
% 1.82/2.06 tff(143,plain,
% 1.82/2.06 (![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[142, 135])).
% 1.82/2.06 tff(144,plain,
% 1.82/2.06 (((~![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) | (m_cell_v_token(c_e_h_2, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0))) <=> ((~![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) | m_cell_v_token(c_e_h_2, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0))),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(145,plain,
% 1.82/2.06 ((~![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) | (m_cell_v_token(c_e_h_2, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0))),
% 1.82/2.06 inference(quant_inst,[status(thm)],[])).
% 1.82/2.06 tff(146,plain,
% 1.82/2.06 ((~![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) | m_cell_v_token(c_e_h_2, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0)),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[145, 144])).
% 1.82/2.06 tff(147,plain,
% 1.82/2.06 (m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0)),
% 1.82/2.06 inference(unit_resolution,[status(thm)],[146, 143, 12])).
% 1.82/2.06 tff(148,plain,
% 1.82/2.06 (^[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)))),
% 1.82/2.06 inference(bind,[status(th)],[])).
% 1.82/2.06 tff(149,plain,
% 1.82/2.06 (![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))),
% 1.82/2.06 inference(quant_intro,[status(thm)],[148])).
% 1.82/2.06 tff(150,plain,
% 1.82/2.06 (![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))),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(151,plain,
% 1.82/2.06 (^[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)))),
% 1.82/2.06 inference(bind,[status(th)],[])).
% 1.82/2.06 tff(152,plain,
% 1.82/2.06 (![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))),
% 1.82/2.06 inference(quant_intro,[status(thm)],[151])).
% 1.82/2.06 tff(153,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/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_h_init_1')).
% 1.82/2.06 tff(154,plain,
% 1.82/2.06 (![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))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[153, 152])).
% 1.82/2.06 tff(155,plain,
% 1.82/2.06 (![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))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[154, 150])).
% 1.82/2.06 tff(156,plain,(
% 1.82/2.06 ![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))),
% 1.82/2.06 inference(skolemize,[status(sab)],[155])).
% 1.82/2.06 tff(157,plain,
% 1.82/2.06 (![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))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[156, 149])).
% 1.82/2.06 tff(158,plain,
% 1.82/2.06 (((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0))) <=> ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0))),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(159,plain,
% 1.82/2.06 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0))),
% 1.82/2.06 inference(quant_inst,[status(thm)],[])).
% 1.82/2.06 tff(160,plain,
% 1.82/2.06 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[159, 158])).
% 1.82/2.06 tff(161,plain,
% 1.82/2.06 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)),
% 1.82/2.06 inference(unit_resolution,[status(thm)],[160, 157, 147])).
% 1.82/2.06 tff(162,plain,
% 1.82/2.06 (^[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))))),
% 1.82/2.06 inference(bind,[status(th)],[])).
% 1.82/2.06 tff(163,plain,
% 1.82/2.06 (![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)))),
% 1.82/2.06 inference(quant_intro,[status(thm)],[162])).
% 1.82/2.06 tff(164,plain,
% 1.82/2.06 (![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)))),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(165,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/sandbox2/benchmark/theBenchmark.p','m_cell_54')).
% 1.82/2.06 tff(166,plain,
% 1.82/2.06 (![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)))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[165, 164])).
% 1.82/2.06 tff(167,plain,(
% 1.82/2.06 ![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)))),
% 1.82/2.06 inference(skolemize,[status(sab)],[166])).
% 1.82/2.06 tff(168,plain,
% 1.82/2.06 (![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)))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[167, 163])).
% 1.82/2.06 tff(169,plain,
% 1.82/2.06 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)))),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(170,plain,
% 1.82/2.06 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)))),
% 1.82/2.06 inference(quant_inst,[status(thm)],[])).
% 1.82/2.06 tff(171,plain,
% 1.82/2.06 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[170, 169])).
% 1.82/2.06 tff(172,plain,
% 1.82/2.06 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0)),
% 1.82/2.06 inference(unit_resolution,[status(thm)],[171, 168, 161])).
% 1.82/2.06 tff(173,plain,
% 1.82/2.06 (^[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)))),
% 1.82/2.06 inference(bind,[status(th)],[])).
% 1.82/2.06 tff(174,plain,
% 1.82/2.06 (![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))),
% 1.82/2.06 inference(quant_intro,[status(thm)],[173])).
% 1.82/2.06 tff(175,plain,
% 1.82/2.06 (![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))),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(176,plain,
% 1.82/2.06 (^[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)))),
% 1.82/2.06 inference(bind,[status(th)],[])).
% 1.82/2.06 tff(177,plain,
% 1.82/2.06 (![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))),
% 1.82/2.06 inference(quant_intro,[status(thm)],[176])).
% 1.82/2.06 tff(178,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/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_h_init_4')).
% 1.82/2.06 tff(179,plain,
% 1.82/2.06 (![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[178, 177])).
% 1.82/2.06 tff(180,plain,
% 1.82/2.06 (![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[179, 175])).
% 1.82/2.06 tff(181,plain,(
% 1.82/2.06 ![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 1.82/2.06 inference(skolemize,[status(sab)],[180])).
% 1.82/2.06 tff(182,plain,
% 1.82/2.06 (![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[181, 174])).
% 1.82/2.06 tff(183,plain,
% 1.82/2.06 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0))),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(184,plain,
% 1.82/2.06 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0))),
% 1.82/2.06 inference(quant_inst,[status(thm)],[])).
% 1.82/2.06 tff(185,plain,
% 1.82/2.06 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0)),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[184, 183])).
% 1.82/2.06 tff(186,plain,
% 1.82/2.06 (~node9(c_e_h_2, c_m, s0)),
% 1.82/2.06 inference(unit_resolution,[status(thm)],[185, 182, 172])).
% 1.82/2.06 tff(187,plain,
% 1.82/2.06 (^[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))))),
% 1.82/2.06 inference(bind,[status(th)],[])).
% 1.82/2.06 tff(188,plain,
% 1.82/2.06 (![Y: $i, I0: $i, 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)))),
% 1.82/2.06 inference(quant_intro,[status(thm)],[187])).
% 1.82/2.06 tff(189,plain,
% 1.82/2.06 (![Y: $i, I0: $i, 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)))),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(190,plain,
% 1.82/2.06 (^[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))))),
% 1.82/2.06 inference(bind,[status(th)],[])).
% 1.82/2.06 tff(191,plain,
% 1.82/2.06 (![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)))),
% 1.82/2.06 inference(quant_intro,[status(thm)],[190])).
% 1.82/2.06 tff(192,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/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_h_init_6')).
% 1.82/2.06 tff(193,plain,
% 1.82/2.06 (![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[192, 191])).
% 1.82/2.06 tff(194,plain,
% 1.82/2.06 (![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[193, 189])).
% 1.82/2.06 tff(195,plain,(
% 1.82/2.06 ![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 1.82/2.06 inference(skolemize,[status(sab)],[194])).
% 1.82/2.06 tff(196,plain,
% 1.82/2.06 (![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[195, 188])).
% 1.82/2.06 tff(197,plain,
% 1.82/2.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node10(c_e_h_2, c_m, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node10(c_e_h_2, c_m, s0, s1)))),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(198,plain,
% 1.82/2.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node10(c_e_h_2, c_m, s0, s1)))),
% 1.82/2.06 inference(quant_inst,[status(thm)],[])).
% 1.82/2.06 tff(199,plain,
% 1.82/2.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node10(c_e_h_2, c_m, s0, s1))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[198, 197])).
% 1.82/2.06 tff(200,plain,
% 1.82/2.06 ($false),
% 1.82/2.06 inference(unit_resolution,[status(thm)],[199, 196, 186, 132, 133])).
% 1.82/2.06 tff(201,plain,((~node10(c_e_h_2, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))), inference(lemma,lemma(discharge,[]))).
% 1.82/2.06 tff(202,plain,
% 1.82/2.06 (~node10(c_e_h_2, c_m, s0, s1)),
% 1.82/2.06 inference(unit_resolution,[status(thm)],[201, 132])).
% 1.82/2.06 tff(203,plain,
% 1.82/2.06 (^[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)))),
% 1.82/2.06 inference(bind,[status(th)],[])).
% 1.82/2.06 tff(204,plain,
% 1.82/2.06 (![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))),
% 1.82/2.06 inference(quant_intro,[status(thm)],[203])).
% 1.82/2.06 tff(205,plain,
% 1.82/2.06 (![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))),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(206,plain,
% 1.82/2.06 (^[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)))),
% 1.82/2.06 inference(bind,[status(th)],[])).
% 1.82/2.06 tff(207,plain,
% 1.82/2.06 (![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))),
% 1.82/2.06 inference(quant_intro,[status(thm)],[206])).
% 1.82/2.06 tff(208,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/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_h_init_9')).
% 1.82/2.06 tff(209,plain,
% 1.82/2.06 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[208, 207])).
% 1.82/2.06 tff(210,plain,
% 1.82/2.06 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[209, 205])).
% 1.82/2.06 tff(211,plain,(
% 1.82/2.06 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 1.82/2.06 inference(skolemize,[status(sab)],[210])).
% 1.82/2.06 tff(212,plain,
% 1.82/2.06 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[211, 204])).
% 1.82/2.06 tff(213,plain,
% 1.82/2.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_2, c_m, s0, s1) | node11(c_e_h_2, c_m, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_2, c_m, s0, s1) | node11(c_e_h_2, c_m, s0, s1))),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(214,plain,
% 1.82/2.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_2, c_m, s0, s1) | node11(c_e_h_2, c_m, s0, s1))),
% 1.82/2.06 inference(quant_inst,[status(thm)],[])).
% 1.82/2.06 tff(215,plain,
% 1.82/2.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_2, c_m, s0, s1) | node11(c_e_h_2, c_m, s0, s1)),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[214, 213])).
% 1.82/2.06 tff(216,plain,
% 1.82/2.06 (node10(c_e_h_2, c_m, s0, s1) | node11(c_e_h_2, c_m, s0, s1)),
% 1.82/2.06 inference(unit_resolution,[status(thm)],[215, 212, 91])).
% 1.82/2.06 tff(217,plain,
% 1.82/2.06 (node11(c_e_h_2, c_m, s0, s1)),
% 1.82/2.06 inference(unit_resolution,[status(thm)],[216, 202])).
% 1.82/2.06 tff(218,plain,
% 1.82/2.06 (^[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)))),
% 1.82/2.06 inference(bind,[status(th)],[])).
% 1.82/2.06 tff(219,plain,
% 1.82/2.06 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 1.82/2.06 inference(quant_intro,[status(thm)],[218])).
% 1.82/2.06 tff(220,plain,
% 1.82/2.06 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(221,plain,
% 1.82/2.06 (^[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)))),
% 1.82/2.06 inference(bind,[status(th)],[])).
% 1.82/2.06 tff(222,plain,
% 1.82/2.06 (![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))),
% 1.82/2.06 inference(quant_intro,[status(thm)],[221])).
% 1.82/2.06 tff(223,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/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_h_init_8')).
% 1.82/2.06 tff(224,plain,
% 1.82/2.06 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[223, 222])).
% 1.82/2.06 tff(225,plain,
% 1.82/2.06 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[224, 220])).
% 1.82/2.06 tff(226,plain,(
% 1.82/2.06 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 1.82/2.06 inference(skolemize,[status(sab)],[225])).
% 1.82/2.06 tff(227,plain,
% 1.82/2.06 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[226, 219])).
% 1.82/2.06 tff(228,plain,
% 1.82/2.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node11(c_e_h_2, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node11(c_e_h_2, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(229,plain,
% 1.82/2.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node11(c_e_h_2, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))),
% 1.82/2.06 inference(quant_inst,[status(thm)],[])).
% 1.82/2.06 tff(230,plain,
% 1.82/2.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node11(c_e_h_2, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0)),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[229, 228])).
% 1.82/2.06 tff(231,plain,
% 1.82/2.06 ($false),
% 1.82/2.06 inference(unit_resolution,[status(thm)],[230, 227, 34, 132, 217])).
% 1.82/2.06 tff(232,plain,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.06 tff(233,plain,
% 1.82/2.06 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(234,plain,
% 1.82/2.06 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))),
% 1.82/2.06 inference(quant_inst,[status(thm)],[])).
% 1.82/2.06 tff(235,plain,
% 1.82/2.06 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[234, 233])).
% 1.82/2.06 tff(236,plain,
% 1.82/2.06 (~m_and_h_gate_v_in2(c_e_h_2, c_r, s1)),
% 1.82/2.06 inference(unit_resolution,[status(thm)],[235, 41, 232])).
% 1.82/2.06 tff(237,plain,
% 1.82/2.06 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s1)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s1)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s1))),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(238,plain,
% 1.82/2.06 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s1)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s1))),
% 1.82/2.06 inference(quant_inst,[status(thm)],[])).
% 1.82/2.06 tff(239,plain,
% 1.82/2.06 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s1)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s1)),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[238, 237])).
% 1.82/2.06 tff(240,plain,
% 1.82/2.06 (~node20(c_e_h_2, c_r, s1)),
% 1.82/2.06 inference(unit_resolution,[status(thm)],[239, 55, 236])).
% 1.82/2.06 tff(241,assumption,(~node20(c_e_h_2, c_r, s1)), introduced(assumption)).
% 1.82/2.06 tff(242,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s2)), introduced(assumption)).
% 1.82/2.06 tff(243,plain,
% 1.82/2.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s1) | (~node21(c_e_h_2, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s1) | (~node21(c_e_h_2, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)))),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(244,plain,
% 1.82/2.06 ((node20(c_e_h_2, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)) | (~node21(c_e_h_2, c_r, s1, s2))) <=> (node20(c_e_h_2, c_r, s1) | (~node21(c_e_h_2, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)))),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(245,plain,
% 1.82/2.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)) | (~node21(c_e_h_2, c_r, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s1) | (~node21(c_e_h_2, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2))))),
% 1.82/2.06 inference(monotonicity,[status(thm)],[244])).
% 1.82/2.06 tff(246,plain,
% 1.82/2.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)) | (~node21(c_e_h_2, c_r, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s1) | (~node21(c_e_h_2, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)))),
% 1.82/2.06 inference(transitivity,[status(thm)],[245, 243])).
% 1.82/2.06 tff(247,plain,
% 1.82/2.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)) | (~node21(c_e_h_2, c_r, s1, s2)))),
% 1.82/2.06 inference(quant_inst,[status(thm)],[])).
% 1.82/2.06 tff(248,plain,
% 1.82/2.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s1) | (~node21(c_e_h_2, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2))),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[247, 246])).
% 1.82/2.06 tff(249,plain,
% 1.82/2.06 (node20(c_e_h_2, c_r, s1) | (~node21(c_e_h_2, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2))),
% 1.82/2.06 inference(unit_resolution,[status(thm)],[248, 69])).
% 1.82/2.06 tff(250,plain,
% 1.82/2.06 (~node21(c_e_h_2, c_r, s1, s2)),
% 1.82/2.06 inference(unit_resolution,[status(thm)],[249, 242, 241])).
% 1.82/2.06 tff(251,plain,
% 1.82/2.06 (succ(s1, s2) <=> succ(s1, s2)),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(252,axiom,(succ(s1, s2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound2')).
% 1.82/2.06 tff(253,plain,
% 1.82/2.06 (succ(s1, s2)),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[252, 251])).
% 1.82/2.06 tff(254,plain,
% 1.82/2.06 (((~![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))),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(255,plain,
% 1.82/2.06 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s1, s2)) | trans(s1, s2))),
% 1.82/2.06 inference(quant_inst,[status(thm)],[])).
% 1.82/2.06 tff(256,plain,
% 1.82/2.06 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s1, s2)) | trans(s1, s2)),
% 1.82/2.06 inference(modus_ponens,[status(thm)],[255, 254])).
% 1.82/2.06 tff(257,plain,
% 1.82/2.06 (trans(s1, s2)),
% 1.82/2.06 inference(unit_resolution,[status(thm)],[256, 253, 84])).
% 1.82/2.06 tff(258,plain,
% 1.82/2.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_2, c_r, s1, s2) | node22(c_e_h_2, c_r, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_2, c_r, s1, s2) | node22(c_e_h_2, c_r, s1, s2))),
% 1.82/2.06 inference(rewrite,[status(thm)],[])).
% 1.82/2.06 tff(259,plain,
% 1.82/2.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_2, c_r, s1, s2) | node22(c_e_h_2, c_r, s1, s2))),
% 1.82/2.07 inference(quant_inst,[status(thm)],[])).
% 1.82/2.07 tff(260,plain,
% 1.82/2.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_2, c_r, s1, s2) | node22(c_e_h_2, c_r, s1, s2)),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[259, 258])).
% 1.82/2.07 tff(261,plain,
% 1.82/2.07 (node22(c_e_h_2, c_r, s1, s2)),
% 1.82/2.07 inference(unit_resolution,[status(thm)],[260, 101, 257, 250])).
% 1.82/2.07 tff(262,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_r, s1)), introduced(assumption)).
% 1.82/2.07 tff(263,plain,
% 1.82/2.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s2)) | (~node22(c_e_h_2, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_r, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)) | (~node22(c_e_h_2, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_r, s1))),
% 1.82/2.07 inference(rewrite,[status(thm)],[])).
% 1.82/2.07 tff(264,plain,
% 1.82/2.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s2)) | (~node22(c_e_h_2, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_r, s1))),
% 1.82/2.07 inference(quant_inst,[status(thm)],[])).
% 1.82/2.07 tff(265,plain,
% 1.82/2.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)) | (~node22(c_e_h_2, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_r, s1)),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[264, 263])).
% 1.82/2.07 tff(266,plain,
% 1.82/2.07 ($false),
% 1.82/2.07 inference(unit_resolution,[status(thm)],[265, 126, 262, 242, 261])).
% 1.82/2.07 tff(267,plain,((~m_and_h_gate_v_out(c_e_h_2, c_r, s2)) | m_and_h_gate_v_out(c_e_h_2, c_r, s1) | node20(c_e_h_2, c_r, s1)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.07 tff(268,plain,
% 1.82/2.07 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s2)) | m_and_h_gate_v_out(c_e_h_2, c_r, s1)),
% 1.82/2.07 inference(unit_resolution,[status(thm)],[267, 240])).
% 1.82/2.07 tff(269,plain,
% 1.82/2.07 (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)),
% 1.82/2.07 inference(unit_resolution,[status(thm)],[268, 131])).
% 1.82/2.07 tff(270,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s3)), introduced(assumption)).
% 1.82/2.07 tff(271,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s1)), introduced(assumption)).
% 1.82/2.07 tff(272,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s0)), introduced(assumption)).
% 1.82/2.07 tff(273,plain,
% 1.82/2.07 (^[I0: $i, I1: $i] : refl((~m_c_h_element_v_out(I0, I1, s0)) <=> (~m_c_h_element_v_out(I0, I1, s0)))),
% 1.82/2.07 inference(bind,[status(th)],[])).
% 1.82/2.07 tff(274,plain,
% 1.82/2.07 (![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))),
% 1.82/2.07 inference(quant_intro,[status(thm)],[273])).
% 1.82/2.07 tff(275,plain,
% 1.82/2.07 (![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))),
% 1.82/2.07 inference(rewrite,[status(thm)],[])).
% 1.82/2.07 tff(276,axiom,(![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_c_h_element_1')).
% 1.82/2.07 tff(277,plain,
% 1.82/2.07 (![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[276, 275])).
% 1.82/2.07 tff(278,plain,(
% 1.82/2.07 ![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))),
% 1.82/2.07 inference(skolemize,[status(sab)],[277])).
% 1.82/2.07 tff(279,plain,
% 1.82/2.07 (![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[278, 274])).
% 1.82/2.07 tff(280,plain,
% 1.82/2.07 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s0))),
% 1.82/2.07 inference(quant_inst,[status(thm)],[])).
% 1.82/2.07 tff(281,plain,
% 1.82/2.07 ($false),
% 1.82/2.07 inference(unit_resolution,[status(thm)],[280, 279, 272])).
% 1.82/2.07 tff(282,plain,(~m_c_h_element_v_out(c_e_h_2, c_e, s0)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.07 tff(283,plain,
% 1.82/2.07 (^[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)))),
% 1.82/2.07 inference(bind,[status(th)],[])).
% 1.82/2.07 tff(284,plain,
% 1.82/2.07 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 1.82/2.07 inference(quant_intro,[status(thm)],[283])).
% 1.82/2.07 tff(285,plain,
% 1.82/2.07 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 1.82/2.07 inference(rewrite,[status(thm)],[])).
% 1.82/2.07 tff(286,plain,
% 1.82/2.07 (^[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)))),
% 1.82/2.07 inference(bind,[status(th)],[])).
% 1.82/2.07 tff(287,plain,
% 1.82/2.07 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X)) | (~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))),
% 1.82/2.07 inference(quant_intro,[status(thm)],[286])).
% 1.82/2.07 tff(288,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/sandbox2/benchmark/theBenchmark.p','m_c_h_element_5')).
% 1.82/2.07 tff(289,plain,
% 1.82/2.07 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[288, 287])).
% 1.82/2.07 tff(290,plain,
% 1.82/2.07 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[289, 285])).
% 1.82/2.07 tff(291,plain,(
% 1.82/2.07 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 1.82/2.07 inference(skolemize,[status(sab)],[290])).
% 1.82/2.07 tff(292,plain,
% 1.82/2.07 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[291, 284])).
% 1.82/2.07 tff(293,plain,
% 1.82/2.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | (~node15(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | (~node15(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0))),
% 1.82/2.07 inference(rewrite,[status(thm)],[])).
% 1.82/2.07 tff(294,plain,
% 1.82/2.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | (~node15(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0))),
% 1.82/2.07 inference(quant_inst,[status(thm)],[])).
% 1.82/2.07 tff(295,plain,
% 1.82/2.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | (~node15(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0)),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[294, 293])).
% 1.82/2.07 tff(296,plain,
% 1.82/2.07 ((~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | (~node15(c_e_h_2, c_e, s0, s1))),
% 1.82/2.07 inference(unit_resolution,[status(thm)],[295, 292, 282])).
% 1.82/2.07 tff(297,plain,
% 1.82/2.07 (~node15(c_e_h_2, c_e, s0, s1)),
% 1.82/2.07 inference(unit_resolution,[status(thm)],[296, 271])).
% 1.82/2.07 tff(298,plain,
% 1.82/2.07 (^[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))))),
% 1.82/2.07 inference(bind,[status(th)],[])).
% 1.82/2.07 tff(299,plain,
% 1.82/2.07 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 1.82/2.07 inference(quant_intro,[status(thm)],[298])).
% 1.82/2.07 tff(300,plain,
% 1.82/2.07 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 1.82/2.07 inference(rewrite,[status(thm)],[])).
% 1.82/2.07 tff(301,plain,
% 1.82/2.07 (^[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))))),
% 1.82/2.07 inference(bind,[status(th)],[])).
% 1.82/2.07 tff(302,plain,
% 1.82/2.07 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 1.82/2.07 inference(quant_intro,[status(thm)],[301])).
% 1.82/2.07 tff(303,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/sandbox2/benchmark/theBenchmark.p','m_c_h_element_11')).
% 1.82/2.07 tff(304,plain,
% 1.82/2.07 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[303, 302])).
% 1.82/2.07 tff(305,plain,
% 1.82/2.07 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[304, 300])).
% 1.82/2.07 tff(306,plain,(
% 1.82/2.07 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 1.82/2.07 inference(skolemize,[status(sab)],[305])).
% 1.82/2.07 tff(307,plain,
% 1.82/2.07 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[306, 299])).
% 1.82/2.07 tff(308,plain,
% 1.82/2.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~node18(c_e_h_2, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~node18(c_e_h_2, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)))),
% 1.82/2.07 inference(rewrite,[status(thm)],[])).
% 1.82/2.07 tff(309,plain,
% 1.82/2.07 (((~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~node18(c_e_h_2, c_e, s0, s1))) <=> (m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~node18(c_e_h_2, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)))),
% 1.82/2.07 inference(rewrite,[status(thm)],[])).
% 1.82/2.07 tff(310,plain,
% 1.82/2.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~node18(c_e_h_2, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~node18(c_e_h_2, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1))))),
% 1.82/2.07 inference(monotonicity,[status(thm)],[309])).
% 1.82/2.07 tff(311,plain,
% 1.82/2.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~node18(c_e_h_2, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~node18(c_e_h_2, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)))),
% 1.82/2.07 inference(transitivity,[status(thm)],[310, 308])).
% 1.82/2.07 tff(312,plain,
% 1.82/2.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~node18(c_e_h_2, c_e, s0, s1)))),
% 1.82/2.07 inference(quant_inst,[status(thm)],[])).
% 1.82/2.07 tff(313,plain,
% 1.82/2.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~node18(c_e_h_2, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1))),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[312, 311])).
% 1.82/2.07 tff(314,plain,
% 1.82/2.07 ((~node18(c_e_h_2, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1))),
% 1.82/2.07 inference(unit_resolution,[status(thm)],[313, 307, 282])).
% 1.82/2.07 tff(315,plain,
% 1.82/2.07 (~node18(c_e_h_2, c_e, s0, s1)),
% 1.82/2.07 inference(unit_resolution,[status(thm)],[314, 271])).
% 1.82/2.07 tff(316,assumption,(~node19(c_e_h_2, c_e, s0, s1)), introduced(assumption)).
% 1.82/2.07 tff(317,plain,
% 1.82/2.07 (^[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)))),
% 1.82/2.07 inference(bind,[status(th)],[])).
% 1.82/2.07 tff(318,plain,
% 1.82/2.07 (![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))),
% 1.82/2.07 inference(quant_intro,[status(thm)],[317])).
% 1.82/2.07 tff(319,plain,
% 1.82/2.07 (![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))),
% 1.82/2.07 inference(rewrite,[status(thm)],[])).
% 1.82/2.07 tff(320,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_c_h_element_14')).
% 1.82/2.07 tff(321,plain,
% 1.82/2.07 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[320, 319])).
% 1.82/2.07 tff(322,plain,(
% 1.82/2.07 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))),
% 1.82/2.07 inference(skolemize,[status(sab)],[321])).
% 1.82/2.07 tff(323,plain,
% 1.82/2.07 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[322, 318])).
% 1.82/2.07 tff(324,plain,
% 1.82/2.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_2, c_e, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_2, c_e, s0, s1))),
% 1.82/2.07 inference(rewrite,[status(thm)],[])).
% 1.82/2.07 tff(325,plain,
% 1.82/2.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_2, c_e, s0, s1))),
% 1.82/2.07 inference(quant_inst,[status(thm)],[])).
% 1.82/2.07 tff(326,plain,
% 1.82/2.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_2, c_e, s0, s1)),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[325, 324])).
% 1.82/2.07 tff(327,plain,
% 1.82/2.07 ($false),
% 1.82/2.07 inference(unit_resolution,[status(thm)],[326, 323, 91, 316])).
% 1.82/2.07 tff(328,plain,(node19(c_e_h_2, c_e, s0, s1)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.07 tff(329,plain,
% 1.82/2.07 (^[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))))),
% 1.82/2.07 inference(bind,[status(th)],[])).
% 1.82/2.07 tff(330,plain,
% 1.82/2.07 (![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)))),
% 1.82/2.07 inference(quant_intro,[status(thm)],[329])).
% 1.82/2.07 tff(331,plain,
% 1.82/2.07 (![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)))),
% 1.82/2.07 inference(rewrite,[status(thm)],[])).
% 1.82/2.07 tff(332,plain,
% 1.82/2.07 (^[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))))),
% 1.82/2.07 inference(bind,[status(th)],[])).
% 1.82/2.07 tff(333,plain,
% 1.82/2.07 (![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)))),
% 1.82/2.07 inference(quant_intro,[status(thm)],[332])).
% 1.82/2.07 tff(334,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/sandbox2/benchmark/theBenchmark.p','m_c_h_element_13')).
% 1.82/2.07 tff(335,plain,
% 1.82/2.07 (![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[334, 333])).
% 1.82/2.07 tff(336,plain,
% 1.82/2.07 (![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[335, 331])).
% 1.82/2.07 tff(337,plain,(
% 1.82/2.07 ![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 1.82/2.07 inference(skolemize,[status(sab)],[336])).
% 1.82/2.07 tff(338,plain,
% 1.82/2.07 (![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[337, 330])).
% 1.82/2.07 tff(339,plain,
% 1.82/2.07 (((~![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_e, s0, s1) | node17(c_e_h_2, c_e, s0) | (~node19(c_e_h_2, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_e, s0, s1) | node17(c_e_h_2, c_e, s0) | (~node19(c_e_h_2, c_e, s0, s1)))),
% 1.82/2.07 inference(rewrite,[status(thm)],[])).
% 1.82/2.07 tff(340,plain,
% 1.82/2.07 ((node17(c_e_h_2, c_e, s0) | node18(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1))) <=> (node18(c_e_h_2, c_e, s0, s1) | node17(c_e_h_2, c_e, s0) | (~node19(c_e_h_2, c_e, s0, s1)))),
% 1.82/2.07 inference(rewrite,[status(thm)],[])).
% 1.82/2.07 tff(341,plain,
% 1.82/2.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s0) | node18(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_e, s0, s1) | node17(c_e_h_2, c_e, s0) | (~node19(c_e_h_2, c_e, s0, s1))))),
% 1.82/2.07 inference(monotonicity,[status(thm)],[340])).
% 1.82/2.07 tff(342,plain,
% 1.82/2.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s0) | node18(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_e, s0, s1) | node17(c_e_h_2, c_e, s0) | (~node19(c_e_h_2, c_e, s0, s1)))),
% 1.82/2.07 inference(transitivity,[status(thm)],[341, 339])).
% 1.82/2.07 tff(343,plain,
% 1.82/2.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s0) | node18(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)))),
% 1.82/2.07 inference(quant_inst,[status(thm)],[])).
% 1.82/2.07 tff(344,plain,
% 1.82/2.07 ((~![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_e, s0, s1) | node17(c_e_h_2, c_e, s0) | (~node19(c_e_h_2, c_e, s0, s1))),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[343, 342])).
% 1.82/2.07 tff(345,plain,
% 1.82/2.07 (node18(c_e_h_2, c_e, s0, s1) | node17(c_e_h_2, c_e, s0)),
% 1.82/2.07 inference(unit_resolution,[status(thm)],[344, 338, 328])).
% 1.82/2.07 tff(346,plain,
% 1.82/2.07 (node17(c_e_h_2, c_e, s0)),
% 1.82/2.07 inference(unit_resolution,[status(thm)],[345, 315])).
% 1.82/2.07 tff(347,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s0)), introduced(assumption)).
% 1.82/2.07 tff(348,plain,
% 1.82/2.07 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s0))),
% 1.82/2.07 inference(quant_inst,[status(thm)],[])).
% 1.82/2.07 tff(349,plain,
% 1.82/2.07 ($false),
% 1.82/2.07 inference(unit_resolution,[status(thm)],[348, 113, 347])).
% 1.82/2.07 tff(350,plain,(~m_and_h_gate_v_out(c_e_h_2, c_i, s0)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.07 tff(351,plain,
% 1.82/2.07 (^[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)))),
% 1.82/2.07 inference(bind,[status(th)],[])).
% 1.82/2.07 tff(352,plain,
% 1.82/2.07 (![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))),
% 1.82/2.07 inference(quant_intro,[status(thm)],[351])).
% 1.82/2.07 tff(353,plain,
% 1.82/2.07 (![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))),
% 1.82/2.07 inference(rewrite,[status(thm)],[])).
% 1.82/2.07 tff(354,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/sandbox2/benchmark/theBenchmark.p','m_cell_22')).
% 1.82/2.07 tff(355,plain,
% 1.82/2.07 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[354, 353])).
% 1.82/2.07 tff(356,plain,(
% 1.82/2.07 ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 1.82/2.07 inference(skolemize,[status(sab)],[355])).
% 1.82/2.07 tff(357,plain,
% 1.82/2.07 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[356, 352])).
% 1.82/2.07 tff(358,plain,
% 1.82/2.07 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, 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_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s0)) | m_and_h_gate_v_out(c_e_h_2, c_i, s0))),
% 1.82/2.07 inference(rewrite,[status(thm)],[])).
% 1.82/2.07 tff(359,plain,
% 1.82/2.07 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s0)) | m_and_h_gate_v_out(c_e_h_2, c_i, s0))),
% 1.82/2.07 inference(quant_inst,[status(thm)],[])).
% 1.82/2.07 tff(360,plain,
% 1.82/2.07 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s0)) | m_and_h_gate_v_out(c_e_h_2, c_i, s0)),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[359, 358])).
% 1.82/2.07 tff(361,plain,
% 1.82/2.07 (~m_c_h_element_v_in2(c_e_h_2, c_e, s0)),
% 1.82/2.07 inference(unit_resolution,[status(thm)],[360, 357, 350])).
% 1.82/2.07 tff(362,plain,
% 1.82/2.07 (^[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))))),
% 1.82/2.07 inference(bind,[status(th)],[])).
% 1.82/2.07 tff(363,plain,
% 1.82/2.07 (![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 1.82/2.07 inference(quant_intro,[status(thm)],[362])).
% 1.82/2.07 tff(364,plain,
% 1.82/2.07 (![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 1.82/2.07 inference(rewrite,[status(thm)],[])).
% 1.82/2.07 tff(365,plain,
% 1.82/2.07 (^[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))))),
% 1.82/2.07 inference(bind,[status(th)],[])).
% 1.82/2.07 tff(366,plain,
% 1.82/2.07 (![I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 1.82/2.07 inference(quant_intro,[status(thm)],[365])).
% 1.82/2.07 tff(367,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/sandbox2/benchmark/theBenchmark.p','m_c_h_element_9')).
% 1.82/2.07 tff(368,plain,
% 1.82/2.07 (![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[367, 366])).
% 1.82/2.07 tff(369,plain,
% 1.82/2.07 (![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[368, 364])).
% 1.82/2.07 tff(370,plain,(
% 1.82/2.07 ![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 1.82/2.07 inference(skolemize,[status(sab)],[369])).
% 1.82/2.07 tff(371,plain,
% 1.82/2.07 (![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[370, 363])).
% 1.82/2.07 tff(372,plain,
% 1.82/2.07 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_e, s0) | (~node17(c_e_h_2, c_e, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s0) | (~node17(c_e_h_2, c_e, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s0)))),
% 1.82/2.07 inference(rewrite,[status(thm)],[])).
% 1.82/2.07 tff(373,plain,
% 1.82/2.07 (((~m_c_h_element_v_in1(c_e_h_2, c_e, s0)) | m_c_h_element_v_in2(c_e_h_2, c_e, s0) | (~node17(c_e_h_2, c_e, s0))) <=> (m_c_h_element_v_in2(c_e_h_2, c_e, s0) | (~node17(c_e_h_2, c_e, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s0)))),
% 1.82/2.07 inference(rewrite,[status(thm)],[])).
% 1.82/2.07 tff(374,plain,
% 1.82/2.07 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s0)) | m_c_h_element_v_in2(c_e_h_2, c_e, s0) | (~node17(c_e_h_2, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_e, s0) | (~node17(c_e_h_2, c_e, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s0))))),
% 1.82/2.07 inference(monotonicity,[status(thm)],[373])).
% 1.82/2.07 tff(375,plain,
% 1.82/2.07 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s0)) | m_c_h_element_v_in2(c_e_h_2, c_e, s0) | (~node17(c_e_h_2, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s0) | (~node17(c_e_h_2, c_e, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s0)))),
% 1.82/2.07 inference(transitivity,[status(thm)],[374, 372])).
% 1.82/2.07 tff(376,plain,
% 1.82/2.07 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s0)) | m_c_h_element_v_in2(c_e_h_2, c_e, s0) | (~node17(c_e_h_2, c_e, s0)))),
% 1.82/2.07 inference(quant_inst,[status(thm)],[])).
% 1.82/2.07 tff(377,plain,
% 1.82/2.07 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s0) | (~node17(c_e_h_2, c_e, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s0))),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[376, 375])).
% 1.82/2.07 tff(378,plain,
% 1.82/2.07 ((~node17(c_e_h_2, c_e, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s0))),
% 1.82/2.07 inference(unit_resolution,[status(thm)],[377, 371, 361])).
% 1.82/2.07 tff(379,plain,
% 1.82/2.07 (~m_c_h_element_v_in1(c_e_h_2, c_e, s0)),
% 1.82/2.07 inference(unit_resolution,[status(thm)],[378, 346])).
% 1.82/2.07 tff(380,plain,
% 1.82/2.07 (^[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)))),
% 1.82/2.07 inference(bind,[status(th)],[])).
% 1.82/2.07 tff(381,plain,
% 1.82/2.07 (![I0: $i, X: $i, 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))),
% 1.82/2.07 inference(quant_intro,[status(thm)],[380])).
% 1.82/2.07 tff(382,plain,
% 1.82/2.07 (![I0: $i, X: $i, 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))),
% 1.82/2.07 inference(rewrite,[status(thm)],[])).
% 1.82/2.07 tff(383,plain,
% 1.82/2.07 (^[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)))),
% 1.82/2.07 inference(bind,[status(th)],[])).
% 1.82/2.07 tff(384,plain,
% 1.82/2.07 (![I0: $i, X: $i, I1: $i] : ((m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X)) | (~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))),
% 1.82/2.07 inference(quant_intro,[status(thm)],[383])).
% 1.82/2.07 tff(385,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/sandbox2/benchmark/theBenchmark.p','m_c_h_element_6')).
% 1.82/2.07 tff(386,plain,
% 1.82/2.07 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[385, 384])).
% 1.82/2.07 tff(387,plain,
% 1.82/2.07 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[386, 382])).
% 1.82/2.07 tff(388,plain,(
% 1.82/2.07 ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 1.82/2.07 inference(skolemize,[status(sab)],[387])).
% 1.82/2.07 tff(389,plain,
% 1.82/2.07 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[388, 381])).
% 1.82/2.07 tff(390,plain,
% 1.82/2.07 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s0)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | m_c_h_element_v_in2(c_e_h_2, c_e, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s0)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | m_c_h_element_v_in2(c_e_h_2, c_e, s0))),
% 1.82/2.07 inference(rewrite,[status(thm)],[])).
% 1.82/2.07 tff(391,plain,
% 1.82/2.07 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s0)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | m_c_h_element_v_in2(c_e_h_2, c_e, s0))),
% 1.82/2.07 inference(quant_inst,[status(thm)],[])).
% 1.82/2.07 tff(392,plain,
% 1.82/2.07 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s0)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | m_c_h_element_v_in2(c_e_h_2, c_e, s0)),
% 1.82/2.07 inference(modus_ponens,[status(thm)],[391, 390])).
% 1.82/2.07 tff(393,plain,
% 1.82/2.07 ((~node16(c_e_h_2, c_e, s0)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0)),
% 1.82/2.07 inference(unit_resolution,[status(thm)],[392, 389, 361])).
% 1.82/2.07 tff(394,plain,
% 1.82/2.07 (~node16(c_e_h_2, c_e, s0)),
% 1.82/2.07 inference(unit_resolution,[status(thm)],[393, 379])).
% 1.82/2.07 tff(395,plain,
% 1.82/2.07 (^[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))))),
% 1.82/2.08 inference(bind,[status(th)],[])).
% 1.82/2.08 tff(396,plain,
% 1.82/2.08 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 1.82/2.08 inference(quant_intro,[status(thm)],[395])).
% 1.82/2.08 tff(397,plain,
% 1.82/2.08 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 1.82/2.08 inference(rewrite,[status(thm)],[])).
% 1.82/2.08 tff(398,plain,
% 1.82/2.08 (^[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))))),
% 1.82/2.08 inference(bind,[status(th)],[])).
% 1.82/2.08 tff(399,plain,
% 1.82/2.08 (![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)))),
% 1.82/2.08 inference(quant_intro,[status(thm)],[398])).
% 1.82/2.08 tff(400,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/sandbox2/benchmark/theBenchmark.p','m_c_h_element_3')).
% 1.82/2.08 tff(401,plain,
% 1.82/2.08 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 1.82/2.08 inference(modus_ponens,[status(thm)],[400, 399])).
% 1.82/2.08 tff(402,plain,
% 1.82/2.08 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 1.82/2.08 inference(modus_ponens,[status(thm)],[401, 397])).
% 1.82/2.08 tff(403,plain,(
% 1.82/2.08 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 1.82/2.08 inference(skolemize,[status(sab)],[402])).
% 1.82/2.08 tff(404,plain,
% 1.82/2.08 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 1.82/2.08 inference(modus_ponens,[status(thm)],[403, 396])).
% 1.82/2.08 tff(405,plain,
% 1.82/2.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~node14(c_e_h_2, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~node14(c_e_h_2, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)))),
% 1.82/2.08 inference(rewrite,[status(thm)],[])).
% 1.82/2.08 tff(406,plain,
% 1.82/2.08 (((~node14(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1))) <=> (m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~node14(c_e_h_2, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)))),
% 1.82/2.08 inference(rewrite,[status(thm)],[])).
% 1.82/2.08 tff(407,plain,
% 1.82/2.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~node14(c_e_h_2, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1))))),
% 1.82/2.08 inference(monotonicity,[status(thm)],[406])).
% 1.82/2.08 tff(408,plain,
% 1.82/2.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~node14(c_e_h_2, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)))),
% 1.82/2.08 inference(transitivity,[status(thm)],[407, 405])).
% 1.82/2.08 tff(409,plain,
% 1.82/2.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)))),
% 1.82/2.08 inference(quant_inst,[status(thm)],[])).
% 1.82/2.08 tff(410,plain,
% 1.82/2.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~node14(c_e_h_2, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1))),
% 1.82/2.08 inference(modus_ponens,[status(thm)],[409, 408])).
% 1.82/2.08 tff(411,plain,
% 1.82/2.08 (m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~node14(c_e_h_2, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1))),
% 1.82/2.08 inference(unit_resolution,[status(thm)],[410, 404])).
% 1.82/2.08 tff(412,plain,
% 1.82/2.08 (~node14(c_e_h_2, c_e, s0, s1)),
% 1.82/2.08 inference(unit_resolution,[status(thm)],[411, 379, 271])).
% 1.82/2.08 tff(413,plain,
% 1.82/2.08 (^[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))))),
% 1.82/2.08 inference(bind,[status(th)],[])).
% 1.82/2.08 tff(414,plain,
% 1.82/2.08 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 1.82/2.08 inference(quant_intro,[status(thm)],[413])).
% 1.82/2.08 tff(415,plain,
% 1.82/2.08 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 1.82/2.08 inference(rewrite,[status(thm)],[])).
% 1.82/2.08 tff(416,plain,
% 1.82/2.08 (^[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)))))),
% 1.82/2.08 inference(bind,[status(th)],[])).
% 1.82/2.08 tff(417,plain,
% 1.82/2.08 (![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)))),
% 1.82/2.08 inference(quant_intro,[status(thm)],[416])).
% 1.82/2.08 tff(418,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/sandbox2/benchmark/theBenchmark.p','m_c_h_element_12')).
% 1.82/2.08 tff(419,plain,
% 1.82/2.08 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 1.82/2.08 inference(modus_ponens,[status(thm)],[418, 417])).
% 1.82/2.08 tff(420,plain,
% 1.82/2.08 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 1.82/2.08 inference(modus_ponens,[status(thm)],[419, 415])).
% 1.82/2.08 tff(421,plain,(
% 1.82/2.08 ![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 1.82/2.08 inference(skolemize,[status(sab)],[420])).
% 1.82/2.08 tff(422,plain,
% 1.82/2.08 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 1.82/2.08 inference(modus_ponens,[status(thm)],[421, 414])).
% 1.82/2.08 tff(423,plain,
% 1.82/2.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_2, c_e, s0, s1) | node16(c_e_h_2, c_e, s0) | node15(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_2, c_e, s0, s1) | node16(c_e_h_2, c_e, s0) | node15(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)))),
% 1.82/2.08 inference(rewrite,[status(thm)],[])).
% 1.82/2.08 tff(424,plain,
% 1.82/2.08 ((node16(c_e_h_2, c_e, s0) | node14(c_e_h_2, c_e, s0, s1) | node15(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1))) <=> (node14(c_e_h_2, c_e, s0, s1) | node16(c_e_h_2, c_e, s0) | node15(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)))),
% 1.82/2.08 inference(rewrite,[status(thm)],[])).
% 1.82/2.08 tff(425,plain,
% 1.82/2.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s0) | node14(c_e_h_2, c_e, s0, s1) | node15(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_2, c_e, s0, s1) | node16(c_e_h_2, c_e, s0) | node15(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1))))),
% 1.82/2.08 inference(monotonicity,[status(thm)],[424])).
% 1.82/2.08 tff(426,plain,
% 1.82/2.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s0) | node14(c_e_h_2, c_e, s0, s1) | node15(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_2, c_e, s0, s1) | node16(c_e_h_2, c_e, s0) | node15(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)))),
% 1.82/2.08 inference(transitivity,[status(thm)],[425, 423])).
% 1.82/2.08 tff(427,plain,
% 1.82/2.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s0) | node14(c_e_h_2, c_e, s0, s1) | node15(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)))),
% 1.82/2.08 inference(quant_inst,[status(thm)],[])).
% 1.82/2.08 tff(428,plain,
% 1.82/2.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_2, c_e, s0, s1) | node16(c_e_h_2, c_e, s0) | node15(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1))),
% 1.82/2.08 inference(modus_ponens,[status(thm)],[427, 426])).
% 1.82/2.08 tff(429,plain,
% 1.82/2.08 (node14(c_e_h_2, c_e, s0, s1) | node16(c_e_h_2, c_e, s0) | node15(c_e_h_2, c_e, s0, s1)),
% 1.82/2.08 inference(unit_resolution,[status(thm)],[428, 422, 328])).
% 1.82/2.08 tff(430,plain,
% 1.82/2.08 ($false),
% 1.82/2.08 inference(unit_resolution,[status(thm)],[429, 412, 394, 297])).
% 1.82/2.08 tff(431,plain,(~m_c_h_element_v_out(c_e_h_2, c_e, s1)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.08 tff(432,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s2)), introduced(assumption)).
% 1.82/2.08 tff(433,plain,
% 1.82/2.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~node18(c_e_h_2, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~node18(c_e_h_2, c_e, s1, s2)))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(434,plain,
% 1.92/2.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~node18(c_e_h_2, c_e, s1, s2)))),
% 1.92/2.08 inference(quant_inst,[status(thm)],[])).
% 1.92/2.08 tff(435,plain,
% 1.92/2.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~node18(c_e_h_2, c_e, s1, s2))),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[434, 433])).
% 1.92/2.08 tff(436,plain,
% 1.92/2.08 ((~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~node18(c_e_h_2, c_e, s1, s2))),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[435, 307])).
% 1.92/2.08 tff(437,plain,
% 1.92/2.08 (~node18(c_e_h_2, c_e, s1, s2)),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[436, 432, 431])).
% 1.92/2.08 tff(438,plain,
% 1.92/2.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_2, c_e, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_2, c_e, s1, s2))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(439,plain,
% 1.92/2.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_2, c_e, s1, s2))),
% 1.92/2.08 inference(quant_inst,[status(thm)],[])).
% 1.92/2.08 tff(440,plain,
% 1.92/2.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_2, c_e, s1, s2)),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[439, 438])).
% 1.92/2.08 tff(441,plain,
% 1.92/2.08 (node19(c_e_h_2, c_e, s1, s2)),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[440, 323, 257])).
% 1.92/2.08 tff(442,plain,
% 1.92/2.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s1, s2)) | node17(c_e_h_2, c_e, s1) | node18(c_e_h_2, c_e, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s1, s2)) | node17(c_e_h_2, c_e, s1) | node18(c_e_h_2, c_e, s1, s2))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(443,plain,
% 1.92/2.08 ((node17(c_e_h_2, c_e, s1) | node18(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2))) <=> ((~node19(c_e_h_2, c_e, s1, s2)) | node17(c_e_h_2, c_e, s1) | node18(c_e_h_2, c_e, s1, s2))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(444,plain,
% 1.92/2.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s1) | node18(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s1, s2)) | node17(c_e_h_2, c_e, s1) | node18(c_e_h_2, c_e, s1, s2)))),
% 1.92/2.08 inference(monotonicity,[status(thm)],[443])).
% 1.92/2.08 tff(445,plain,
% 1.92/2.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s1) | node18(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s1, s2)) | node17(c_e_h_2, c_e, s1) | node18(c_e_h_2, c_e, s1, s2))),
% 1.92/2.08 inference(transitivity,[status(thm)],[444, 442])).
% 1.92/2.08 tff(446,plain,
% 1.92/2.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s1) | node18(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)))),
% 1.92/2.08 inference(quant_inst,[status(thm)],[])).
% 1.92/2.08 tff(447,plain,
% 1.92/2.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s1, s2)) | node17(c_e_h_2, c_e, s1) | node18(c_e_h_2, c_e, s1, s2)),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[446, 445])).
% 1.92/2.08 tff(448,plain,
% 1.92/2.08 (node17(c_e_h_2, c_e, s1) | node18(c_e_h_2, c_e, s1, s2)),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[447, 338, 441])).
% 1.92/2.08 tff(449,plain,
% 1.92/2.08 (node17(c_e_h_2, c_e, s1)),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[448, 437])).
% 1.92/2.08 tff(450,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s1)), introduced(assumption)).
% 1.92/2.08 tff(451,plain,
% 1.92/2.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, 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))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(452,plain,
% 1.92/2.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, 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))),
% 1.92/2.08 inference(quant_inst,[status(thm)],[])).
% 1.92/2.08 tff(453,plain,
% 1.92/2.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, 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)),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[452, 451])).
% 1.92/2.08 tff(454,plain,
% 1.92/2.08 ((~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)),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[453, 126])).
% 1.92/2.08 tff(455,plain,
% 1.92/2.08 ((~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | (~node22(c_e_h_2, c_i, s0, s1))),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[454, 350])).
% 1.92/2.08 tff(456,plain,
% 1.92/2.08 (~node22(c_e_h_2, c_i, s0, s1)),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[455, 450])).
% 1.92/2.08 tff(457,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s0)), introduced(assumption)).
% 1.92/2.08 tff(458,plain,
% 1.92/2.08 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s0))),
% 1.92/2.08 inference(quant_inst,[status(thm)],[])).
% 1.92/2.08 tff(459,plain,
% 1.92/2.08 ($false),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[458, 279, 457])).
% 1.92/2.08 tff(460,plain,(~m_c_h_element_v_out(c_e_h_2, c_h, s0)), inference(lemma,lemma(discharge,[]))).
% 1.92/2.08 tff(461,plain,
% 1.92/2.08 (^[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)))),
% 1.92/2.08 inference(bind,[status(th)],[])).
% 1.92/2.08 tff(462,plain,
% 1.92/2.08 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))),
% 1.92/2.08 inference(quant_intro,[status(thm)],[461])).
% 1.92/2.08 tff(463,plain,
% 1.92/2.08 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(464,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/sandbox2/benchmark/theBenchmark.p','m_cell_36')).
% 1.92/2.08 tff(465,plain,
% 1.92/2.08 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[464, 463])).
% 1.92/2.08 tff(466,plain,(
% 1.92/2.08 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))),
% 1.92/2.08 inference(skolemize,[status(sab)],[465])).
% 1.92/2.08 tff(467,plain,
% 1.92/2.08 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[466, 462])).
% 1.92/2.08 tff(468,plain,
% 1.92/2.08 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_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))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(469,plain,
% 1.92/2.08 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s0)) | m_c_h_element_v_out(c_e_h_2, c_h, s0))),
% 1.92/2.08 inference(quant_inst,[status(thm)],[])).
% 1.92/2.08 tff(470,plain,
% 1.92/2.08 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s0)) | m_c_h_element_v_out(c_e_h_2, c_h, s0)),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[469, 468])).
% 1.92/2.08 tff(471,plain,
% 1.92/2.08 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s0)),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[470, 467, 460])).
% 1.92/2.08 tff(472,plain,
% 1.92/2.08 (^[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)))),
% 1.92/2.08 inference(bind,[status(th)],[])).
% 1.92/2.08 tff(473,plain,
% 1.92/2.08 (![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))),
% 1.92/2.08 inference(quant_intro,[status(thm)],[472])).
% 1.92/2.08 tff(474,plain,
% 1.92/2.08 (![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))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(475,plain,
% 1.92/2.08 (^[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)))),
% 1.92/2.08 inference(bind,[status(th)],[])).
% 1.92/2.08 tff(476,plain,
% 1.92/2.08 (![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))),
% 1.92/2.08 inference(quant_intro,[status(thm)],[475])).
% 1.92/2.08 tff(477,axiom,(![I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_in1(I0, I1, X) | (~node20(I0, I1, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_2')).
% 1.92/2.08 tff(478,plain,
% 1.92/2.08 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[477, 476])).
% 1.92/2.08 tff(479,plain,
% 1.92/2.08 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[478, 474])).
% 1.92/2.08 tff(480,plain,(
% 1.92/2.08 ![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 1.92/2.08 inference(skolemize,[status(sab)],[479])).
% 1.92/2.08 tff(481,plain,
% 1.92/2.08 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[480, 473])).
% 1.92/2.08 tff(482,plain,
% 1.92/2.08 (((~![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))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(483,plain,
% 1.92/2.08 ((~![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))),
% 1.92/2.08 inference(quant_inst,[status(thm)],[])).
% 1.92/2.08 tff(484,plain,
% 1.92/2.08 ((~![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)),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[483, 482])).
% 1.92/2.08 tff(485,plain,
% 1.92/2.08 (~node20(c_e_h_2, c_i, s0)),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[484, 481, 471])).
% 1.92/2.08 tff(486,plain,
% 1.92/2.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (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)))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(487,plain,
% 1.92/2.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (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)))),
% 1.92/2.08 inference(quant_inst,[status(thm)],[])).
% 1.92/2.08 tff(488,plain,
% 1.92/2.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (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))),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[487, 486])).
% 1.92/2.08 tff(489,plain,
% 1.92/2.08 ((~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | (~node21(c_e_h_2, c_i, s0, s1))),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[488, 69, 485])).
% 1.92/2.08 tff(490,plain,
% 1.92/2.08 (~node21(c_e_h_2, c_i, s0, s1)),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[489, 450])).
% 1.92/2.08 tff(491,plain,
% 1.92/2.08 (((~![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))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(492,plain,
% 1.92/2.08 ((~![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))),
% 1.92/2.08 inference(quant_inst,[status(thm)],[])).
% 1.92/2.08 tff(493,plain,
% 1.92/2.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_i, s0, s1) | node22(c_e_h_2, c_i, s0, s1)),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[492, 491])).
% 1.92/2.08 tff(494,plain,
% 1.92/2.08 ($false),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[493, 101, 91, 490, 456])).
% 1.92/2.08 tff(495,plain,(~m_and_h_gate_v_out(c_e_h_2, c_i, s1)), inference(lemma,lemma(discharge,[]))).
% 1.92/2.08 tff(496,plain,
% 1.92/2.08 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, 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_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s1)) | m_and_h_gate_v_out(c_e_h_2, c_i, s1))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(497,plain,
% 1.92/2.08 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s1)) | m_and_h_gate_v_out(c_e_h_2, c_i, s1))),
% 1.92/2.08 inference(quant_inst,[status(thm)],[])).
% 1.92/2.08 tff(498,plain,
% 1.92/2.08 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s1)) | m_and_h_gate_v_out(c_e_h_2, c_i, s1)),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[497, 496])).
% 1.92/2.08 tff(499,plain,
% 1.92/2.08 (~m_c_h_element_v_in2(c_e_h_2, c_e, s1)),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[498, 357, 495])).
% 1.92/2.08 tff(500,plain,
% 1.92/2.08 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s1)) | m_c_h_element_v_in2(c_e_h_2, c_e, s1) | (~node17(c_e_h_2, c_e, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s1)) | m_c_h_element_v_in2(c_e_h_2, c_e, s1) | (~node17(c_e_h_2, c_e, s1)))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(501,plain,
% 1.92/2.08 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s1)) | m_c_h_element_v_in2(c_e_h_2, c_e, s1) | (~node17(c_e_h_2, c_e, s1)))),
% 1.92/2.08 inference(quant_inst,[status(thm)],[])).
% 1.92/2.08 tff(502,plain,
% 1.92/2.08 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s1)) | m_c_h_element_v_in2(c_e_h_2, c_e, s1) | (~node17(c_e_h_2, c_e, s1))),
% 1.92/2.09 inference(modus_ponens,[status(thm)],[501, 500])).
% 1.92/2.09 tff(503,plain,
% 1.92/2.09 ((~m_c_h_element_v_in1(c_e_h_2, c_e, s1)) | (~node17(c_e_h_2, c_e, s1))),
% 1.92/2.09 inference(unit_resolution,[status(thm)],[502, 371, 499])).
% 1.92/2.09 tff(504,plain,
% 1.92/2.09 (~m_c_h_element_v_in1(c_e_h_2, c_e, s1)),
% 1.92/2.09 inference(unit_resolution,[status(thm)],[503, 449])).
% 1.92/2.09 tff(505,plain,
% 1.92/2.09 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | m_c_h_element_v_in2(c_e_h_2, c_e, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | m_c_h_element_v_in2(c_e_h_2, c_e, s1))),
% 1.92/2.09 inference(rewrite,[status(thm)],[])).
% 1.92/2.09 tff(506,plain,
% 1.92/2.09 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | m_c_h_element_v_in2(c_e_h_2, c_e, s1))),
% 1.92/2.09 inference(quant_inst,[status(thm)],[])).
% 1.92/2.09 tff(507,plain,
% 1.92/2.09 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | m_c_h_element_v_in2(c_e_h_2, c_e, s1)),
% 1.92/2.09 inference(modus_ponens,[status(thm)],[506, 505])).
% 1.92/2.09 tff(508,plain,
% 1.92/2.09 ((~node16(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1)),
% 1.92/2.09 inference(unit_resolution,[status(thm)],[507, 389, 499])).
% 1.92/2.09 tff(509,plain,
% 1.92/2.09 (~node16(c_e_h_2, c_e, s1)),
% 1.92/2.09 inference(unit_resolution,[status(thm)],[508, 504])).
% 1.92/2.09 tff(510,assumption,(node14(c_e_h_2, c_e, s1, s2)), introduced(assumption)).
% 1.92/2.09 tff(511,plain,
% 1.92/2.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node14(c_e_h_2, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node14(c_e_h_2, c_e, s1, s2)))),
% 1.92/2.09 inference(rewrite,[status(thm)],[])).
% 1.92/2.09 tff(512,plain,
% 1.92/2.09 (((~node14(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2))) <=> (m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node14(c_e_h_2, c_e, s1, s2)))),
% 1.92/2.09 inference(rewrite,[status(thm)],[])).
% 1.92/2.09 tff(513,plain,
% 1.92/2.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node14(c_e_h_2, c_e, s1, s2))))),
% 1.92/2.09 inference(monotonicity,[status(thm)],[512])).
% 1.92/2.09 tff(514,plain,
% 1.92/2.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node14(c_e_h_2, c_e, s1, s2)))),
% 1.92/2.09 inference(transitivity,[status(thm)],[513, 511])).
% 1.92/2.09 tff(515,plain,
% 1.92/2.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)))),
% 1.92/2.09 inference(quant_inst,[status(thm)],[])).
% 1.92/2.09 tff(516,plain,
% 1.92/2.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node14(c_e_h_2, c_e, s1, s2))),
% 1.92/2.09 inference(modus_ponens,[status(thm)],[515, 514])).
% 1.92/2.09 tff(517,plain,
% 1.92/2.09 ($false),
% 1.92/2.09 inference(unit_resolution,[status(thm)],[516, 404, 510, 432, 504])).
% 1.92/2.09 tff(518,plain,((~node14(c_e_h_2, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 1.92/2.09 tff(519,plain,
% 1.92/2.09 (~node14(c_e_h_2, c_e, s1, s2)),
% 1.92/2.09 inference(unit_resolution,[status(thm)],[518, 432])).
% 1.92/2.09 tff(520,plain,
% 1.92/2.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s1, s2)) | node15(c_e_h_2, c_e, s1, s2) | node16(c_e_h_2, c_e, s1) | node14(c_e_h_2, c_e, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s1, s2)) | node15(c_e_h_2, c_e, s1, s2) | node16(c_e_h_2, c_e, s1) | node14(c_e_h_2, c_e, s1, s2))),
% 1.92/2.09 inference(rewrite,[status(thm)],[])).
% 1.92/2.09 tff(521,plain,
% 1.92/2.09 ((node16(c_e_h_2, c_e, s1) | node14(c_e_h_2, c_e, s1, s2) | node15(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2))) <=> ((~node19(c_e_h_2, c_e, s1, s2)) | node15(c_e_h_2, c_e, s1, s2) | node16(c_e_h_2, c_e, s1) | node14(c_e_h_2, c_e, s1, s2))),
% 1.92/2.09 inference(rewrite,[status(thm)],[])).
% 1.92/2.09 tff(522,plain,
% 1.92/2.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s1) | node14(c_e_h_2, c_e, s1, s2) | node15(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s1, s2)) | node15(c_e_h_2, c_e, s1, s2) | node16(c_e_h_2, c_e, s1) | node14(c_e_h_2, c_e, s1, s2)))),
% 1.92/2.09 inference(monotonicity,[status(thm)],[521])).
% 1.92/2.09 tff(523,plain,
% 1.92/2.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s1) | node14(c_e_h_2, c_e, s1, s2) | node15(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s1, s2)) | node15(c_e_h_2, c_e, s1, s2) | node16(c_e_h_2, c_e, s1) | node14(c_e_h_2, c_e, s1, s2))),
% 1.92/2.09 inference(transitivity,[status(thm)],[522, 520])).
% 1.92/2.09 tff(524,plain,
% 1.92/2.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s1) | node14(c_e_h_2, c_e, s1, s2) | node15(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)))),
% 1.92/2.09 inference(quant_inst,[status(thm)],[])).
% 1.92/2.09 tff(525,plain,
% 1.92/2.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s1, s2)) | node15(c_e_h_2, c_e, s1, s2) | node16(c_e_h_2, c_e, s1) | node14(c_e_h_2, c_e, s1, s2)),
% 1.92/2.09 inference(modus_ponens,[status(thm)],[524, 523])).
% 1.92/2.09 tff(526,plain,
% 1.92/2.09 (node15(c_e_h_2, c_e, s1, s2) | node16(c_e_h_2, c_e, s1) | node14(c_e_h_2, c_e, s1, s2)),
% 1.92/2.09 inference(unit_resolution,[status(thm)],[525, 422, 441])).
% 1.92/2.09 tff(527,plain,
% 1.92/2.09 (node15(c_e_h_2, c_e, s1, s2)),
% 1.92/2.09 inference(unit_resolution,[status(thm)],[526, 519, 509])).
% 1.92/2.09 tff(528,plain,
% 1.92/2.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node15(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node15(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1))),
% 1.92/2.09 inference(rewrite,[status(thm)],[])).
% 1.92/2.09 tff(529,plain,
% 1.92/2.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node15(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1))),
% 1.92/2.09 inference(quant_inst,[status(thm)],[])).
% 1.92/2.09 tff(530,plain,
% 1.92/2.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node15(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1)),
% 1.92/2.09 inference(modus_ponens,[status(thm)],[529, 528])).
% 1.92/2.09 tff(531,plain,
% 1.92/2.09 ($false),
% 1.92/2.09 inference(unit_resolution,[status(thm)],[530, 292, 527, 432, 431])).
% 1.92/2.09 tff(532,plain,(~m_c_h_element_v_out(c_e_h_2, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 1.92/2.09 tff(533,plain,
% 1.92/2.09 (^[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)))),
% 1.92/2.09 inference(bind,[status(th)],[])).
% 1.92/2.09 tff(534,plain,
% 1.92/2.09 (![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))),
% 1.92/2.09 inference(quant_intro,[status(thm)],[533])).
% 1.92/2.09 tff(535,plain,
% 1.92/2.09 (![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))),
% 1.92/2.09 inference(rewrite,[status(thm)],[])).
% 1.92/2.09 tff(536,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/sandbox2/benchmark/theBenchmark.p','m_cell_72')).
% 1.92/2.09 tff(537,plain,
% 1.92/2.09 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))),
% 1.92/2.09 inference(modus_ponens,[status(thm)],[536, 535])).
% 1.92/2.09 tff(538,plain,(
% 1.92/2.09 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))),
% 1.92/2.09 inference(skolemize,[status(sab)],[537])).
% 1.92/2.09 tff(539,plain,
% 1.92/2.09 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))),
% 1.92/2.09 inference(modus_ponens,[status(thm)],[538, 534])).
% 1.92/2.09 tff(540,plain,
% 1.92/2.09 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_r, s2)) | m_c_h_element_v_out(c_e_h_2, 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_2, c_r, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s2))),
% 1.92/2.09 inference(rewrite,[status(thm)],[])).
% 1.92/2.09 tff(541,plain,
% 1.92/2.09 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_r, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s2))),
% 1.92/2.09 inference(quant_inst,[status(thm)],[])).
% 1.92/2.09 tff(542,plain,
% 1.92/2.09 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_r, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s2)),
% 1.92/2.09 inference(modus_ponens,[status(thm)],[541, 540])).
% 1.92/2.09 tff(543,plain,
% 1.92/2.09 (~m_and_h_gate_v_in1(c_e_h_2, c_r, s2)),
% 1.92/2.09 inference(unit_resolution,[status(thm)],[542, 539, 532])).
% 1.92/2.09 tff(544,plain,
% 1.92/2.09 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s2)) | m_and_h_gate_v_in1(c_e_h_2, 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_2, c_r, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s2))),
% 1.92/2.09 inference(rewrite,[status(thm)],[])).
% 1.92/2.09 tff(545,plain,
% 1.92/2.09 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s2))),
% 1.92/2.09 inference(quant_inst,[status(thm)],[])).
% 1.92/2.09 tff(546,plain,
% 1.92/2.09 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_r, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s2)),
% 1.92/2.09 inference(modus_ponens,[status(thm)],[545, 544])).
% 1.92/2.09 tff(547,plain,
% 1.92/2.09 (~node20(c_e_h_2, c_r, s2)),
% 1.92/2.09 inference(unit_resolution,[status(thm)],[546, 481, 543])).
% 1.92/2.09 tff(548,assumption,(node21(c_e_h_2, c_r, s2, s3)), introduced(assumption)).
% 1.92/2.09 tff(549,assumption,(~node20(c_e_h_2, c_r, s2)), introduced(assumption)).
% 1.92/2.09 tff(550,plain,
% 1.92/2.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | (~node21(c_e_h_2, c_r, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | (~node21(c_e_h_2, c_r, s2, s3)))),
% 1.92/2.09 inference(rewrite,[status(thm)],[])).
% 1.92/2.09 tff(551,plain,
% 1.92/2.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | (~node21(c_e_h_2, c_r, s2, s3)))),
% 1.92/2.09 inference(quant_inst,[status(thm)],[])).
% 1.92/2.09 tff(552,plain,
% 1.92/2.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | (~node21(c_e_h_2, c_r, s2, s3))),
% 1.92/2.09 inference(modus_ponens,[status(thm)],[551, 550])).
% 1.92/2.09 tff(553,plain,
% 1.92/2.09 ($false),
% 1.92/2.09 inference(unit_resolution,[status(thm)],[552, 69, 270, 549, 548])).
% 1.92/2.09 tff(554,plain,((~node21(c_e_h_2, c_r, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | node20(c_e_h_2, c_r, s2)), inference(lemma,lemma(discharge,[]))).
% 1.92/2.09 tff(555,plain,
% 1.92/2.09 ((~node21(c_e_h_2, c_r, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s3))),
% 1.92/2.09 inference(unit_resolution,[status(thm)],[554, 547])).
% 1.92/2.09 tff(556,plain,
% 1.92/2.09 (~node21(c_e_h_2, c_r, s2, s3)),
% 1.92/2.09 inference(unit_resolution,[status(thm)],[555, 270])).
% 1.92/2.09 tff(557,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_r, s2)), introduced(assumption)).
% 1.92/2.09 tff(558,plain,
% 1.92/2.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | (~node22(c_e_h_2, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_r, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | (~node22(c_e_h_2, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_r, s2))),
% 1.92/2.09 inference(rewrite,[status(thm)],[])).
% 1.92/2.09 tff(559,plain,
% 1.92/2.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | (~node22(c_e_h_2, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_r, s2))),
% 1.92/2.09 inference(quant_inst,[status(thm)],[])).
% 1.92/2.09 tff(560,plain,
% 1.92/2.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | (~node22(c_e_h_2, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_r, s2)),
% 1.92/2.09 inference(modus_ponens,[status(thm)],[559, 558])).
% 1.92/2.09 tff(561,plain,
% 1.92/2.09 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | (~node22(c_e_h_2, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_r, s2)),
% 1.92/2.09 inference(unit_resolution,[status(thm)],[560, 126])).
% 1.92/2.09 tff(562,plain,
% 1.92/2.09 (~node22(c_e_h_2, c_r, s2, s3)),
% 1.92/2.09 inference(unit_resolution,[status(thm)],[561, 270, 557])).
% 1.92/2.09 tff(563,plain,
% 1.92/2.09 (succ(s2, s3) <=> succ(s2, s3)),
% 1.92/2.09 inference(rewrite,[status(thm)],[])).
% 1.92/2.09 tff(564,axiom,(succ(s2, s3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound3')).
% 1.92/2.09 tff(565,plain,
% 1.92/2.09 (succ(s2, s3)),
% 1.92/2.09 inference(modus_ponens,[status(thm)],[564, 563])).
% 1.92/2.09 tff(566,plain,
% 1.92/2.09 (((~![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))),
% 1.92/2.09 inference(rewrite,[status(thm)],[])).
% 1.92/2.09 tff(567,plain,
% 1.92/2.09 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s2, s3)) | trans(s2, s3))),
% 1.92/2.09 inference(quant_inst,[status(thm)],[])).
% 1.92/2.09 tff(568,plain,
% 1.92/2.09 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s2, s3)) | trans(s2, s3)),
% 1.92/2.09 inference(modus_ponens,[status(thm)],[567, 566])).
% 1.92/2.09 tff(569,plain,
% 1.92/2.09 (trans(s2, s3)),
% 1.92/2.09 inference(unit_resolution,[status(thm)],[568, 565, 84])).
% 1.92/2.09 tff(570,plain,
% 1.92/2.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_2, c_r, s2, s3) | node22(c_e_h_2, c_r, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_2, c_r, s2, s3) | node22(c_e_h_2, c_r, s2, s3))),
% 1.92/2.09 inference(rewrite,[status(thm)],[])).
% 1.92/2.09 tff(571,plain,
% 1.92/2.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_2, c_r, s2, s3) | node22(c_e_h_2, c_r, s2, s3))),
% 1.92/2.09 inference(quant_inst,[status(thm)],[])).
% 1.92/2.09 tff(572,plain,
% 1.92/2.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_2, c_r, s2, s3) | node22(c_e_h_2, c_r, s2, s3)),
% 1.92/2.09 inference(modus_ponens,[status(thm)],[571, 570])).
% 1.92/2.09 tff(573,plain,
% 1.92/2.09 ($false),
% 1.92/2.09 inference(unit_resolution,[status(thm)],[572, 101, 569, 562, 556])).
% 1.92/2.09 tff(574,plain,((~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | m_and_h_gate_v_out(c_e_h_2, c_r, s2)), inference(lemma,lemma(discharge,[]))).
% 1.92/2.09 tff(575,plain,
% 1.92/2.09 (~m_and_h_gate_v_out(c_e_h_2, c_r, s3)),
% 1.92/2.09 inference(unit_resolution,[status(thm)],[574, 269])).
% 1.92/2.09 tff(576,plain,
% 1.92/2.09 (^[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)))),
% 1.92/2.09 inference(bind,[status(th)],[])).
% 1.92/2.09 tff(577,plain,
% 1.92/2.09 (![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))),
% 1.92/2.09 inference(quant_intro,[status(thm)],[576])).
% 1.92/2.09 tff(578,plain,
% 1.92/2.09 (![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))),
% 1.92/2.09 inference(rewrite,[status(thm)],[])).
% 1.92/2.09 tff(579,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/sandbox2/benchmark/theBenchmark.p','m_cell_81')).
% 1.92/2.09 tff(580,plain,
% 1.92/2.09 (![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))),
% 1.92/2.09 inference(modus_ponens,[status(thm)],[579, 578])).
% 1.92/2.09 tff(581,plain,(
% 1.92/2.09 ![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))),
% 1.92/2.09 inference(skolemize,[status(sab)],[580])).
% 1.92/2.09 tff(582,plain,
% 1.92/2.09 (![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))),
% 1.92/2.09 inference(modus_ponens,[status(thm)],[581, 577])).
% 1.92/2.09 tff(583,plain,
% 1.92/2.09 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s3)) | m_and_h_gate_v_out(c_e_h_2, c_r, s3))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s3)) | m_and_h_gate_v_out(c_e_h_2, c_r, s3))),
% 1.92/2.09 inference(rewrite,[status(thm)],[])).
% 1.92/2.09 tff(584,plain,
% 1.92/2.09 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s3)) | m_and_h_gate_v_out(c_e_h_2, c_r, s3))),
% 1.92/2.09 inference(quant_inst,[status(thm)],[])).
% 1.92/2.09 tff(585,plain,
% 1.92/2.09 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s3)) | m_and_h_gate_v_out(c_e_h_2, c_r, s3)),
% 1.92/2.09 inference(modus_ponens,[status(thm)],[584, 583])).
% 1.92/2.09 tff(586,plain,
% 1.92/2.09 (~m_user_v_ack(c_e_h_2, c_u, s3)),
% 1.92/2.09 inference(unit_resolution,[status(thm)],[585, 582, 575])).
% 1.92/2.09 tff(587,plain,
% 1.92/2.09 (^[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))))),
% 1.92/2.09 inference(bind,[status(th)],[])).
% 1.92/2.09 tff(588,plain,
% 1.92/2.09 (![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)))),
% 1.92/2.09 inference(quant_intro,[status(thm)],[587])).
% 1.92/2.09 tff(589,plain,
% 1.92/2.09 (![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)))),
% 1.92/2.09 inference(rewrite,[status(thm)],[])).
% 1.92/2.09 tff(590,axiom,(![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty5')).
% 1.92/2.09 tff(591,plain,
% 1.92/2.09 (![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))),
% 1.92/2.09 inference(modus_ponens,[status(thm)],[590, 589])).
% 1.92/2.09 tff(592,plain,(
% 1.92/2.09 ![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))),
% 1.92/2.09 inference(skolemize,[status(sab)],[591])).
% 1.92/2.09 tff(593,plain,
% 1.92/2.09 (![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))),
% 1.92/2.09 inference(modus_ponens,[status(thm)],[592, 588])).
% 1.92/2.09 tff(594,plain,
% 1.92/2.09 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s3) | (~node25(s3)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s3) | (~node25(s3)))),
% 1.92/2.09 inference(rewrite,[status(thm)],[])).
% 1.92/2.09 tff(595,plain,
% 1.92/2.09 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s3) | (~node25(s3)))),
% 1.92/2.09 inference(quant_inst,[status(thm)],[])).
% 1.92/2.09 tff(596,plain,
% 1.92/2.09 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s3) | (~node25(s3))),
% 1.92/2.09 inference(modus_ponens,[status(thm)],[595, 594])).
% 1.92/2.09 tff(597,plain,
% 1.92/2.09 (~node25(s3)),
% 1.92/2.09 inference(unit_resolution,[status(thm)],[596, 593, 586])).
% 1.92/2.09 tff(598,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s4)), introduced(assumption)).
% 1.92/2.09 tff(599,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s3)), introduced(assumption)).
% 1.92/2.09 tff(600,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)), introduced(assumption)).
% 1.92/2.09 tff(601,assumption,(m_cell_v_token(c_e_h_1, s0)), introduced(assumption)).
% 1.92/2.09 tff(602,plain,
% 1.92/2.09 (^[X: $i] : refl((~m_cell_v_token(c_e_h_1, X)) <=> (~m_cell_v_token(c_e_h_1, X)))),
% 1.92/2.09 inference(bind,[status(th)],[])).
% 1.92/2.09 tff(603,plain,
% 1.92/2.09 (![X: $i] : (~m_cell_v_token(c_e_h_1, X)) <=> ![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 1.92/2.09 inference(quant_intro,[status(thm)],[602])).
% 1.92/2.09 tff(604,plain,
% 1.92/2.09 (![X: $i] : (~m_cell_v_token(c_e_h_1, X)) <=> ![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 1.92/2.09 inference(rewrite,[status(thm)],[])).
% 1.92/2.09 tff(605,axiom,(![X: $i] : (~m_cell_v_token(c_e_h_1, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_3')).
% 1.92/2.09 tff(606,plain,
% 1.92/2.09 (![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 1.92/2.09 inference(modus_ponens,[status(thm)],[605, 604])).
% 1.92/2.09 tff(607,plain,(
% 1.92/2.09 ![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 1.92/2.09 inference(skolemize,[status(sab)],[606])).
% 1.92/2.09 tff(608,plain,
% 1.92/2.09 (![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 1.92/2.09 inference(modus_ponens,[status(thm)],[607, 603])).
% 1.92/2.09 tff(609,plain,
% 1.92/2.09 ((~![X: $i] : (~m_cell_v_token(c_e_h_1, X))) | (~m_cell_v_token(c_e_h_1, s0))),
% 1.92/2.09 inference(quant_inst,[status(thm)],[])).
% 1.92/2.09 tff(610,plain,
% 1.92/2.09 ($false),
% 1.92/2.09 inference(unit_resolution,[status(thm)],[609, 608, 601])).
% 1.92/2.09 tff(611,plain,(~m_cell_v_token(c_e_h_1, s0)), inference(lemma,lemma(discharge,[]))).
% 1.92/2.09 tff(612,plain,
% 1.92/2.09 (((~![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))),
% 1.93/2.09 inference(rewrite,[status(thm)],[])).
% 1.93/2.09 tff(613,plain,
% 1.93/2.09 ((~![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))),
% 1.93/2.09 inference(quant_inst,[status(thm)],[])).
% 1.93/2.09 tff(614,plain,
% 1.93/2.09 ((~![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)),
% 1.93/2.09 inference(modus_ponens,[status(thm)],[613, 612])).
% 1.93/2.09 tff(615,plain,
% 1.93/2.09 (m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[614, 143, 611])).
% 1.93/2.09 tff(616,plain,
% 1.93/2.09 (((~![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))),
% 1.93/2.09 inference(rewrite,[status(thm)],[])).
% 1.93/2.09 tff(617,plain,
% 1.93/2.09 ((~![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))),
% 1.93/2.09 inference(quant_inst,[status(thm)],[])).
% 1.93/2.09 tff(618,plain,
% 1.93/2.09 ((~![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)),
% 1.93/2.09 inference(modus_ponens,[status(thm)],[617, 616])).
% 1.93/2.09 tff(619,plain,
% 1.93/2.09 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[618, 157, 615])).
% 1.93/2.09 tff(620,plain,
% 1.93/2.09 (^[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))))),
% 1.93/2.09 inference(bind,[status(th)],[])).
% 1.93/2.09 tff(621,plain,
% 1.93/2.09 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_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)))),
% 1.93/2.09 inference(quant_intro,[status(thm)],[620])).
% 1.93/2.09 tff(622,plain,
% 1.93/2.09 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_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)))),
% 1.93/2.09 inference(rewrite,[status(thm)],[])).
% 1.93/2.09 tff(623,plain,
% 1.93/2.09 (^[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)))))),
% 1.93/2.09 inference(bind,[status(th)],[])).
% 1.93/2.09 tff(624,plain,
% 1.93/2.09 (![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)))),
% 1.93/2.10 inference(quant_intro,[status(thm)],[623])).
% 1.93/2.10 tff(625,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/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_h_init_7')).
% 1.93/2.10 tff(626,plain,
% 1.93/2.10 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[625, 624])).
% 1.93/2.10 tff(627,plain,
% 1.93/2.10 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[626, 622])).
% 1.93/2.10 tff(628,plain,(
% 1.93/2.10 ![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 1.93/2.10 inference(skolemize,[status(sab)],[627])).
% 1.93/2.10 tff(629,plain,
% 1.93/2.10 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[628, 621])).
% 1.93/2.10 tff(630,plain,
% 1.93/2.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~node11(c_e_h_1, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_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)))) | (~node11(c_e_h_1, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(631,plain,
% 1.93/2.10 ((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))) <=> ((~node11(c_e_h_1, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(632,plain,
% 1.93/2.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, 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)))) | ((~node11(c_e_h_1, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0))))),
% 1.93/2.10 inference(monotonicity,[status(thm)],[631])).
% 1.93/2.10 tff(633,plain,
% 1.93/2.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, 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)))) | (~node11(c_e_h_1, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)))),
% 1.93/2.10 inference(transitivity,[status(thm)],[632, 630])).
% 1.93/2.10 tff(634,plain,
% 1.93/2.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, 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)))),
% 1.93/2.10 inference(quant_inst,[status(thm)],[])).
% 1.93/2.10 tff(635,plain,
% 1.93/2.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~node11(c_e_h_1, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0))),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[634, 633])).
% 1.93/2.10 tff(636,plain,
% 1.93/2.10 ((~node11(c_e_h_1, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0))),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[635, 629])).
% 1.93/2.10 tff(637,plain,
% 1.93/2.10 ((~node11(c_e_h_1, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[636, 619])).
% 1.93/2.10 tff(638,plain,
% 1.93/2.10 (~node11(c_e_h_1, c_n, s0, s1)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[637, 600])).
% 1.93/2.10 tff(639,plain,
% 1.93/2.10 (((~![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))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(640,plain,
% 1.93/2.10 ((~![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))),
% 1.93/2.10 inference(quant_inst,[status(thm)],[])).
% 1.93/2.10 tff(641,plain,
% 1.93/2.10 ((~![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)),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[640, 639])).
% 1.93/2.10 tff(642,plain,
% 1.93/2.10 (node10(c_e_h_1, c_n, s0, s1)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[641, 212, 91, 638])).
% 1.93/2.10 tff(643,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s0)), introduced(assumption)).
% 1.93/2.10 tff(644,plain,
% 1.93/2.10 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s0))),
% 1.93/2.10 inference(quant_inst,[status(thm)],[])).
% 1.93/2.10 tff(645,plain,
% 1.93/2.10 ($false),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[644, 279, 643])).
% 1.93/2.10 tff(646,plain,(~m_c_h_element_v_out(c_e_h_1, c_e, s0)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.10 tff(647,plain,
% 1.93/2.10 (^[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)))),
% 1.93/2.10 inference(bind,[status(th)],[])).
% 1.93/2.10 tff(648,plain,
% 1.93/2.10 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X)) <=> ![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))),
% 1.93/2.10 inference(quant_intro,[status(thm)],[647])).
% 1.93/2.10 tff(649,plain,
% 1.93/2.10 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X)) <=> ![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))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(650,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/sandbox2/benchmark/theBenchmark.p','m_cell_57')).
% 1.93/2.10 tff(651,plain,
% 1.93/2.10 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[650, 649])).
% 1.93/2.10 tff(652,plain,(
% 1.93/2.10 ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))),
% 1.93/2.10 inference(skolemize,[status(sab)],[651])).
% 1.93/2.10 tff(653,plain,
% 1.93/2.10 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[652, 648])).
% 1.93/2.10 tff(654,plain,
% 1.93/2.10 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, 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))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(655,plain,
% 1.93/2.10 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0) | m_c_h_element_v_out(c_e_h_1, c_e, s0))),
% 1.93/2.10 inference(quant_inst,[status(thm)],[])).
% 1.93/2.10 tff(656,plain,
% 1.93/2.10 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0) | m_c_h_element_v_out(c_e_h_1, c_e, s0)),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[655, 654])).
% 1.93/2.10 tff(657,plain,
% 1.93/2.10 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[656, 653, 646])).
% 1.93/2.10 tff(658,plain,
% 1.93/2.10 (((~![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))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(659,plain,
% 1.93/2.10 ((~![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))),
% 1.93/2.10 inference(quant_inst,[status(thm)],[])).
% 1.93/2.10 tff(660,plain,
% 1.93/2.10 ((~![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)),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[659, 658])).
% 1.93/2.10 tff(661,plain,
% 1.93/2.10 ((~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)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[660, 19])).
% 1.93/2.10 tff(662,plain,
% 1.93/2.10 (~m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_m, s0)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[661, 611])).
% 1.93/2.10 tff(663,plain,
% 1.93/2.10 (((~![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))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(664,plain,
% 1.93/2.10 ((~![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))),
% 1.93/2.10 inference(quant_inst,[status(thm)],[])).
% 1.93/2.10 tff(665,plain,
% 1.93/2.10 ((~![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)),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[664, 663])).
% 1.93/2.10 tff(666,plain,
% 1.93/2.10 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[665, 30, 662])).
% 1.93/2.10 tff(667,plain,
% 1.93/2.10 (^[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)))),
% 1.93/2.10 inference(bind,[status(th)],[])).
% 1.93/2.10 tff(668,plain,
% 1.93/2.10 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X)) <=> ![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))),
% 1.93/2.10 inference(quant_intro,[status(thm)],[667])).
% 1.93/2.10 tff(669,plain,
% 1.93/2.10 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X)) <=> ![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))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(670,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/sandbox2/benchmark/theBenchmark.p','m_cell_59')).
% 1.93/2.10 tff(671,plain,
% 1.93/2.10 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[670, 669])).
% 1.93/2.10 tff(672,plain,(
% 1.93/2.10 ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 1.93/2.10 inference(skolemize,[status(sab)],[671])).
% 1.93/2.10 tff(673,plain,
% 1.93/2.10 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[672, 668])).
% 1.93/2.10 tff(674,plain,
% 1.93/2.10 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, 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))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(675,plain,
% 1.93/2.10 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))),
% 1.93/2.10 inference(quant_inst,[status(thm)],[])).
% 1.93/2.10 tff(676,plain,
% 1.93/2.10 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[675, 674])).
% 1.93/2.10 tff(677,plain,
% 1.93/2.10 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[676, 673, 666])).
% 1.93/2.10 tff(678,plain,
% 1.93/2.10 (^[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)))),
% 1.93/2.10 inference(bind,[status(th)],[])).
% 1.93/2.10 tff(679,plain,
% 1.93/2.10 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 1.93/2.10 inference(quant_intro,[status(thm)],[678])).
% 1.93/2.10 tff(680,plain,
% 1.93/2.10 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(681,plain,
% 1.93/2.10 (^[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))))),
% 1.93/2.10 inference(bind,[status(th)],[])).
% 1.93/2.10 tff(682,plain,
% 1.93/2.10 (![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))),
% 1.93/2.10 inference(quant_intro,[status(thm)],[681])).
% 1.93/2.10 tff(683,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/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_h_init_5')).
% 1.93/2.10 tff(684,plain,
% 1.93/2.10 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[683, 682])).
% 1.93/2.10 tff(685,plain,
% 1.93/2.10 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[684, 680])).
% 1.93/2.10 tff(686,plain,(
% 1.93/2.10 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 1.93/2.10 inference(skolemize,[status(sab)],[685])).
% 1.93/2.10 tff(687,plain,
% 1.93/2.10 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[686, 679])).
% 1.93/2.10 tff(688,plain,
% 1.93/2.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~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)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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) | (~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)))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(689,plain,
% 1.93/2.10 (((~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) | (~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)))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(690,plain,
% 1.93/2.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, 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) | (~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))))),
% 1.93/2.10 inference(monotonicity,[status(thm)],[689])).
% 1.93/2.10 tff(691,plain,
% 1.93/2.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, 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) | (~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)))),
% 1.93/2.10 inference(transitivity,[status(thm)],[690, 688])).
% 1.93/2.10 tff(692,plain,
% 1.93/2.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, 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))),
% 1.93/2.10 inference(quant_inst,[status(thm)],[])).
% 1.93/2.10 tff(693,plain,
% 1.93/2.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node10(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0))),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[692, 691])).
% 1.93/2.10 tff(694,plain,
% 1.93/2.10 ($false),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[693, 687, 600, 677, 657, 642])).
% 1.93/2.10 tff(695,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.10 tff(696,plain,
% 1.93/2.10 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, 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)))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(697,plain,
% 1.93/2.10 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)))),
% 1.93/2.10 inference(quant_inst,[status(thm)],[])).
% 1.93/2.10 tff(698,plain,
% 1.93/2.10 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1))),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[697, 696])).
% 1.93/2.10 tff(699,plain,
% 1.93/2.10 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[698, 168, 695])).
% 1.93/2.10 tff(700,plain,
% 1.93/2.10 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, 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))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(701,plain,
% 1.93/2.10 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1))),
% 1.93/2.10 inference(quant_inst,[status(thm)],[])).
% 1.93/2.10 tff(702,plain,
% 1.93/2.10 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1)),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[701, 700])).
% 1.93/2.10 tff(703,plain,
% 1.93/2.10 (~node9(c_e_h_1, c_m, s1)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[702, 182, 699])).
% 1.93/2.10 tff(704,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)), introduced(assumption)).
% 1.93/2.10 tff(705,assumption,(node11(c_e_h_1, c_m, s1, s2)), introduced(assumption)).
% 1.93/2.10 tff(706,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)), introduced(assumption)).
% 1.93/2.10 tff(707,assumption,(node11(c_e_h_1, c_m, s0, s1)), introduced(assumption)).
% 1.93/2.10 tff(708,plain,
% 1.93/2.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, 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))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(709,plain,
% 1.93/2.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, 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))),
% 1.93/2.10 inference(quant_inst,[status(thm)],[])).
% 1.93/2.10 tff(710,plain,
% 1.93/2.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | (~node11(c_e_h_1, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[709, 708])).
% 1.93/2.10 tff(711,plain,
% 1.93/2.10 ($false),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[710, 227, 666, 706, 707])).
% 1.93/2.10 tff(712,plain,((~node11(c_e_h_1, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))), inference(lemma,lemma(discharge,[]))).
% 1.93/2.10 tff(713,plain,
% 1.93/2.10 (~node11(c_e_h_1, c_m, s0, s1)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[712, 706])).
% 1.93/2.10 tff(714,plain,
% 1.93/2.10 (((~![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))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(715,plain,
% 1.93/2.10 ((~![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))),
% 1.93/2.10 inference(quant_inst,[status(thm)],[])).
% 1.93/2.10 tff(716,plain,
% 1.93/2.10 ((~![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)),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[715, 714])).
% 1.93/2.10 tff(717,plain,
% 1.93/2.10 (node10(c_e_h_1, c_m, s0, s1) | node11(c_e_h_1, c_m, s0, s1)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[716, 212, 91])).
% 1.93/2.10 tff(718,plain,
% 1.93/2.10 (node10(c_e_h_1, c_m, s0, s1)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[717, 713])).
% 1.93/2.10 tff(719,plain,
% 1.93/2.10 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, 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)))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(720,plain,
% 1.93/2.10 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)))),
% 1.93/2.10 inference(quant_inst,[status(thm)],[])).
% 1.93/2.10 tff(721,plain,
% 1.93/2.10 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0))),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[720, 719])).
% 1.93/2.10 tff(722,plain,
% 1.93/2.10 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[721, 168, 619])).
% 1.93/2.10 tff(723,plain,
% 1.93/2.10 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, 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))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(724,plain,
% 1.93/2.10 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0))),
% 1.93/2.10 inference(quant_inst,[status(thm)],[])).
% 1.93/2.10 tff(725,plain,
% 1.93/2.10 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0)),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[724, 723])).
% 1.93/2.10 tff(726,plain,
% 1.93/2.10 (~node9(c_e_h_1, c_m, s0)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[725, 182, 722])).
% 1.93/2.10 tff(727,plain,
% 1.93/2.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~node10(c_e_h_1, c_m, s0, s1)) | node9(c_e_h_1, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, 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)))) | (~node10(c_e_h_1, c_m, s0, s1)) | node9(c_e_h_1, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(728,plain,
% 1.93/2.10 ((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))) <=> ((~node10(c_e_h_1, c_m, s0, s1)) | node9(c_e_h_1, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(729,plain,
% 1.93/2.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, 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)))) | ((~node10(c_e_h_1, c_m, s0, s1)) | node9(c_e_h_1, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))))),
% 1.93/2.10 inference(monotonicity,[status(thm)],[728])).
% 1.93/2.10 tff(730,plain,
% 1.93/2.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, 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)))) | (~node10(c_e_h_1, c_m, s0, s1)) | node9(c_e_h_1, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)))),
% 1.93/2.10 inference(transitivity,[status(thm)],[729, 727])).
% 1.93/2.10 tff(731,plain,
% 1.93/2.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, 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)))),
% 1.93/2.10 inference(quant_inst,[status(thm)],[])).
% 1.93/2.10 tff(732,plain,
% 1.93/2.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~node10(c_e_h_1, c_m, s0, s1)) | node9(c_e_h_1, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[731, 730])).
% 1.93/2.11 tff(733,plain,
% 1.93/2.11 ($false),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[732, 196, 706, 726, 718])).
% 1.93/2.11 tff(734,plain,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.11 tff(735,plain,
% 1.93/2.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_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))),
% 1.93/2.11 inference(rewrite,[status(thm)],[])).
% 1.93/2.11 tff(736,plain,
% 1.93/2.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_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))),
% 1.93/2.11 inference(quant_inst,[status(thm)],[])).
% 1.93/2.11 tff(737,plain,
% 1.93/2.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | (~node11(c_e_h_1, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)),
% 1.93/2.11 inference(modus_ponens,[status(thm)],[736, 735])).
% 1.93/2.11 tff(738,plain,
% 1.93/2.11 ($false),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[737, 227, 734, 704, 705])).
% 1.93/2.11 tff(739,plain,((~node11(c_e_h_1, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))), inference(lemma,lemma(discharge,[]))).
% 1.93/2.11 tff(740,plain,
% 1.93/2.11 (~node11(c_e_h_1, c_m, s1, s2)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[739, 704])).
% 1.93/2.11 tff(741,plain,
% 1.93/2.11 (((~![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))),
% 1.93/2.11 inference(rewrite,[status(thm)],[])).
% 1.93/2.11 tff(742,plain,
% 1.93/2.11 ((~![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))),
% 1.93/2.11 inference(quant_inst,[status(thm)],[])).
% 1.93/2.11 tff(743,plain,
% 1.93/2.11 ((~![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)),
% 1.93/2.11 inference(modus_ponens,[status(thm)],[742, 741])).
% 1.93/2.11 tff(744,plain,
% 1.93/2.11 (node10(c_e_h_1, c_m, s1, s2) | node11(c_e_h_1, c_m, s1, s2)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[743, 212, 257])).
% 1.93/2.11 tff(745,plain,
% 1.93/2.11 (node10(c_e_h_1, c_m, s1, s2)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[744, 740])).
% 1.93/2.11 tff(746,plain,
% 1.93/2.11 (((~![Y: $i, I0: $i, 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, s2)) | node9(c_e_h_1, c_m, s1) | (~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)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | node9(c_e_h_1, c_m, s1) | (~node10(c_e_h_1, c_m, s1, s2)))),
% 1.93/2.11 inference(rewrite,[status(thm)],[])).
% 1.93/2.11 tff(747,plain,
% 1.93/2.11 ((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))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | node9(c_e_h_1, c_m, s1) | (~node10(c_e_h_1, c_m, s1, s2)))),
% 1.93/2.11 inference(rewrite,[status(thm)],[])).
% 1.93/2.11 tff(748,plain,
% 1.93/2.11 (((~![Y: $i, I0: $i, 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)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | node9(c_e_h_1, c_m, s1) | (~node10(c_e_h_1, c_m, s1, s2))))),
% 1.93/2.11 inference(monotonicity,[status(thm)],[747])).
% 1.93/2.11 tff(749,plain,
% 1.93/2.11 (((~![Y: $i, I0: $i, 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)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | node9(c_e_h_1, c_m, s1) | (~node10(c_e_h_1, c_m, s1, s2)))),
% 1.93/2.11 inference(transitivity,[status(thm)],[748, 746])).
% 1.93/2.11 tff(750,plain,
% 1.93/2.11 ((~![Y: $i, I0: $i, 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)))),
% 1.93/2.11 inference(quant_inst,[status(thm)],[])).
% 1.93/2.11 tff(751,plain,
% 1.93/2.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | node9(c_e_h_1, c_m, s1) | (~node10(c_e_h_1, c_m, s1, s2))),
% 1.93/2.11 inference(modus_ponens,[status(thm)],[750, 749])).
% 1.93/2.11 tff(752,plain,
% 1.93/2.11 ($false),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[751, 196, 704, 745, 703])).
% 1.93/2.11 tff(753,plain,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.11 tff(754,plain,
% 1.93/2.11 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))),
% 1.93/2.11 inference(rewrite,[status(thm)],[])).
% 1.93/2.11 tff(755,plain,
% 1.93/2.11 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))),
% 1.93/2.11 inference(quant_inst,[status(thm)],[])).
% 1.93/2.11 tff(756,plain,
% 1.93/2.11 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)),
% 1.93/2.11 inference(modus_ponens,[status(thm)],[755, 754])).
% 1.93/2.11 tff(757,plain,
% 1.93/2.11 ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[756, 41])).
% 1.93/2.11 tff(758,plain,
% 1.93/2.11 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s2)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[757, 753])).
% 1.93/2.11 tff(759,plain,
% 1.93/2.11 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s2)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s2)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s2))),
% 1.93/2.11 inference(rewrite,[status(thm)],[])).
% 1.93/2.11 tff(760,plain,
% 1.93/2.11 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s2)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s2))),
% 1.93/2.11 inference(quant_inst,[status(thm)],[])).
% 1.93/2.11 tff(761,plain,
% 1.93/2.11 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s2)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s2)),
% 1.93/2.11 inference(modus_ponens,[status(thm)],[760, 759])).
% 1.93/2.11 tff(762,plain,
% 1.93/2.11 (~node20(c_e_h_1, c_r, s2)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[761, 55, 758])).
% 1.93/2.11 tff(763,plain,
% 1.93/2.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3)) | node20(c_e_h_1, c_r, 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, s3)) | (~node21(c_e_h_1, c_r, s2, s3)) | node20(c_e_h_1, c_r, s2))),
% 1.93/2.11 inference(rewrite,[status(thm)],[])).
% 1.93/2.11 tff(764,plain,
% 1.93/2.11 ((node20(c_e_h_1, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3)) | node20(c_e_h_1, c_r, s2))),
% 1.93/2.11 inference(rewrite,[status(thm)],[])).
% 1.93/2.11 tff(765,plain,
% 1.93/2.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3)) | node20(c_e_h_1, c_r, s2)))),
% 1.93/2.11 inference(monotonicity,[status(thm)],[764])).
% 1.93/2.11 tff(766,plain,
% 1.93/2.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3)) | node20(c_e_h_1, c_r, s2))),
% 1.93/2.11 inference(transitivity,[status(thm)],[765, 763])).
% 1.93/2.11 tff(767,plain,
% 1.93/2.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3)))),
% 1.93/2.11 inference(quant_inst,[status(thm)],[])).
% 1.93/2.11 tff(768,plain,
% 1.93/2.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3)) | node20(c_e_h_1, c_r, s2)),
% 1.93/2.11 inference(modus_ponens,[status(thm)],[767, 766])).
% 1.93/2.11 tff(769,plain,
% 1.93/2.11 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3))),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[768, 69, 762])).
% 1.93/2.11 tff(770,plain,
% 1.93/2.11 (~node21(c_e_h_1, c_r, s2, s3)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[769, 599])).
% 1.93/2.11 tff(771,plain,
% 1.93/2.11 (((~![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))),
% 1.93/2.11 inference(rewrite,[status(thm)],[])).
% 1.93/2.11 tff(772,plain,
% 1.93/2.11 ((~![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))),
% 1.93/2.11 inference(quant_inst,[status(thm)],[])).
% 1.93/2.11 tff(773,plain,
% 1.93/2.11 ((~![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)),
% 1.93/2.11 inference(modus_ponens,[status(thm)],[772, 771])).
% 1.93/2.11 tff(774,plain,
% 1.93/2.11 (node22(c_e_h_1, c_r, s2, s3)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[773, 101, 569, 770])).
% 1.93/2.11 tff(775,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s1)), introduced(assumption)).
% 1.93/2.11 tff(776,plain,
% 1.93/2.11 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))),
% 1.93/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(777,plain,
% 1.95/2.11 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))),
% 1.95/2.11 inference(quant_inst,[status(thm)],[])).
% 1.95/2.11 tff(778,plain,
% 1.95/2.11 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[777, 776])).
% 1.95/2.11 tff(779,plain,
% 1.95/2.11 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s0)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[778, 41, 666])).
% 1.95/2.11 tff(780,plain,
% 1.95/2.11 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s0)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s0)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s0))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(781,plain,
% 1.95/2.11 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s0)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s0))),
% 1.95/2.11 inference(quant_inst,[status(thm)],[])).
% 1.95/2.11 tff(782,plain,
% 1.95/2.11 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s0)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s0)),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[781, 780])).
% 1.95/2.11 tff(783,plain,
% 1.95/2.11 (~node20(c_e_h_1, c_r, s0)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[782, 55, 779])).
% 1.95/2.11 tff(784,plain,
% 1.95/2.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_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)))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(785,plain,
% 1.95/2.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node21(c_e_h_1, c_r, s0, s1)))),
% 1.95/2.11 inference(quant_inst,[status(thm)],[])).
% 1.95/2.11 tff(786,plain,
% 1.95/2.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node21(c_e_h_1, c_r, s0, s1))),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[785, 784])).
% 1.95/2.11 tff(787,plain,
% 1.95/2.11 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node21(c_e_h_1, c_r, s0, s1))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[786, 69, 783])).
% 1.95/2.11 tff(788,plain,
% 1.95/2.11 (~node21(c_e_h_1, c_r, s0, s1)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[787, 775])).
% 1.95/2.11 tff(789,plain,
% 1.95/2.11 (((~![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))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(790,plain,
% 1.95/2.11 ((~![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))),
% 1.95/2.11 inference(quant_inst,[status(thm)],[])).
% 1.95/2.11 tff(791,plain,
% 1.95/2.11 ((~![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)),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[790, 789])).
% 1.95/2.11 tff(792,plain,
% 1.95/2.11 (node22(c_e_h_1, c_r, s0, s1)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[791, 101, 91, 788])).
% 1.95/2.11 tff(793,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s0)), introduced(assumption)).
% 1.95/2.11 tff(794,plain,
% 1.95/2.11 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s0))),
% 1.95/2.11 inference(quant_inst,[status(thm)],[])).
% 1.95/2.11 tff(795,plain,
% 1.95/2.11 ($false),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[794, 113, 793])).
% 1.95/2.11 tff(796,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s0)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.11 tff(797,plain,
% 1.95/2.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, 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))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(798,plain,
% 1.95/2.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node22(c_e_h_1, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0))),
% 1.95/2.11 inference(quant_inst,[status(thm)],[])).
% 1.95/2.11 tff(799,plain,
% 1.95/2.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node22(c_e_h_1, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0)),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[798, 797])).
% 1.95/2.11 tff(800,plain,
% 1.95/2.11 ($false),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[799, 126, 796, 775, 792])).
% 1.95/2.11 tff(801,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.11 tff(802,plain,
% 1.95/2.11 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(803,plain,
% 1.95/2.11 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))),
% 1.95/2.11 inference(quant_inst,[status(thm)],[])).
% 1.95/2.11 tff(804,plain,
% 1.95/2.11 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[803, 802])).
% 1.95/2.11 tff(805,plain,
% 1.95/2.11 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s1)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[804, 41, 734])).
% 1.95/2.11 tff(806,plain,
% 1.95/2.11 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s1)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s1)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s1))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(807,plain,
% 1.95/2.11 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s1)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s1))),
% 1.95/2.11 inference(quant_inst,[status(thm)],[])).
% 1.95/2.11 tff(808,plain,
% 1.95/2.11 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s1)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s1)),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[807, 806])).
% 1.95/2.11 tff(809,plain,
% 1.95/2.11 (~node20(c_e_h_1, c_r, s1)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[808, 55, 805])).
% 1.95/2.11 tff(810,assumption,(~node20(c_e_h_1, c_r, s1)), introduced(assumption)).
% 1.95/2.11 tff(811,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s2)), introduced(assumption)).
% 1.95/2.11 tff(812,plain,
% 1.95/2.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~node21(c_e_h_1, c_r, s1, s2)) | node20(c_e_h_1, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_1, c_r, s1, s2)) | node20(c_e_h_1, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(813,plain,
% 1.95/2.11 ((node20(c_e_h_1, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node21(c_e_h_1, c_r, s1, s2))) <=> ((~node21(c_e_h_1, c_r, s1, s2)) | node20(c_e_h_1, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(814,plain,
% 1.95/2.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node21(c_e_h_1, c_r, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~node21(c_e_h_1, c_r, s1, s2)) | node20(c_e_h_1, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2))))),
% 1.95/2.11 inference(monotonicity,[status(thm)],[813])).
% 1.95/2.11 tff(815,plain,
% 1.95/2.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node21(c_e_h_1, c_r, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_1, c_r, s1, s2)) | node20(c_e_h_1, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)))),
% 1.95/2.11 inference(transitivity,[status(thm)],[814, 812])).
% 1.95/2.11 tff(816,plain,
% 1.95/2.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node21(c_e_h_1, c_r, s1, s2)))),
% 1.95/2.11 inference(quant_inst,[status(thm)],[])).
% 1.95/2.11 tff(817,plain,
% 1.95/2.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_1, c_r, s1, s2)) | node20(c_e_h_1, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2))),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[816, 815])).
% 1.95/2.11 tff(818,plain,
% 1.95/2.11 ((~node21(c_e_h_1, c_r, s1, s2)) | node20(c_e_h_1, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[817, 69])).
% 1.95/2.11 tff(819,plain,
% 1.95/2.11 (~node21(c_e_h_1, c_r, s1, s2)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[818, 811, 810])).
% 1.95/2.11 tff(820,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s1)), introduced(assumption)).
% 1.95/2.11 tff(821,plain,
% 1.95/2.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, 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))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(822,plain,
% 1.95/2.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node22(c_e_h_1, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1))),
% 1.95/2.11 inference(quant_inst,[status(thm)],[])).
% 1.95/2.11 tff(823,plain,
% 1.95/2.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node22(c_e_h_1, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1)),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[822, 821])).
% 1.95/2.11 tff(824,plain,
% 1.95/2.11 ((~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)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[823, 126])).
% 1.95/2.11 tff(825,plain,
% 1.95/2.12 (~node22(c_e_h_1, c_r, s1, s2)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[824, 811, 820])).
% 1.95/2.12 tff(826,plain,
% 1.95/2.12 (((~![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))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(827,plain,
% 1.95/2.12 ((~![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))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(828,plain,
% 1.95/2.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_r, s1, s2) | node22(c_e_h_1, c_r, s1, s2)),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[827, 826])).
% 1.95/2.12 tff(829,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[828, 101, 257, 825, 819])).
% 1.95/2.12 tff(830,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1) | node20(c_e_h_1, c_r, s1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(831,plain,
% 1.95/2.12 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[830, 809])).
% 1.95/2.12 tff(832,plain,
% 1.95/2.12 (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[831, 801])).
% 1.95/2.12 tff(833,plain,
% 1.95/2.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, 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))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(834,plain,
% 1.95/2.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node22(c_e_h_1, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(835,plain,
% 1.95/2.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node22(c_e_h_1, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2)),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[834, 833])).
% 1.95/2.12 tff(836,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[835, 126, 599, 832, 774])).
% 1.95/2.12 tff(837,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(838,plain,
% 1.95/2.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, 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))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(839,plain,
% 1.95/2.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node22(c_e_h_1, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(840,plain,
% 1.95/2.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node22(c_e_h_1, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3)),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[839, 838])).
% 1.95/2.12 tff(841,plain,
% 1.95/2.12 ((~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)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[840, 126])).
% 1.95/2.12 tff(842,plain,
% 1.95/2.12 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node22(c_e_h_1, c_r, s3, s4))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[841, 837])).
% 1.95/2.12 tff(843,plain,
% 1.95/2.12 (~node22(c_e_h_1, c_r, s3, s4)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[842, 598])).
% 1.95/2.12 tff(844,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)), introduced(assumption)).
% 1.95/2.12 tff(845,assumption,(node11(c_e_h_1, c_n, s1, s2)), introduced(assumption)).
% 1.95/2.12 tff(846,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)), introduced(assumption)).
% 1.95/2.12 tff(847,plain,
% 1.95/2.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_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)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(848,plain,
% 1.95/2.12 ((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)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(849,plain,
% 1.95/2.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_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))))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[848])).
% 1.95/2.12 tff(850,plain,
% 1.95/2.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_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)))),
% 1.95/2.12 inference(transitivity,[status(thm)],[849, 847])).
% 1.95/2.12 tff(851,plain,
% 1.95/2.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_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)))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(852,plain,
% 1.95/2.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~node11(c_e_h_1, c_n, s1, s2))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[851, 850])).
% 1.95/2.12 tff(853,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[852, 629, 846, 844, 845])).
% 1.95/2.12 tff(854,plain,((~node11(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(855,plain,
% 1.95/2.12 ((~node11(c_e_h_1, c_n, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[854, 695])).
% 1.95/2.12 tff(856,plain,
% 1.95/2.12 (~node11(c_e_h_1, c_n, s1, s2)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[855, 844])).
% 1.95/2.12 tff(857,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s1)), introduced(assumption)).
% 1.95/2.12 tff(858,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s0)), introduced(assumption)).
% 1.95/2.12 tff(859,assumption,(~node16(c_e_h_1, c_e, s0)), introduced(assumption)).
% 1.95/2.12 tff(860,assumption,(node15(c_e_h_1, c_e, s0, s1)), introduced(assumption)).
% 1.95/2.12 tff(861,plain,
% 1.95/2.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, 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))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(862,plain,
% 1.95/2.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node15(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(863,plain,
% 1.95/2.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node15(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0)),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[862, 861])).
% 1.95/2.12 tff(864,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[863, 292, 646, 860, 857])).
% 1.95/2.12 tff(865,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,[]))).
% 1.95/2.12 tff(866,plain,
% 1.95/2.12 (~node15(c_e_h_1, c_e, s0, s1)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[865, 857])).
% 1.95/2.12 tff(867,plain,
% 1.95/2.12 (((~![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))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(868,plain,
% 1.95/2.12 ((~![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))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(869,plain,
% 1.95/2.12 ((~![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)),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[868, 867])).
% 1.95/2.12 tff(870,plain,
% 1.95/2.12 (node19(c_e_h_1, c_e, s0, s1)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[869, 323, 91])).
% 1.95/2.12 tff(871,plain,
% 1.95/2.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (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)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(872,plain,
% 1.95/2.12 ((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)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(873,plain,
% 1.95/2.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, 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))))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[872])).
% 1.95/2.12 tff(874,plain,
% 1.95/2.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, 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)))),
% 1.95/2.12 inference(transitivity,[status(thm)],[873, 871])).
% 1.95/2.12 tff(875,plain,
% 1.95/2.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, 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)))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(876,plain,
% 1.95/2.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | 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))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[875, 874])).
% 1.95/2.12 tff(877,plain,
% 1.95/2.12 (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)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[876, 422, 870])).
% 1.95/2.12 tff(878,plain,
% 1.95/2.12 (node14(c_e_h_1, c_e, s0, s1)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[877, 866, 859])).
% 1.95/2.12 tff(879,plain,
% 1.95/2.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node14(c_e_h_1, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node14(c_e_h_1, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(880,plain,
% 1.95/2.12 (((~node14(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1))) <=> (m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node14(c_e_h_1, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(881,plain,
% 1.95/2.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node14(c_e_h_1, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1))))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[880])).
% 1.95/2.12 tff(882,plain,
% 1.95/2.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node14(c_e_h_1, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)))),
% 1.95/2.12 inference(transitivity,[status(thm)],[881, 879])).
% 1.95/2.12 tff(883,plain,
% 1.95/2.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, 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)))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(884,plain,
% 1.95/2.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node14(c_e_h_1, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[883, 882])).
% 1.95/2.12 tff(885,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[884, 404, 878, 858, 857])).
% 1.95/2.12 tff(886,plain,((~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) | node16(c_e_h_1, c_e, s0)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(887,plain,
% 1.95/2.12 (node16(c_e_h_1, c_e, s0)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[886, 858, 857])).
% 1.95/2.12 tff(888,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s0)), introduced(assumption)).
% 1.95/2.12 tff(889,plain,
% 1.95/2.12 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s0))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(890,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[889, 113, 888])).
% 1.95/2.12 tff(891,plain,(~m_and_h_gate_v_out(c_e_h_1, c_i, s0)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(892,plain,
% 1.95/2.12 (((~![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))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(893,plain,
% 1.95/2.12 ((~![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))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(894,plain,
% 1.95/2.12 ((~![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)),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[893, 892])).
% 1.95/2.12 tff(895,plain,
% 1.95/2.12 (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[894, 357, 891])).
% 1.95/2.12 tff(896,plain,
% 1.95/2.12 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, 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))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(897,plain,
% 1.95/2.12 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, 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))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(898,plain,
% 1.95/2.12 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | m_c_h_element_v_in2(c_e_h_1, c_e, s0)),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[897, 896])).
% 1.95/2.12 tff(899,plain,
% 1.95/2.12 ((~node16(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[898, 389, 895])).
% 1.95/2.12 tff(900,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[899, 887, 858])).
% 1.95/2.12 tff(901,plain,(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))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(902,plain,
% 1.95/2.12 (m_c_h_element_v_in1(c_e_h_1, c_e, s0)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[901, 857])).
% 1.95/2.12 tff(903,plain,
% 1.95/2.12 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s0)) | m_c_h_element_v_in2(c_e_h_1, c_e, s0) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_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, s0)) | m_c_h_element_v_in2(c_e_h_1, c_e, s0) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s0)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(904,plain,
% 1.95/2.12 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s0)) | m_c_h_element_v_in2(c_e_h_1, c_e, s0) | (~node17(c_e_h_1, c_e, s0))) <=> ((~node17(c_e_h_1, c_e, s0)) | m_c_h_element_v_in2(c_e_h_1, c_e, s0) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s0)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(905,plain,
% 1.95/2.12 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s0)) | m_c_h_element_v_in2(c_e_h_1, c_e, s0) | (~node17(c_e_h_1, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s0)) | m_c_h_element_v_in2(c_e_h_1, c_e, s0) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s0))))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[904])).
% 1.95/2.12 tff(906,plain,
% 1.95/2.12 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s0)) | m_c_h_element_v_in2(c_e_h_1, c_e, s0) | (~node17(c_e_h_1, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s0)) | m_c_h_element_v_in2(c_e_h_1, c_e, s0) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s0)))),
% 1.95/2.12 inference(transitivity,[status(thm)],[905, 903])).
% 1.95/2.12 tff(907,plain,
% 1.95/2.12 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s0)) | m_c_h_element_v_in2(c_e_h_1, c_e, s0) | (~node17(c_e_h_1, c_e, s0)))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(908,plain,
% 1.95/2.12 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s0)) | m_c_h_element_v_in2(c_e_h_1, c_e, s0) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s0))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[907, 906])).
% 1.95/2.12 tff(909,plain,
% 1.95/2.12 ((~node17(c_e_h_1, c_e, s0)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s0))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[908, 371, 895])).
% 1.95/2.12 tff(910,plain,
% 1.95/2.12 (~node17(c_e_h_1, c_e, s0)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[909, 902])).
% 1.95/2.12 tff(911,plain,
% 1.95/2.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s0) | node18(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s0) | node18(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(912,plain,
% 1.95/2.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s0) | node18(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(913,plain,
% 1.95/2.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s0) | node18(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[912, 911])).
% 1.95/2.12 tff(914,plain,
% 1.95/2.12 (node17(c_e_h_1, c_e, s0) | node18(c_e_h_1, c_e, s0, s1)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[913, 338, 870])).
% 1.95/2.12 tff(915,plain,
% 1.95/2.12 (node18(c_e_h_1, c_e, s0, s1)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[914, 910])).
% 1.95/2.12 tff(916,plain,
% 1.95/2.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_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, s0) | (~node18(c_e_h_1, c_e, s0, s1)) | (~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)) | m_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, s0) | (~node18(c_e_h_1, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(917,plain,
% 1.95/2.13 (((~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~node18(c_e_h_1, c_e, s0, s1))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~node18(c_e_h_1, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(918,plain,
% 1.95/2.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~node18(c_e_h_1, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~node18(c_e_h_1, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[917])).
% 1.95/2.13 tff(919,plain,
% 1.95/2.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~node18(c_e_h_1, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~node18(c_e_h_1, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)))),
% 1.95/2.13 inference(transitivity,[status(thm)],[918, 916])).
% 1.95/2.13 tff(920,plain,
% 1.95/2.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~node18(c_e_h_1, c_e, s0, s1)))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(921,plain,
% 1.95/2.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~node18(c_e_h_1, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[920, 919])).
% 1.95/2.13 tff(922,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[921, 307, 646, 915, 857])).
% 1.95/2.13 tff(923,plain,(~m_c_h_element_v_out(c_e_h_1, c_e, s1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(924,plain,
% 1.95/2.13 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_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))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(925,plain,
% 1.95/2.13 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1) | m_c_h_element_v_out(c_e_h_1, c_e, s1))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(926,plain,
% 1.95/2.13 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1) | m_c_h_element_v_out(c_e_h_1, c_e, s1)),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[925, 924])).
% 1.95/2.13 tff(927,plain,
% 1.95/2.13 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[926, 653, 923])).
% 1.95/2.13 tff(928,plain,
% 1.95/2.13 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, 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))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(929,plain,
% 1.95/2.13 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(930,plain,
% 1.95/2.13 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[929, 928])).
% 1.95/2.13 tff(931,plain,
% 1.95/2.13 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[930, 673, 734])).
% 1.95/2.13 tff(932,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)), introduced(assumption)).
% 1.95/2.13 tff(933,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)), introduced(assumption)).
% 1.95/2.13 tff(934,assumption,(node10(c_e_h_1, c_n, s1, s2)), introduced(assumption)).
% 1.95/2.13 tff(935,plain,
% 1.95/2.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~node10(c_e_h_1, c_n, s1, s2)) | (~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) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(936,plain,
% 1.95/2.13 (((~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(937,plain,
% 1.95/2.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[936])).
% 1.95/2.13 tff(938,plain,
% 1.95/2.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)))),
% 1.95/2.13 inference(transitivity,[status(thm)],[937, 935])).
% 1.95/2.13 tff(939,plain,
% 1.95/2.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, 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))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(940,plain,
% 1.95/2.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[939, 938])).
% 1.95/2.13 tff(941,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[940, 687, 844, 934, 933, 932])).
% 1.95/2.13 tff(942,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_in1(c_e_h_1, c_n, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(943,plain,
% 1.95/2.13 (~node10(c_e_h_1, c_n, s1, s2)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[942, 844, 931, 927])).
% 1.95/2.13 tff(944,plain,
% 1.95/2.13 (((~![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))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(945,plain,
% 1.95/2.13 ((~![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))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(946,plain,
% 1.95/2.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_1, c_n, s1, s2) | node11(c_e_h_1, c_n, s1, s2)),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[945, 944])).
% 1.95/2.13 tff(947,plain,
% 1.95/2.13 (node10(c_e_h_1, c_n, s1, s2) | node11(c_e_h_1, c_n, s1, s2)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[946, 212, 257])).
% 1.95/2.13 tff(948,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[947, 943, 856])).
% 1.95/2.13 tff(949,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(950,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2)), introduced(assumption)).
% 1.95/2.13 tff(951,plain,
% 1.95/2.13 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, 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)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(952,plain,
% 1.95/2.13 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(953,plain,
% 1.95/2.13 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[952, 951])).
% 1.95/2.13 tff(954,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[953, 168, 950, 949])).
% 1.95/2.13 tff(955,plain,(~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(956,plain,
% 1.95/2.13 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, 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))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(957,plain,
% 1.95/2.13 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(958,plain,
% 1.95/2.13 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2)),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[957, 956])).
% 1.95/2.13 tff(959,plain,
% 1.95/2.13 (~node9(c_e_h_1, c_m, s2)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[958, 182, 955])).
% 1.95/2.13 tff(960,assumption,(~node9(c_e_h_1, c_m, s2)), introduced(assumption)).
% 1.95/2.13 tff(961,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)), introduced(assumption)).
% 1.95/2.13 tff(962,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)), introduced(assumption)).
% 1.95/2.13 tff(963,assumption,(node11(c_e_h_1, c_m, s2, s3)), introduced(assumption)).
% 1.95/2.13 tff(964,plain,
% 1.95/2.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, 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))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(965,plain,
% 1.95/2.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, 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))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(966,plain,
% 1.95/2.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node11(c_e_h_1, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[965, 964])).
% 1.95/2.13 tff(967,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[966, 227, 961, 962, 963])).
% 1.95/2.13 tff(968,plain,((~node11(c_e_h_1, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(969,plain,
% 1.95/2.13 (~node11(c_e_h_1, c_m, s2, s3)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[968, 962, 961])).
% 1.95/2.13 tff(970,plain,
% 1.95/2.13 (((~![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))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(971,plain,
% 1.95/2.13 ((~![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))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(972,plain,
% 1.95/2.13 ((~![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)),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[971, 970])).
% 1.95/2.13 tff(973,plain,
% 1.95/2.13 (node10(c_e_h_1, c_m, s2, s3) | node11(c_e_h_1, c_m, s2, s3)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[972, 212, 569])).
% 1.95/2.13 tff(974,plain,
% 1.95/2.13 (node10(c_e_h_1, c_m, s2, s3)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[973, 969])).
% 1.95/2.13 tff(975,plain,
% 1.95/2.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node10(c_e_h_1, c_m, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node10(c_e_h_1, c_m, s2, s3)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(976,plain,
% 1.95/2.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, 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)))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(977,plain,
% 1.95/2.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node10(c_e_h_1, c_m, s2, s3))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[976, 975])).
% 1.95/2.13 tff(978,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[977, 196, 962, 974, 960])).
% 1.95/2.13 tff(979,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | node9(c_e_h_1, c_m, s2) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(980,plain,
% 1.95/2.13 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | node9(c_e_h_1, c_m, s2)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[979, 753])).
% 1.95/2.13 tff(981,plain,
% 1.95/2.13 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[980, 959])).
% 1.95/2.13 tff(982,plain,
% 1.95/2.13 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, 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))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(983,plain,
% 1.95/2.13 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(984,plain,
% 1.95/2.13 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[983, 982])).
% 1.95/2.13 tff(985,plain,
% 1.95/2.13 ((~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)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[984, 41])).
% 1.95/2.13 tff(986,plain,
% 1.95/2.13 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s3)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[985, 981])).
% 1.95/2.13 tff(987,plain,
% 1.95/2.13 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, 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))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(988,plain,
% 1.95/2.13 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s3)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s3))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(989,plain,
% 1.95/2.13 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s3)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s3)),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[988, 987])).
% 1.95/2.13 tff(990,plain,
% 1.95/2.13 (~node20(c_e_h_1, c_r, s3)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[989, 55, 986])).
% 1.95/2.13 tff(991,plain,
% 1.95/2.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node21(c_e_h_1, c_r, s3, s4)) | node20(c_e_h_1, c_r, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node21(c_e_h_1, c_r, s3, s4)) | node20(c_e_h_1, c_r, s3))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(992,plain,
% 1.95/2.13 ((node20(c_e_h_1, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node21(c_e_h_1, c_r, s3, s4))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node21(c_e_h_1, c_r, s3, s4)) | node20(c_e_h_1, c_r, s3))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(993,plain,
% 1.95/2.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node21(c_e_h_1, c_r, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node21(c_e_h_1, c_r, s3, s4)) | node20(c_e_h_1, c_r, s3)))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[992])).
% 1.95/2.13 tff(994,plain,
% 1.95/2.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node21(c_e_h_1, c_r, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node21(c_e_h_1, c_r, s3, s4)) | node20(c_e_h_1, c_r, s3))),
% 1.95/2.13 inference(transitivity,[status(thm)],[993, 991])).
% 1.95/2.13 tff(995,plain,
% 1.95/2.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node21(c_e_h_1, c_r, s3, s4)))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(996,plain,
% 1.95/2.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node21(c_e_h_1, c_r, s3, s4)) | node20(c_e_h_1, c_r, s3)),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[995, 994])).
% 1.95/2.13 tff(997,plain,
% 1.95/2.13 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node21(c_e_h_1, c_r, s3, s4)) | node20(c_e_h_1, c_r, s3)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[996, 69])).
% 1.95/2.13 tff(998,plain,
% 1.95/2.13 (~node21(c_e_h_1, c_r, s3, s4)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[997, 598, 990])).
% 1.95/2.13 tff(999,plain,
% 1.95/2.13 (succ(s3, s4) <=> succ(s3, s4)),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(1000,axiom,(succ(s3, s4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound4')).
% 1.95/2.13 tff(1001,plain,
% 1.95/2.13 (succ(s3, s4)),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[1000, 999])).
% 1.95/2.13 tff(1002,plain,
% 1.95/2.13 (((~![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))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(1003,plain,
% 1.95/2.13 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s3, s4)) | trans(s3, s4))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(1004,plain,
% 1.95/2.13 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s3, s4)) | trans(s3, s4)),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[1003, 1002])).
% 1.95/2.13 tff(1005,plain,
% 1.95/2.13 (trans(s3, s4)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1004, 1001, 84])).
% 1.95/2.13 tff(1006,plain,
% 1.95/2.13 (((~![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))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(1007,plain,
% 1.95/2.13 ((~![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))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(1008,plain,
% 1.95/2.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_r, s3, s4) | node22(c_e_h_1, c_r, s3, s4)),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 1.95/2.13 tff(1009,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1008, 101, 1005, 998, 843])).
% 1.95/2.13 tff(1010,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s4)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(1011,plain,
% 1.95/2.13 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, 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))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(1012,plain,
% 1.95/2.13 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(1013,plain,
% 1.95/2.13 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4)),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[1012, 1011])).
% 1.95/2.13 tff(1014,plain,
% 1.95/2.13 ((~m_user_v_ack(c_e_h_1, c_u, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1013, 582])).
% 1.95/2.13 tff(1015,plain,
% 1.95/2.13 (~m_user_v_ack(c_e_h_1, c_u, s4)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1014, 1010])).
% 1.95/2.13 tff(1016,plain,
% 1.95/2.13 (^[X: $i] : refl((m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X))) <=> (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X))))),
% 1.95/2.13 inference(bind,[status(th)],[])).
% 1.95/2.13 tff(1017,plain,
% 1.95/2.13 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X))) <=> ![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))),
% 1.95/2.13 inference(quant_intro,[status(thm)],[1016])).
% 1.95/2.13 tff(1018,plain,
% 1.95/2.13 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X))) <=> ![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(1019,axiom,(![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty3')).
% 1.95/2.13 tff(1020,plain,
% 1.95/2.13 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[1019, 1018])).
% 1.95/2.13 tff(1021,plain,(
% 1.95/2.13 ![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))),
% 1.95/2.13 inference(skolemize,[status(sab)],[1020])).
% 1.95/2.13 tff(1022,plain,
% 1.95/2.13 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[1021, 1017])).
% 1.95/2.13 tff(1023,plain,
% 1.95/2.13 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s4) | (~node24(s4)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s4) | (~node24(s4)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(1024,plain,
% 1.95/2.13 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s4) | (~node24(s4)))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(1025,plain,
% 1.95/2.13 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s4) | (~node24(s4))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[1024, 1023])).
% 1.95/2.13 tff(1026,plain,
% 1.95/2.13 (~node24(s4)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1025, 1022, 1015])).
% 1.95/2.13 tff(1027,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)), introduced(assumption)).
% 1.95/2.13 tff(1028,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)), introduced(assumption)).
% 1.95/2.13 tff(1029,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)), introduced(assumption)).
% 1.95/2.13 tff(1030,plain,
% 1.95/2.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)) | (~node11(c_e_h_2, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)) | (~node11(c_e_h_2, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1031,plain,
% 1.95/2.14 ((m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)) | (~node11(c_e_h_2, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1032,plain,
% 1.95/2.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)) | (~node11(c_e_h_2, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[1031])).
% 1.95/2.14 tff(1033,plain,
% 1.95/2.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)) | (~node11(c_e_h_2, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1))),
% 1.95/2.14 inference(transitivity,[status(thm)],[1032, 1030])).
% 1.95/2.14 tff(1034,plain,
% 1.95/2.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1035,plain,
% 1.95/2.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)) | (~node11(c_e_h_2, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1034, 1033])).
% 1.95/2.14 tff(1036,plain,
% 1.95/2.14 ((~node11(c_e_h_2, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1035, 629, 161])).
% 1.95/2.14 tff(1037,plain,
% 1.95/2.14 (~node11(c_e_h_2, c_n, s0, s1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1036, 1029])).
% 1.95/2.14 tff(1038,plain,
% 1.95/2.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_2, c_n, s0, s1) | node11(c_e_h_2, c_n, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_2, c_n, s0, s1) | node11(c_e_h_2, c_n, s0, s1))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1039,plain,
% 1.95/2.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_2, c_n, s0, s1) | node11(c_e_h_2, c_n, s0, s1))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1040,plain,
% 1.95/2.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_2, c_n, s0, s1) | node11(c_e_h_2, c_n, s0, s1)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1039, 1038])).
% 1.95/2.14 tff(1041,plain,
% 1.95/2.14 (node10(c_e_h_2, c_n, s0, s1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1040, 212, 91, 1037])).
% 1.95/2.14 tff(1042,plain,
% 1.95/2.14 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0) | m_c_h_element_v_out(c_e_h_2, c_e, s0))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0) | m_c_h_element_v_out(c_e_h_2, c_e, s0))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1043,plain,
% 1.95/2.14 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0) | m_c_h_element_v_out(c_e_h_2, c_e, s0))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1044,plain,
% 1.95/2.14 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0) | m_c_h_element_v_out(c_e_h_2, c_e, s0)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1043, 1042])).
% 1.95/2.14 tff(1045,plain,
% 1.95/2.14 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1044, 653, 282])).
% 1.95/2.14 tff(1046,plain,
% 1.95/2.14 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1047,plain,
% 1.95/2.14 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1048,plain,
% 1.95/2.14 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1047, 1046])).
% 1.95/2.14 tff(1049,plain,
% 1.95/2.14 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1048, 673, 34])).
% 1.95/2.14 tff(1050,plain,
% 1.95/2.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1051,plain,
% 1.95/2.14 (((~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1052,plain,
% 1.95/2.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[1051])).
% 1.95/2.14 tff(1053,plain,
% 1.95/2.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)))),
% 1.95/2.14 inference(transitivity,[status(thm)],[1052, 1050])).
% 1.95/2.14 tff(1054,plain,
% 1.95/2.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1055,plain,
% 1.95/2.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1054, 1053])).
% 1.95/2.14 tff(1056,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1055, 687, 1049, 1029, 1045, 1041])).
% 1.95/2.14 tff(1057,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(1058,plain,
% 1.95/2.14 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1059,plain,
% 1.95/2.14 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1060,plain,
% 1.95/2.14 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1059, 1058])).
% 1.95/2.14 tff(1061,plain,
% 1.95/2.14 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1060, 168, 1057])).
% 1.95/2.14 tff(1062,plain,
% 1.95/2.14 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1063,plain,
% 1.95/2.14 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1064,plain,
% 1.95/2.14 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1063, 1062])).
% 1.95/2.14 tff(1065,plain,
% 1.95/2.14 (~node9(c_e_h_2, c_m, s1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1064, 182, 1061])).
% 1.95/2.14 tff(1066,assumption,(node10(c_e_h_2, c_m, s1, s2)), introduced(assumption)).
% 1.95/2.14 tff(1067,plain,
% 1.95/2.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | node9(c_e_h_2, c_m, s1) | (~node10(c_e_h_2, c_m, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | node9(c_e_h_2, c_m, s1) | (~node10(c_e_h_2, c_m, s1, s2)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1068,plain,
% 1.95/2.14 ((node9(c_e_h_2, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node10(c_e_h_2, c_m, s1, s2))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | node9(c_e_h_2, c_m, s1) | (~node10(c_e_h_2, c_m, s1, s2)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1069,plain,
% 1.95/2.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node10(c_e_h_2, c_m, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | node9(c_e_h_2, c_m, s1) | (~node10(c_e_h_2, c_m, s1, s2))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[1068])).
% 1.95/2.14 tff(1070,plain,
% 1.95/2.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node10(c_e_h_2, c_m, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | node9(c_e_h_2, c_m, s1) | (~node10(c_e_h_2, c_m, s1, s2)))),
% 1.95/2.14 inference(transitivity,[status(thm)],[1069, 1067])).
% 1.95/2.14 tff(1071,plain,
% 1.95/2.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node10(c_e_h_2, c_m, s1, s2)))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1072,plain,
% 1.95/2.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | node9(c_e_h_2, c_m, s1) | (~node10(c_e_h_2, c_m, s1, s2))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1071, 1070])).
% 1.95/2.14 tff(1073,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1072, 196, 1028, 1066, 1065])).
% 1.95/2.14 tff(1074,plain,((~node10(c_e_h_2, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(1075,plain,
% 1.95/2.14 (~node10(c_e_h_2, c_m, s1, s2)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1074, 1028])).
% 1.95/2.14 tff(1076,assumption,(node11(c_e_h_2, c_m, s1, s2)), introduced(assumption)).
% 1.95/2.14 tff(1077,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)), introduced(assumption)).
% 1.95/2.14 tff(1078,plain,
% 1.95/2.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node11(c_e_h_2, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node11(c_e_h_2, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1079,plain,
% 1.95/2.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node11(c_e_h_2, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1080,plain,
% 1.95/2.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node11(c_e_h_2, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1079, 1078])).
% 1.95/2.14 tff(1081,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1080, 227, 1028, 1077, 1076])).
% 1.95/2.14 tff(1082,plain,((~node11(c_e_h_2, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(1083,plain,
% 1.95/2.14 ((~node11(c_e_h_2, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1082, 232])).
% 1.95/2.14 tff(1084,plain,
% 1.95/2.14 (~node11(c_e_h_2, c_m, s1, s2)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1083, 1028])).
% 1.95/2.14 tff(1085,plain,
% 1.95/2.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_2, c_m, s1, s2) | node11(c_e_h_2, c_m, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_2, c_m, s1, s2) | node11(c_e_h_2, c_m, s1, s2))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1086,plain,
% 1.95/2.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_2, c_m, s1, s2) | node11(c_e_h_2, c_m, s1, s2))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1087,plain,
% 1.95/2.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_2, c_m, s1, s2) | node11(c_e_h_2, c_m, s1, s2)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1086, 1085])).
% 1.95/2.14 tff(1088,plain,
% 1.95/2.14 (node10(c_e_h_2, c_m, s1, s2) | node11(c_e_h_2, c_m, s1, s2)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1087, 212, 257])).
% 1.95/2.14 tff(1089,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1088, 1084, 1075])).
% 1.95/2.14 tff(1090,plain,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(1091,plain,
% 1.95/2.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node11(c_e_h_2, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node11(c_e_h_2, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1092,plain,
% 1.95/2.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node11(c_e_h_2, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1093,plain,
% 1.95/2.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node11(c_e_h_2, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1092, 1091])).
% 1.95/2.14 tff(1094,plain,
% 1.95/2.14 ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node11(c_e_h_2, c_m, s2, s3))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1093, 227, 1090])).
% 1.95/2.14 tff(1095,plain,
% 1.95/2.14 (~node11(c_e_h_2, c_m, s2, s3)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1094, 1027])).
% 1.95/2.14 tff(1096,plain,
% 1.95/2.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_2, c_m, s2, s3) | node11(c_e_h_2, c_m, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_2, c_m, s2, s3) | node11(c_e_h_2, c_m, s2, s3))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1097,plain,
% 1.95/2.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_2, c_m, s2, s3) | node11(c_e_h_2, c_m, s2, s3))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1098,plain,
% 1.95/2.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_2, c_m, s2, s3) | node11(c_e_h_2, c_m, s2, s3)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1097, 1096])).
% 1.95/2.14 tff(1099,plain,
% 1.95/2.14 (node10(c_e_h_2, c_m, s2, s3)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1098, 212, 569, 1095])).
% 1.95/2.14 tff(1100,plain,
% 1.95/2.14 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1) | m_c_h_element_v_out(c_e_h_2, c_e, s1))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1) | m_c_h_element_v_out(c_e_h_2, c_e, s1))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1101,plain,
% 1.95/2.14 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1) | m_c_h_element_v_out(c_e_h_2, c_e, s1))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1102,plain,
% 1.95/2.14 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1) | m_c_h_element_v_out(c_e_h_2, c_e, s1)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1101, 1100])).
% 1.95/2.14 tff(1103,plain,
% 1.95/2.14 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1102, 653, 431])).
% 1.95/2.14 tff(1104,plain,
% 1.95/2.14 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1105,plain,
% 1.95/2.14 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1106,plain,
% 1.95/2.14 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1105, 1104])).
% 1.95/2.14 tff(1107,plain,
% 1.95/2.14 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1106, 673, 232])).
% 1.95/2.14 tff(1108,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)), introduced(assumption)).
% 1.95/2.14 tff(1109,assumption,(node11(c_e_h_2, c_n, s1, s2)), introduced(assumption)).
% 1.95/2.14 tff(1110,plain,
% 1.95/2.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)) | (~node11(c_e_h_2, c_n, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)) | (~node11(c_e_h_2, c_n, s1, s2)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1111,plain,
% 1.95/2.14 ((m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~node11(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1))) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)) | (~node11(c_e_h_2, c_n, s1, s2)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1112,plain,
% 1.95/2.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~node11(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)) | (~node11(c_e_h_2, c_n, s1, s2))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[1111])).
% 1.95/2.14 tff(1113,plain,
% 1.95/2.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~node11(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)) | (~node11(c_e_h_2, c_n, s1, s2)))),
% 1.95/2.14 inference(transitivity,[status(thm)],[1112, 1110])).
% 1.95/2.14 tff(1114,plain,
% 1.95/2.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~node11(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1115,plain,
% 1.95/2.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)) | (~node11(c_e_h_2, c_n, s1, s2))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1114, 1113])).
% 1.95/2.14 tff(1116,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1115, 629, 1108, 1057, 1109])).
% 1.95/2.14 tff(1117,plain,((~node11(c_e_h_2, c_n, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(1118,plain,
% 1.95/2.14 (~node11(c_e_h_2, c_n, s1, s2)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1117, 1108])).
% 1.95/2.14 tff(1119,plain,
% 1.95/2.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_2, c_n, s1, s2) | node11(c_e_h_2, c_n, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_2, c_n, s1, s2) | node11(c_e_h_2, c_n, s1, s2))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1120,plain,
% 1.95/2.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_2, c_n, s1, s2) | node11(c_e_h_2, c_n, s1, s2))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1121,plain,
% 1.95/2.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_2, c_n, s1, s2) | node11(c_e_h_2, c_n, s1, s2)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1120, 1119])).
% 1.95/2.14 tff(1122,plain,
% 1.95/2.14 (node10(c_e_h_2, c_n, s1, s2) | node11(c_e_h_2, c_n, s1, s2)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1121, 212, 257])).
% 1.95/2.14 tff(1123,plain,
% 1.95/2.14 (node10(c_e_h_2, c_n, s1, s2)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1122, 1118])).
% 1.95/2.14 tff(1124,plain,
% 1.95/2.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)) | (~node10(c_e_h_2, c_n, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)) | (~node10(c_e_h_2, c_n, s1, s2)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1125,plain,
% 1.95/2.15 (((~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)) | (~node10(c_e_h_2, c_n, s1, s2)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1126,plain,
% 1.95/2.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)) | (~node10(c_e_h_2, c_n, s1, s2))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[1125])).
% 1.95/2.15 tff(1127,plain,
% 1.95/2.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)) | (~node10(c_e_h_2, c_n, s1, s2)))),
% 1.95/2.15 inference(transitivity,[status(thm)],[1126, 1124])).
% 1.95/2.15 tff(1128,plain,
% 1.95/2.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(1129,plain,
% 1.95/2.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)) | (~node10(c_e_h_2, c_n, s1, s2))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1128, 1127])).
% 1.95/2.15 tff(1130,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1129, 687, 1108, 1123, 1107, 1103])).
% 1.95/2.15 tff(1131,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(1132,plain,
% 1.95/2.15 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1133,plain,
% 1.95/2.15 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(1134,plain,
% 1.95/2.15 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1133, 1132])).
% 1.95/2.15 tff(1135,plain,
% 1.95/2.15 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1134, 168, 1131])).
% 1.95/2.15 tff(1136,plain,
% 1.95/2.15 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1137,plain,
% 1.95/2.15 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(1138,plain,
% 1.95/2.15 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2)),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1137, 1136])).
% 1.95/2.15 tff(1139,plain,
% 1.95/2.15 (~node9(c_e_h_2, c_m, s2)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1138, 182, 1135])).
% 1.95/2.15 tff(1140,plain,
% 1.95/2.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | node9(c_e_h_2, c_m, s2) | (~node10(c_e_h_2, c_m, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | node9(c_e_h_2, c_m, s2) | (~node10(c_e_h_2, c_m, s2, s3)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1141,plain,
% 1.95/2.15 ((node9(c_e_h_2, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node10(c_e_h_2, c_m, s2, s3))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | node9(c_e_h_2, c_m, s2) | (~node10(c_e_h_2, c_m, s2, s3)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1142,plain,
% 1.95/2.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node10(c_e_h_2, c_m, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | node9(c_e_h_2, c_m, s2) | (~node10(c_e_h_2, c_m, s2, s3))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[1141])).
% 1.95/2.15 tff(1143,plain,
% 1.95/2.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node10(c_e_h_2, c_m, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | node9(c_e_h_2, c_m, s2) | (~node10(c_e_h_2, c_m, s2, s3)))),
% 1.95/2.15 inference(transitivity,[status(thm)],[1142, 1140])).
% 1.95/2.15 tff(1144,plain,
% 1.95/2.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node10(c_e_h_2, c_m, s2, s3)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(1145,plain,
% 1.95/2.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | node9(c_e_h_2, c_m, s2) | (~node10(c_e_h_2, c_m, s2, s3))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1144, 1143])).
% 1.95/2.15 tff(1146,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1145, 196, 1027, 1139, 1099])).
% 1.95/2.15 tff(1147,plain,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(1148,plain,
% 1.95/2.15 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1149,plain,
% 1.95/2.15 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(1150,plain,
% 1.95/2.15 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1149, 1148])).
% 1.95/2.15 tff(1151,plain,
% 1.95/2.15 ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1150, 41])).
% 1.95/2.15 tff(1152,plain,
% 1.95/2.15 (~m_and_h_gate_v_in2(c_e_h_2, c_r, s3)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1151, 1147])).
% 1.95/2.15 tff(1153,plain,
% 1.95/2.15 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s3)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s3)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s3))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1154,plain,
% 1.95/2.15 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s3)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s3))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(1155,plain,
% 1.95/2.15 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s3)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s3)),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1154, 1153])).
% 1.95/2.15 tff(1156,plain,
% 1.95/2.15 (~node20(c_e_h_2, c_r, s3)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1155, 55, 1152])).
% 1.95/2.15 tff(1157,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_r, s3)), introduced(assumption)).
% 1.95/2.15 tff(1158,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s4)), introduced(assumption)).
% 1.95/2.15 tff(1159,plain,
% 1.95/2.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | (~node22(c_e_h_2, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | (~node22(c_e_h_2, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s3))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1160,plain,
% 1.95/2.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | (~node22(c_e_h_2, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s3))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(1161,plain,
% 1.95/2.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | (~node22(c_e_h_2, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s3)),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1160, 1159])).
% 1.95/2.15 tff(1162,plain,
% 1.95/2.15 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | (~node22(c_e_h_2, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s3)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1161, 126])).
% 1.95/2.15 tff(1163,plain,
% 1.95/2.15 (~node22(c_e_h_2, c_r, s3, s4)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1162, 1158, 1157])).
% 1.95/2.15 tff(1164,assumption,(~node20(c_e_h_2, c_r, s3)), introduced(assumption)).
% 1.95/2.15 tff(1165,plain,
% 1.95/2.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | (~node21(c_e_h_2, c_r, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | (~node21(c_e_h_2, c_r, s3, s4)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1166,plain,
% 1.95/2.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | (~node21(c_e_h_2, c_r, s3, s4)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(1167,plain,
% 1.95/2.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | (~node21(c_e_h_2, c_r, s3, s4))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1166, 1165])).
% 1.95/2.15 tff(1168,plain,
% 1.95/2.15 (node20(c_e_h_2, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | (~node21(c_e_h_2, c_r, s3, s4))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1167, 69])).
% 1.95/2.15 tff(1169,plain,
% 1.95/2.15 (~node21(c_e_h_2, c_r, s3, s4)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1168, 1158, 1164])).
% 1.95/2.15 tff(1170,plain,
% 1.95/2.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_2, c_r, s3, s4) | node22(c_e_h_2, c_r, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_2, c_r, s3, s4) | node22(c_e_h_2, c_r, s3, s4))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1171,plain,
% 1.95/2.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_2, c_r, s3, s4) | node22(c_e_h_2, c_r, s3, s4))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(1172,plain,
% 1.95/2.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_2, c_r, s3, s4) | node22(c_e_h_2, c_r, s3, s4)),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1171, 1170])).
% 1.95/2.15 tff(1173,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1172, 101, 1005, 1169, 1163])).
% 1.95/2.15 tff(1174,plain,((~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | node20(c_e_h_2, c_r, s3) | m_and_h_gate_v_out(c_e_h_2, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(1175,plain,
% 1.95/2.15 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s3)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1174, 1156])).
% 1.95/2.15 tff(1176,plain,
% 1.95/2.15 (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1175, 575])).
% 1.95/2.15 tff(1177,plain,
% 1.95/2.15 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s4))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s4))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1178,plain,
% 1.95/2.15 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s4))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(1179,plain,
% 1.95/2.15 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s4)),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1178, 1177])).
% 1.95/2.15 tff(1180,plain,
% 1.95/2.15 (~m_user_v_ack(c_e_h_2, c_u, s4)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1179, 582, 1176])).
% 1.95/2.15 tff(1181,plain,
% 1.95/2.15 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | ((~node25(s4)) | m_user_v_ack(c_e_h_2, c_u, s4))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (~node25(s4)) | m_user_v_ack(c_e_h_2, c_u, s4))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1182,plain,
% 1.95/2.15 ((m_user_v_ack(c_e_h_2, c_u, s4) | (~node25(s4))) <=> ((~node25(s4)) | m_user_v_ack(c_e_h_2, c_u, s4))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1183,plain,
% 1.95/2.15 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s4) | (~node25(s4)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | ((~node25(s4)) | m_user_v_ack(c_e_h_2, c_u, s4)))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[1182])).
% 1.95/2.15 tff(1184,plain,
% 1.95/2.15 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s4) | (~node25(s4)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (~node25(s4)) | m_user_v_ack(c_e_h_2, c_u, s4))),
% 1.95/2.15 inference(transitivity,[status(thm)],[1183, 1181])).
% 1.95/2.15 tff(1185,plain,
% 1.95/2.15 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s4) | (~node25(s4)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(1186,plain,
% 1.95/2.15 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (~node25(s4)) | m_user_v_ack(c_e_h_2, c_u, s4)),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1185, 1184])).
% 1.95/2.15 tff(1187,plain,
% 1.95/2.15 (~node25(s4)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1186, 593, 1180])).
% 1.95/2.15 tff(1188,plain,
% 1.95/2.15 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s2)) | m_and_h_gate_v_out(c_e_h_2, c_r, s2))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s2)) | m_and_h_gate_v_out(c_e_h_2, c_r, s2))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1189,plain,
% 1.95/2.15 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s2)) | m_and_h_gate_v_out(c_e_h_2, c_r, s2))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(1190,plain,
% 1.95/2.15 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s2)) | m_and_h_gate_v_out(c_e_h_2, c_r, s2)),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1189, 1188])).
% 1.95/2.15 tff(1191,plain,
% 1.95/2.15 (~m_user_v_ack(c_e_h_2, c_u, s2)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1190, 582, 269])).
% 1.95/2.15 tff(1192,plain,
% 1.95/2.15 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s2) | (~node25(s2)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s2) | (~node25(s2)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1193,plain,
% 1.95/2.15 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s2) | (~node25(s2)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(1194,plain,
% 1.95/2.15 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s2) | (~node25(s2))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1193, 1192])).
% 1.95/2.15 tff(1195,plain,
% 1.95/2.15 (~node25(s2)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1194, 593, 1191])).
% 1.95/2.15 tff(1196,plain,
% 1.95/2.15 (((~![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))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1197,plain,
% 1.95/2.15 ((~![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))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(1198,plain,
% 1.95/2.15 ((~![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)),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1197, 1196])).
% 1.95/2.15 tff(1199,plain,
% 1.95/2.15 (~m_user_v_ack(c_e_h_1, c_u, s2)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1198, 582, 832])).
% 1.95/2.15 tff(1200,plain,
% 1.95/2.15 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s2) | (~node24(s2)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s2) | (~node24(s2)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1201,plain,
% 1.95/2.15 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s2) | (~node24(s2)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(1202,plain,
% 1.95/2.15 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s2) | (~node24(s2))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1201, 1200])).
% 1.95/2.15 tff(1203,plain,
% 1.95/2.15 (~node24(s2)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1202, 1022, 1199])).
% 1.95/2.15 tff(1204,plain,
% 1.95/2.15 (^[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))))),
% 1.95/2.15 inference(bind,[status(th)],[])).
% 1.95/2.15 tff(1205,plain,
% 1.95/2.15 (![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)))),
% 1.95/2.15 inference(quant_intro,[status(thm)],[1204])).
% 1.95/2.15 tff(1206,plain,
% 1.95/2.15 (![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)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1207,axiom,(![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty1')).
% 1.95/2.15 tff(1208,plain,
% 1.95/2.15 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1207, 1206])).
% 1.95/2.15 tff(1209,plain,(
% 1.95/2.15 ![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))),
% 1.95/2.15 inference(skolemize,[status(sab)],[1208])).
% 1.95/2.15 tff(1210,plain,
% 1.95/2.15 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1209, 1205])).
% 1.95/2.15 tff(1211,plain,
% 1.95/2.15 (((~![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)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1212,plain,
% 1.95/2.15 ((~![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)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(1213,plain,
% 1.95/2.15 ((~![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))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1212, 1211])).
% 1.95/2.15 tff(1214,plain,
% 1.95/2.15 (~node23(s2)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1213, 1210, 1199])).
% 1.95/2.15 tff(1215,plain,
% 1.95/2.15 (^[X: $i] : refl((node23(X) | node24(X) | node25(X) | (~node26(X))) <=> (node23(X) | node24(X) | node25(X) | (~node26(X))))),
% 1.95/2.15 inference(bind,[status(th)],[])).
% 1.95/2.15 tff(1216,plain,
% 1.95/2.15 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X))) <=> ![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 1.95/2.15 inference(quant_intro,[status(thm)],[1215])).
% 1.95/2.15 tff(1217,plain,
% 1.95/2.15 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X))) <=> ![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1218,plain,
% 1.95/2.15 (^[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)))))),
% 1.95/2.15 inference(bind,[status(th)],[])).
% 1.95/2.15 tff(1219,plain,
% 1.95/2.15 (![X: $i] : (((node23(X) | node24(X)) | node25(X)) | (~node26(X))) <=> ![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 1.95/2.15 inference(quant_intro,[status(thm)],[1218])).
% 1.95/2.15 tff(1220,axiom,(![X: $i] : (((node23(X) | node24(X)) | node25(X)) | (~node26(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty7')).
% 1.95/2.15 tff(1221,plain,
% 1.95/2.15 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1220, 1219])).
% 1.95/2.15 tff(1222,plain,
% 1.95/2.15 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1221, 1217])).
% 1.95/2.15 tff(1223,plain,(
% 1.95/2.15 ![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 1.95/2.15 inference(skolemize,[status(sab)],[1222])).
% 1.95/2.15 tff(1224,plain,
% 1.95/2.15 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1223, 1216])).
% 1.95/2.15 tff(1225,plain,
% 1.95/2.15 (((~![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)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1226,plain,
% 1.95/2.15 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s2) | node24(s2) | node25(s2) | (~node26(s2)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(1227,plain,
% 1.95/2.15 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s2) | node24(s2) | node25(s2) | (~node26(s2))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1226, 1225])).
% 1.95/2.15 tff(1228,plain,
% 1.95/2.15 (node25(s2) | (~node26(s2))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1227, 1224, 1214, 1203])).
% 1.95/2.15 tff(1229,plain,
% 1.95/2.15 (~node26(s2)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1228, 1195])).
% 1.95/2.15 tff(1230,plain,
% 1.95/2.15 (((~![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))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1231,plain,
% 1.95/2.15 ((~![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))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(1232,plain,
% 1.95/2.15 ((~![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)),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1231, 1230])).
% 1.95/2.15 tff(1233,plain,
% 1.95/2.15 ((~m_user_v_ack(c_e_h_1, c_u, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1232, 582])).
% 1.95/2.15 tff(1234,plain,
% 1.95/2.15 (~m_user_v_ack(c_e_h_1, c_u, s3)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1233, 837])).
% 1.95/2.15 tff(1235,plain,
% 1.95/2.15 (((~![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)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1236,plain,
% 1.95/2.15 ((~![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)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(1237,plain,
% 1.95/2.15 ((~![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))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1236, 1235])).
% 1.95/2.15 tff(1238,plain,
% 1.95/2.15 (~node24(s3)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1237, 1022, 1234])).
% 1.95/2.15 tff(1239,plain,
% 1.95/2.15 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1240,plain,
% 1.95/2.15 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(1241,plain,
% 1.95/2.15 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1)),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1240, 1239])).
% 1.95/2.16 tff(1242,plain,
% 1.95/2.16 (~m_user_v_ack(c_e_h_1, c_u, s1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1241, 582, 801])).
% 1.95/2.16 tff(1243,plain,
% 1.95/2.16 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s1) | (~node23(s1)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s1) | (~node23(s1)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1244,plain,
% 1.95/2.16 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s1) | (~node23(s1)))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(1245,plain,
% 1.95/2.16 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s1) | (~node23(s1))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1244, 1243])).
% 1.95/2.16 tff(1246,plain,
% 1.95/2.16 (~node23(s1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1245, 1210, 1242])).
% 1.95/2.16 tff(1247,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s1)), introduced(assumption)).
% 1.95/2.16 tff(1248,assumption,(node22(c_e_h_3, c_r, s0, s1)), introduced(assumption)).
% 1.95/2.16 tff(1249,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s0)), introduced(assumption)).
% 1.95/2.16 tff(1250,plain,
% 1.95/2.16 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s0))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(1251,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1250, 113, 1249])).
% 1.95/2.16 tff(1252,plain,(~m_and_h_gate_v_out(c_e_h_3, c_r, s0)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(1253,plain,
% 1.95/2.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_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))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1254,plain,
% 1.95/2.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_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))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(1255,plain,
% 1.95/2.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node22(c_e_h_3, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s0)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1254, 1253])).
% 1.95/2.16 tff(1256,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1255, 126, 1252, 1247, 1248])).
% 1.95/2.16 tff(1257,plain,((~node22(c_e_h_3, c_r, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(1258,plain,
% 1.95/2.16 (~node22(c_e_h_3, c_r, s0, s1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1257, 1247])).
% 1.95/2.16 tff(1259,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s0)), introduced(assumption)).
% 1.95/2.16 tff(1260,plain,
% 1.95/2.16 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s0))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(1261,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1260, 279, 1259])).
% 1.95/2.16 tff(1262,plain,(~m_c_h_element_v_out(c_e_h_3, c_e, s0)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(1263,plain,
% 1.95/2.16 (((~![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))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1264,plain,
% 1.95/2.16 ((~![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))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(1265,plain,
% 1.95/2.16 ((~![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)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1264, 1263])).
% 1.95/2.16 tff(1266,plain,
% 1.95/2.16 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s0)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1265, 539, 1262])).
% 1.95/2.16 tff(1267,plain,
% 1.95/2.16 (((~![I0: $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))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1268,plain,
% 1.95/2.16 ((~![I0: $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))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(1269,plain,
% 1.95/2.16 ((~![I0: $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)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1268, 1267])).
% 1.95/2.16 tff(1270,plain,
% 1.95/2.16 (~node20(c_e_h_3, c_r, s0)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1269, 481, 1266])).
% 1.95/2.16 tff(1271,assumption,(node21(c_e_h_3, c_r, s0, s1)), introduced(assumption)).
% 1.95/2.16 tff(1272,assumption,(~node20(c_e_h_3, c_r, s0)), introduced(assumption)).
% 1.95/2.16 tff(1273,plain,
% 1.95/2.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_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)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1274,plain,
% 1.95/2.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_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)))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(1275,plain,
% 1.95/2.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node21(c_e_h_3, c_r, s0, s1))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1274, 1273])).
% 1.95/2.16 tff(1276,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1275, 69, 1247, 1272, 1271])).
% 1.95/2.16 tff(1277,plain,((~node21(c_e_h_3, c_r, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | node20(c_e_h_3, c_r, s0)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(1278,plain,
% 1.95/2.16 ((~node21(c_e_h_3, c_r, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1277, 1270])).
% 1.95/2.16 tff(1279,plain,
% 1.95/2.16 (~node21(c_e_h_3, c_r, s0, s1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1278, 1247])).
% 1.95/2.16 tff(1280,plain,
% 1.95/2.16 (((~![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))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1281,plain,
% 1.95/2.16 ((~![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))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(1282,plain,
% 1.95/2.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_r, s0, s1) | node22(c_e_h_3, c_r, s0, s1)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1281, 1280])).
% 1.95/2.16 tff(1283,plain,
% 1.95/2.16 (node21(c_e_h_3, c_r, s0, s1) | node22(c_e_h_3, c_r, s0, s1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1282, 101, 91])).
% 1.95/2.16 tff(1284,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1283, 1279, 1258])).
% 1.95/2.16 tff(1285,plain,(~m_and_h_gate_v_out(c_e_h_3, c_r, s1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(1286,plain,
% 1.95/2.16 (((~![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))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1287,plain,
% 1.95/2.16 ((~![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))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(1288,plain,
% 1.95/2.16 ((~![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)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1287, 1286])).
% 1.95/2.16 tff(1289,plain,
% 1.95/2.16 ((~m_user_v_ack(c_e_h_3, c_u, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1288, 582])).
% 1.95/2.16 tff(1290,plain,
% 1.95/2.16 (~m_user_v_ack(c_e_h_3, c_u, s1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1289, 1285])).
% 1.95/2.16 tff(1291,plain,
% 1.95/2.16 (^[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))))),
% 1.95/2.16 inference(bind,[status(th)],[])).
% 1.95/2.16 tff(1292,plain,
% 1.95/2.16 (![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)))),
% 1.95/2.16 inference(quant_intro,[status(thm)],[1291])).
% 1.95/2.16 tff(1293,plain,
% 1.95/2.16 (![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)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1294,axiom,(![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty6')).
% 1.95/2.16 tff(1295,plain,
% 1.95/2.16 (![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1294, 1293])).
% 1.95/2.16 tff(1296,plain,(
% 1.95/2.16 ![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))),
% 1.95/2.16 inference(skolemize,[status(sab)],[1295])).
% 1.95/2.16 tff(1297,plain,
% 1.95/2.16 (![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1296, 1292])).
% 1.95/2.16 tff(1298,plain,
% 1.95/2.16 (((~![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)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1299,plain,
% 1.95/2.16 ((~![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)))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(1300,plain,
% 1.95/2.16 ((~![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))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1299, 1298])).
% 1.95/2.16 tff(1301,plain,
% 1.95/2.16 (~node25(s1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1300, 1297, 1290])).
% 1.95/2.16 tff(1302,plain,
% 1.95/2.16 (^[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)))),
% 1.95/2.16 inference(bind,[status(th)],[])).
% 1.95/2.16 tff(1303,plain,
% 1.95/2.16 (![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))),
% 1.95/2.16 inference(quant_intro,[status(thm)],[1302])).
% 1.95/2.16 tff(1304,plain,
% 1.95/2.16 (![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))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1305,plain,
% 1.95/2.16 (^[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)))),
% 1.95/2.16 inference(bind,[status(th)],[])).
% 1.95/2.16 tff(1306,plain,
% 1.95/2.16 (![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))),
% 1.95/2.16 inference(quant_intro,[status(thm)],[1305])).
% 1.95/2.16 tff(1307,axiom,(![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node24(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty4')).
% 1.95/2.16 tff(1308,plain,
% 1.95/2.16 (![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1307, 1306])).
% 1.95/2.16 tff(1309,plain,
% 1.95/2.16 (![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1308, 1304])).
% 1.95/2.16 tff(1310,plain,(
% 1.95/2.16 ![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))),
% 1.95/2.16 inference(skolemize,[status(sab)],[1309])).
% 1.95/2.16 tff(1311,plain,
% 1.95/2.16 (![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1310, 1303])).
% 1.95/2.16 tff(1312,plain,
% 1.95/2.16 (((~![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))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1313,plain,
% 1.95/2.16 ((~![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))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(1314,plain,
% 1.95/2.16 ((~![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)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1313, 1312])).
% 1.95/2.16 tff(1315,plain,
% 1.95/2.16 (~node24(s1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1314, 1311, 1290])).
% 1.95/2.16 tff(1316,plain,
% 1.95/2.16 (((~![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)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1317,plain,
% 1.95/2.16 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s1) | node24(s1) | node25(s1) | (~node26(s1)))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(1318,plain,
% 1.95/2.16 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s1) | node24(s1) | node25(s1) | (~node26(s1))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1317, 1316])).
% 1.95/2.16 tff(1319,plain,
% 1.95/2.16 (node23(s1) | (~node26(s1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1318, 1224, 1315, 1301])).
% 1.95/2.16 tff(1320,plain,
% 1.95/2.16 (~node26(s1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1319, 1246])).
% 1.95/2.16 tff(1321,plain,
% 1.95/2.16 (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1174, 1157, 1164])).
% 1.95/2.16 tff(1322,plain,
% 1.95/2.16 (~m_user_v_ack(c_e_h_2, c_u, s4)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1179, 582, 1321])).
% 1.95/2.16 tff(1323,plain,
% 1.95/2.16 (^[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)))),
% 1.95/2.16 inference(bind,[status(th)],[])).
% 1.95/2.16 tff(1324,plain,
% 1.95/2.16 (![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))),
% 1.95/2.16 inference(quant_intro,[status(thm)],[1323])).
% 1.95/2.16 tff(1325,plain,
% 1.95/2.16 (![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))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1326,plain,
% 1.95/2.16 (^[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)))),
% 1.95/2.16 inference(bind,[status(th)],[])).
% 1.95/2.16 tff(1327,plain,
% 1.95/2.16 (![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))),
% 1.95/2.16 inference(quant_intro,[status(thm)],[1326])).
% 1.95/2.16 tff(1328,axiom,(![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node23(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty2')).
% 1.95/2.16 tff(1329,plain,
% 1.95/2.16 (![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1328, 1327])).
% 1.95/2.16 tff(1330,plain,
% 1.95/2.16 (![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1329, 1325])).
% 1.95/2.16 tff(1331,plain,(
% 1.95/2.16 ![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))),
% 1.95/2.16 inference(skolemize,[status(sab)],[1330])).
% 1.95/2.16 tff(1332,plain,
% 1.95/2.16 (![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1331, 1324])).
% 1.95/2.16 tff(1333,plain,
% 1.95/2.16 (((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | ((~node23(s4)) | m_user_v_ack(c_e_h_2, c_u, s4))) <=> ((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | (~node23(s4)) | m_user_v_ack(c_e_h_2, c_u, s4))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1334,plain,
% 1.95/2.16 ((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | ((~node23(s4)) | m_user_v_ack(c_e_h_2, c_u, s4))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(1335,plain,
% 1.95/2.16 ((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | (~node23(s4)) | m_user_v_ack(c_e_h_2, c_u, s4)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1334, 1333])).
% 1.95/2.16 tff(1336,plain,
% 1.95/2.16 (~node23(s4)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1335, 1332, 1322])).
% 1.95/2.16 tff(1337,assumption,(~node25(s4)), introduced(assumption)).
% 1.95/2.16 tff(1338,assumption,(~node24(s4)), introduced(assumption)).
% 1.95/2.16 tff(1339,plain,
% 1.95/2.16 (((~![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)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1340,plain,
% 1.95/2.16 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s4) | node24(s4) | node25(s4) | (~node26(s4)))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(1341,plain,
% 1.95/2.16 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s4) | node24(s4) | node25(s4) | (~node26(s4))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1340, 1339])).
% 1.95/2.16 tff(1342,plain,
% 1.95/2.16 (node23(s4) | (~node26(s4))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1341, 1224, 1338, 1337])).
% 1.95/2.16 tff(1343,plain,
% 1.95/2.16 (~node26(s4)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1342, 1336])).
% 1.95/2.16 tff(1344,plain,
% 1.95/2.16 (~m_user_v_ack(c_e_h_2, c_u, s3)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[585, 582, 1157])).
% 1.95/2.16 tff(1345,plain,
% 1.95/2.16 (((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | ((~node23(s3)) | m_user_v_ack(c_e_h_2, c_u, s3))) <=> ((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | (~node23(s3)) | m_user_v_ack(c_e_h_2, c_u, s3))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1346,plain,
% 1.95/2.16 ((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | ((~node23(s3)) | m_user_v_ack(c_e_h_2, c_u, s3))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(1347,plain,
% 1.95/2.16 ((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | (~node23(s3)) | m_user_v_ack(c_e_h_2, c_u, s3)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1346, 1345])).
% 1.95/2.16 tff(1348,plain,
% 1.95/2.16 (~node23(s3)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1347, 1332, 1344])).
% 1.95/2.16 tff(1349,assumption,(~node25(s3)), introduced(assumption)).
% 1.95/2.16 tff(1350,assumption,(~node24(s3)), introduced(assumption)).
% 1.95/2.16 tff(1351,plain,
% 1.95/2.16 (((~![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)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1352,plain,
% 1.95/2.16 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s3) | node24(s3) | node25(s3) | (~node26(s3)))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(1353,plain,
% 1.95/2.16 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s3) | node24(s3) | node25(s3) | (~node26(s3))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1352, 1351])).
% 1.95/2.16 tff(1354,plain,
% 1.95/2.16 (node23(s3) | (~node26(s3))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1353, 1224, 1350, 1349])).
% 1.95/2.16 tff(1355,plain,
% 1.95/2.16 (~node26(s3)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1354, 1348])).
% 1.95/2.16 tff(1356,assumption,(~node26(s2)), introduced(assumption)).
% 1.95/2.16 tff(1357,assumption,(~node26(s1)), introduced(assumption)).
% 1.95/2.16 tff(1358,plain,
% 1.95/2.16 (((~![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))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1359,plain,
% 1.95/2.16 ((~![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))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(1360,plain,
% 1.95/2.16 ((~![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)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1359, 1358])).
% 1.95/2.16 tff(1361,plain,
% 1.95/2.16 (~m_user_v_ack(c_e_h_2, c_u, s0)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1360, 582, 116])).
% 1.95/2.16 tff(1362,assumption,(node25(s0)), introduced(assumption)).
% 1.95/2.16 tff(1363,plain,
% 1.95/2.16 (((~![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)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1364,plain,
% 1.95/2.16 ((~![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)))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(1365,plain,
% 1.95/2.16 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s0) | (~node25(s0))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1364, 1363])).
% 1.95/2.16 tff(1366,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1365, 593, 1362, 1361])).
% 1.95/2.16 tff(1367,plain,(~node25(s0)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(1368,plain,
% 1.95/2.16 (((~![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))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1369,plain,
% 1.95/2.16 ((~![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))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(1370,plain,
% 1.95/2.16 ((~![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)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1369, 1368])).
% 1.95/2.16 tff(1371,plain,
% 1.95/2.16 (~m_user_v_ack(c_e_h_1, c_u, s0)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1370, 582, 796])).
% 1.95/2.16 tff(1372,plain,
% 1.95/2.16 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | ((~node24(s0)) | m_user_v_ack(c_e_h_1, c_u, s0))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (~node24(s0)) | m_user_v_ack(c_e_h_1, c_u, s0))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1373,plain,
% 1.95/2.16 ((m_user_v_ack(c_e_h_1, c_u, s0) | (~node24(s0))) <=> ((~node24(s0)) | m_user_v_ack(c_e_h_1, c_u, s0))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1374,plain,
% 1.95/2.16 (((~![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)))) | ((~node24(s0)) | m_user_v_ack(c_e_h_1, c_u, s0)))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[1373])).
% 1.95/2.16 tff(1375,plain,
% 1.95/2.16 (((~![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)))) | (~node24(s0)) | m_user_v_ack(c_e_h_1, c_u, s0))),
% 1.95/2.16 inference(transitivity,[status(thm)],[1374, 1372])).
% 1.95/2.16 tff(1376,plain,
% 1.95/2.16 ((~![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)))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(1377,plain,
% 1.95/2.16 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (~node24(s0)) | m_user_v_ack(c_e_h_1, c_u, s0)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1376, 1375])).
% 1.95/2.16 tff(1378,plain,
% 1.95/2.16 (~node24(s0)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1377, 1022, 1371])).
% 1.95/2.16 tff(1379,plain,
% 1.95/2.16 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s0) | (~node23(s0)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s0) | (~node23(s0)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1380,plain,
% 1.95/2.16 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s0) | (~node23(s0)))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(1381,plain,
% 1.95/2.16 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s0) | (~node23(s0))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1380, 1379])).
% 1.95/2.16 tff(1382,plain,
% 1.95/2.16 (~node23(s0)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1381, 1210, 1371])).
% 1.95/2.16 tff(1383,plain,
% 1.95/2.16 (((~![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)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1384,plain,
% 1.95/2.16 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s0) | node24(s0) | node25(s0) | (~node26(s0)))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(1385,plain,
% 1.95/2.16 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s0) | node24(s0) | node25(s0) | (~node26(s0))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1384, 1383])).
% 1.95/2.16 tff(1386,plain,
% 1.95/2.16 (node25(s0) | (~node26(s0))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1385, 1224, 1382, 1378])).
% 1.95/2.16 tff(1387,plain,
% 1.95/2.16 (~node26(s0)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1386, 1367])).
% 1.95/2.16 tff(1388,plain,
% 1.95/2.16 (until27(s0) <=> until27(s0)),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1389,axiom,(until27(s0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty15')).
% 1.95/2.16 tff(1390,plain,
% 1.95/2.16 (until27(s0)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1389, 1388])).
% 1.95/2.16 tff(1391,plain,
% 1.95/2.16 (^[X: $i] : refl(((~until27(X)) | node26(X) | xuntil28(X)) <=> ((~until27(X)) | node26(X) | xuntil28(X)))),
% 1.95/2.16 inference(bind,[status(th)],[])).
% 1.95/2.16 tff(1392,plain,
% 1.95/2.16 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X)) <=> ![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 1.95/2.16 inference(quant_intro,[status(thm)],[1391])).
% 1.95/2.16 tff(1393,plain,
% 1.95/2.16 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X)) <=> ![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1394,plain,
% 1.95/2.16 (^[X: $i] : rewrite(((node26(X) | xuntil28(X)) | (~until27(X))) <=> ((~until27(X)) | node26(X) | xuntil28(X)))),
% 1.95/2.16 inference(bind,[status(th)],[])).
% 1.95/2.16 tff(1395,plain,
% 1.95/2.16 (![X: $i] : ((node26(X) | xuntil28(X)) | (~until27(X))) <=> ![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 1.95/2.16 inference(quant_intro,[status(thm)],[1394])).
% 1.95/2.16 tff(1396,axiom,(![X: $i] : ((node26(X) | xuntil28(X)) | (~until27(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty8')).
% 1.95/2.16 tff(1397,plain,
% 1.95/2.16 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1396, 1395])).
% 1.95/2.16 tff(1398,plain,
% 1.95/2.16 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1397, 1393])).
% 1.95/2.16 tff(1399,plain,(
% 1.95/2.16 ![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 1.95/2.16 inference(skolemize,[status(sab)],[1398])).
% 1.95/2.16 tff(1400,plain,
% 1.95/2.16 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1399, 1392])).
% 1.95/2.16 tff(1401,plain,
% 1.95/2.16 (((~![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))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1402,plain,
% 1.95/2.16 (((~until27(s0)) | node26(s0) | xuntil28(s0)) <=> (xuntil28(s0) | (~until27(s0)) | node26(s0))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1403,plain,
% 1.95/2.16 (((~![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)))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[1402])).
% 1.95/2.16 tff(1404,plain,
% 1.95/2.16 (((~![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))),
% 1.95/2.16 inference(transitivity,[status(thm)],[1403, 1401])).
% 1.95/2.16 tff(1405,plain,
% 1.95/2.16 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s0)) | node26(s0) | xuntil28(s0))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(1406,plain,
% 1.95/2.16 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s0) | (~until27(s0)) | node26(s0)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1405, 1404])).
% 1.95/2.16 tff(1407,plain,
% 1.95/2.16 (xuntil28(s0) | node26(s0)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1406, 1400, 1390])).
% 1.95/2.16 tff(1408,plain,
% 1.95/2.16 (xuntil28(s0)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1407, 1387])).
% 1.95/2.16 tff(1409,plain,
% 1.95/2.16 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)) <=> ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)))),
% 1.95/2.16 inference(bind,[status(th)],[])).
% 1.95/2.16 tff(1410,plain,
% 1.95/2.16 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 1.95/2.16 inference(quant_intro,[status(thm)],[1409])).
% 1.95/2.16 tff(1411,plain,
% 1.95/2.16 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1412,plain,
% 1.95/2.16 (^[Y: $i, X: $i] : rewrite(((until27(Y) | (~succ(X, Y))) | (~xuntil28(X))) <=> ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)))),
% 1.95/2.16 inference(bind,[status(th)],[])).
% 1.95/2.16 tff(1413,plain,
% 1.95/2.16 (![Y: $i, X: $i] : ((until27(Y) | (~succ(X, Y))) | (~xuntil28(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 1.95/2.16 inference(quant_intro,[status(thm)],[1412])).
% 1.95/2.16 tff(1414,axiom,(![Y: $i, X: $i] : ((until27(Y) | (~succ(X, Y))) | (~xuntil28(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty9')).
% 1.95/2.16 tff(1415,plain,
% 1.95/2.16 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1414, 1413])).
% 1.95/2.16 tff(1416,plain,
% 1.95/2.16 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1415, 1411])).
% 1.95/2.16 tff(1417,plain,(
% 1.95/2.16 ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 1.95/2.16 inference(skolemize,[status(sab)],[1416])).
% 1.95/2.16 tff(1418,plain,
% 1.95/2.16 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1417, 1410])).
% 1.95/2.16 tff(1419,plain,
% 1.95/2.16 (((~![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))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(1420,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s0, s1)) | (~xuntil28(s0)) | until27(s1))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(1421,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s0, s1)) | (~xuntil28(s0)) | until27(s1)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1420, 1419])).
% 1.95/2.16 tff(1422,plain,
% 1.95/2.16 ((~xuntil28(s0)) | until27(s1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1421, 87, 1418])).
% 1.95/2.16 tff(1423,plain,
% 1.95/2.16 (until27(s1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1422, 1408])).
% 1.95/2.16 tff(1424,plain,
% 1.95/2.16 (((~![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)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1425,plain,
% 1.95/2.17 (((~until27(s1)) | node26(s1) | xuntil28(s1)) <=> (xuntil28(s1) | node26(s1) | (~until27(s1)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1426,plain,
% 1.95/2.17 (((~![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))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[1425])).
% 1.95/2.17 tff(1427,plain,
% 1.95/2.17 (((~![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)))),
% 1.95/2.17 inference(transitivity,[status(thm)],[1426, 1424])).
% 1.95/2.17 tff(1428,plain,
% 1.95/2.17 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s1)) | node26(s1) | xuntil28(s1))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(1429,plain,
% 1.95/2.17 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s1) | node26(s1) | (~until27(s1))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1428, 1427])).
% 1.95/2.17 tff(1430,plain,
% 1.95/2.17 (xuntil28(s1) | node26(s1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1429, 1400, 1423])).
% 1.95/2.17 tff(1431,plain,
% 1.95/2.17 (xuntil28(s1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1430, 1357])).
% 1.95/2.17 tff(1432,plain,
% 1.95/2.17 (((~![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))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1433,plain,
% 1.95/2.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s1, s2)) | (~xuntil28(s1)) | until27(s2))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(1434,plain,
% 1.95/2.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s1, s2)) | (~xuntil28(s1)) | until27(s2)),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1433, 1432])).
% 1.95/2.17 tff(1435,plain,
% 1.95/2.17 ((~xuntil28(s1)) | until27(s2)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1434, 253, 1418])).
% 1.95/2.17 tff(1436,plain,
% 1.95/2.17 (until27(s2)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1435, 1431])).
% 1.95/2.17 tff(1437,plain,
% 1.95/2.17 (((~![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)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1438,plain,
% 1.95/2.17 (((~until27(s2)) | node26(s2) | xuntil28(s2)) <=> (xuntil28(s2) | node26(s2) | (~until27(s2)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1439,plain,
% 1.95/2.17 (((~![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))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[1438])).
% 1.95/2.17 tff(1440,plain,
% 1.95/2.17 (((~![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)))),
% 1.95/2.17 inference(transitivity,[status(thm)],[1439, 1437])).
% 1.95/2.17 tff(1441,plain,
% 1.95/2.17 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s2)) | node26(s2) | xuntil28(s2))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(1442,plain,
% 1.95/2.17 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s2) | node26(s2) | (~until27(s2))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1441, 1440])).
% 1.95/2.17 tff(1443,plain,
% 1.95/2.17 (xuntil28(s2)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1442, 1400, 1436, 1356])).
% 1.95/2.17 tff(1444,plain,
% 1.95/2.17 (((~![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))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1445,plain,
% 1.95/2.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s2, s3)) | (~xuntil28(s2)) | until27(s3))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(1446,plain,
% 1.95/2.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s2, s3)) | (~xuntil28(s2)) | until27(s3)),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1445, 1444])).
% 1.95/2.17 tff(1447,plain,
% 1.95/2.17 ((~xuntil28(s2)) | until27(s3)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1446, 565, 1418])).
% 1.95/2.17 tff(1448,plain,
% 1.95/2.17 (until27(s3)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1447, 1443])).
% 1.95/2.17 tff(1449,plain,
% 1.95/2.17 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s3) | node26(s3) | (~until27(s3)))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s3) | node26(s3) | (~until27(s3)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1450,plain,
% 1.95/2.17 (((~until27(s3)) | node26(s3) | xuntil28(s3)) <=> (xuntil28(s3) | node26(s3) | (~until27(s3)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1451,plain,
% 1.95/2.17 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s3)) | node26(s3) | xuntil28(s3))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s3) | node26(s3) | (~until27(s3))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[1450])).
% 1.95/2.17 tff(1452,plain,
% 1.95/2.17 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s3)) | node26(s3) | xuntil28(s3))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s3) | node26(s3) | (~until27(s3)))),
% 1.95/2.17 inference(transitivity,[status(thm)],[1451, 1449])).
% 1.95/2.17 tff(1453,plain,
% 1.95/2.17 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s3)) | node26(s3) | xuntil28(s3))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(1454,plain,
% 1.95/2.17 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s3) | node26(s3) | (~until27(s3))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1453, 1452])).
% 1.95/2.17 tff(1455,plain,
% 1.95/2.17 (xuntil28(s3) | node26(s3)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1454, 1400, 1448])).
% 1.95/2.17 tff(1456,plain,
% 1.95/2.17 (xuntil28(s3)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1455, 1355])).
% 1.95/2.17 tff(1457,plain,
% 1.95/2.17 (((~![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))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1458,plain,
% 1.95/2.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s3, s4)) | (~xuntil28(s3)) | until27(s4))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(1459,plain,
% 1.95/2.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s3, s4)) | (~xuntil28(s3)) | until27(s4)),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1458, 1457])).
% 1.95/2.17 tff(1460,plain,
% 1.95/2.17 ((~xuntil28(s3)) | until27(s4)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1459, 1001, 1418])).
% 1.95/2.17 tff(1461,plain,
% 1.95/2.17 (until27(s4)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1460, 1456])).
% 1.95/2.17 tff(1462,plain,
% 1.95/2.17 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s4) | node26(s4) | (~until27(s4)))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s4) | node26(s4) | (~until27(s4)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1463,plain,
% 1.95/2.17 (((~until27(s4)) | node26(s4) | xuntil28(s4)) <=> (xuntil28(s4) | node26(s4) | (~until27(s4)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1464,plain,
% 1.95/2.17 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s4)) | node26(s4) | xuntil28(s4))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s4) | node26(s4) | (~until27(s4))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[1463])).
% 1.95/2.17 tff(1465,plain,
% 1.95/2.17 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s4)) | node26(s4) | xuntil28(s4))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s4) | node26(s4) | (~until27(s4)))),
% 1.95/2.17 inference(transitivity,[status(thm)],[1464, 1462])).
% 1.95/2.17 tff(1466,plain,
% 1.95/2.17 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s4)) | node26(s4) | xuntil28(s4))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(1467,plain,
% 1.95/2.17 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s4) | node26(s4) | (~until27(s4))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1466, 1465])).
% 1.95/2.17 tff(1468,plain,
% 1.95/2.17 (xuntil28(s4) | node26(s4)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1467, 1400, 1461])).
% 1.95/2.17 tff(1469,plain,
% 1.95/2.17 (xuntil28(s4)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1468, 1343])).
% 1.95/2.17 tff(1470,plain,
% 1.95/2.17 (^[X: $i] : refl(((~last(X)) | (~xuntil2p30(X))) <=> ((~last(X)) | (~xuntil2p30(X))))),
% 1.95/2.17 inference(bind,[status(th)],[])).
% 1.95/2.17 tff(1471,plain,
% 1.95/2.17 (![X: $i] : ((~last(X)) | (~xuntil2p30(X))) <=> ![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 1.95/2.17 inference(quant_intro,[status(thm)],[1470])).
% 1.95/2.17 tff(1472,plain,
% 1.95/2.17 (![X: $i] : ((~last(X)) | (~xuntil2p30(X))) <=> ![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1473,axiom,(![X: $i] : ((~last(X)) | (~xuntil2p30(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty14')).
% 1.95/2.17 tff(1474,plain,
% 1.95/2.17 (![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1473, 1472])).
% 1.95/2.17 tff(1475,plain,(
% 1.95/2.17 ![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 1.95/2.17 inference(skolemize,[status(sab)],[1474])).
% 1.95/2.17 tff(1476,plain,
% 1.95/2.17 (![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1475, 1471])).
% 1.95/2.17 tff(1477,plain,
% 1.95/2.17 (last(s4) <=> last(s4)),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1478,axiom,(last(s4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound5')).
% 1.95/2.17 tff(1479,plain,
% 1.95/2.17 (last(s4)),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1478, 1477])).
% 1.95/2.17 tff(1480,plain,
% 1.95/2.17 (((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | ((~last(s4)) | (~xuntil2p30(s4)))) <=> ((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | (~last(s4)) | (~xuntil2p30(s4)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1481,plain,
% 1.95/2.17 ((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | ((~last(s4)) | (~xuntil2p30(s4)))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(1482,plain,
% 1.95/2.17 ((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | (~last(s4)) | (~xuntil2p30(s4))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1481, 1480])).
% 1.95/2.17 tff(1483,plain,
% 1.95/2.17 (~xuntil2p30(s4)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1482, 1479, 1476])).
% 1.95/2.17 tff(1484,plain,
% 1.95/2.17 (^[X: $i] : refl((node26(X) | xuntil2p30(X) | (~until2p29(X))) <=> (node26(X) | xuntil2p30(X) | (~until2p29(X))))),
% 1.95/2.17 inference(bind,[status(th)],[])).
% 1.95/2.17 tff(1485,plain,
% 1.95/2.17 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X))) <=> ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 1.95/2.17 inference(quant_intro,[status(thm)],[1484])).
% 1.95/2.17 tff(1486,plain,
% 1.95/2.17 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X))) <=> ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1487,plain,
% 1.95/2.17 (^[X: $i] : rewrite(((node26(X) | xuntil2p30(X)) | (~until2p29(X))) <=> (node26(X) | xuntil2p30(X) | (~until2p29(X))))),
% 1.95/2.17 inference(bind,[status(th)],[])).
% 1.95/2.17 tff(1488,plain,
% 1.95/2.17 (![X: $i] : ((node26(X) | xuntil2p30(X)) | (~until2p29(X))) <=> ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 1.95/2.17 inference(quant_intro,[status(thm)],[1487])).
% 1.95/2.17 tff(1489,axiom,(![X: $i] : ((node26(X) | xuntil2p30(X)) | (~until2p29(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty12')).
% 1.95/2.17 tff(1490,plain,
% 1.95/2.17 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1489, 1488])).
% 1.95/2.17 tff(1491,plain,
% 1.95/2.17 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1490, 1486])).
% 1.95/2.17 tff(1492,plain,(
% 1.95/2.17 ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 1.95/2.17 inference(skolemize,[status(sab)],[1491])).
% 1.95/2.17 tff(1493,plain,
% 1.95/2.17 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1492, 1485])).
% 1.95/2.17 tff(1494,plain,
% 1.95/2.17 (((~![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)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1495,plain,
% 1.95/2.17 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s4) | xuntil2p30(s4) | (~until2p29(s4)))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(1496,plain,
% 1.95/2.17 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s4) | xuntil2p30(s4) | (~until2p29(s4))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1495, 1494])).
% 1.95/2.17 tff(1497,plain,
% 1.95/2.17 (node26(s4) | (~until2p29(s4))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1496, 1493, 1483])).
% 1.95/2.17 tff(1498,plain,
% 1.95/2.17 (~until2p29(s4)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1497, 1343])).
% 1.95/2.17 tff(1499,plain,
% 1.95/2.17 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))) <=> ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))))),
% 1.95/2.17 inference(bind,[status(th)],[])).
% 1.95/2.17 tff(1500,plain,
% 1.95/2.17 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 1.95/2.17 inference(quant_intro,[status(thm)],[1499])).
% 1.95/2.17 tff(1501,plain,
% 1.95/2.17 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1502,plain,
% 1.95/2.17 (^[Y: $i, X: $i] : rewrite(((until2p29(Y) | (~succ(X, Y))) | (~xuntil2p30(X))) <=> ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))))),
% 1.95/2.17 inference(bind,[status(th)],[])).
% 1.95/2.17 tff(1503,plain,
% 1.95/2.17 (![Y: $i, X: $i] : ((until2p29(Y) | (~succ(X, Y))) | (~xuntil2p30(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 1.95/2.17 inference(quant_intro,[status(thm)],[1502])).
% 1.95/2.17 tff(1504,axiom,(![Y: $i, X: $i] : ((until2p29(Y) | (~succ(X, Y))) | (~xuntil2p30(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty13')).
% 1.95/2.17 tff(1505,plain,
% 1.95/2.17 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1504, 1503])).
% 1.95/2.17 tff(1506,plain,
% 1.95/2.17 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1505, 1501])).
% 1.95/2.17 tff(1507,plain,(
% 1.95/2.17 ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 1.95/2.17 inference(skolemize,[status(sab)],[1506])).
% 1.95/2.17 tff(1508,plain,
% 1.95/2.17 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1507, 1500])).
% 1.95/2.17 tff(1509,plain,
% 1.95/2.17 (((~![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)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1510,plain,
% 1.95/2.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s3, s4)) | until2p29(s4) | (~xuntil2p30(s3)))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(1511,plain,
% 1.95/2.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s3, s4)) | until2p29(s4) | (~xuntil2p30(s3))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1510, 1509])).
% 1.95/2.17 tff(1512,plain,
% 1.95/2.17 (until2p29(s4) | (~xuntil2p30(s3))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1511, 1001, 1508])).
% 1.95/2.17 tff(1513,plain,
% 1.95/2.17 (~xuntil2p30(s3)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1512, 1498])).
% 1.95/2.17 tff(1514,plain,
% 1.95/2.17 (((~![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)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1515,plain,
% 1.95/2.17 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s3) | xuntil2p30(s3) | (~until2p29(s3)))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(1516,plain,
% 1.95/2.17 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s3) | xuntil2p30(s3) | (~until2p29(s3))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1515, 1514])).
% 1.95/2.17 tff(1517,plain,
% 1.95/2.17 (xuntil2p30(s3) | (~until2p29(s3))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1516, 1493, 1355])).
% 1.95/2.17 tff(1518,plain,
% 1.95/2.17 (~until2p29(s3)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1517, 1513])).
% 1.95/2.17 tff(1519,plain,
% 1.95/2.17 (^[Y: $i, X: $i] : refl(((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y)) <=> ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y)))),
% 1.95/2.17 inference(bind,[status(th)],[])).
% 1.95/2.17 tff(1520,plain,
% 1.95/2.17 (![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))),
% 1.95/2.17 inference(quant_intro,[status(thm)],[1519])).
% 1.95/2.17 tff(1521,plain,
% 1.95/2.17 (![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))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1522,plain,
% 1.95/2.17 (^[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))))),
% 1.95/2.17 inference(bind,[status(th)],[])).
% 1.95/2.17 tff(1523,plain,
% 1.95/2.17 (![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))),
% 1.95/2.17 inference(quant_intro,[status(thm)],[1522])).
% 1.95/2.17 tff(1524,axiom,(![Y: $i, X: $i] : (((until2p29(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil28(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty11')).
% 1.95/2.17 tff(1525,plain,
% 1.95/2.17 (![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1524, 1523])).
% 1.95/2.17 tff(1526,plain,
% 1.95/2.17 (![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1525, 1521])).
% 1.95/2.17 tff(1527,plain,(
% 1.95/2.17 ![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 1.95/2.17 inference(skolemize,[status(sab)],[1526])).
% 1.95/2.17 tff(1528,plain,
% 1.95/2.17 (![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1527, 1520])).
% 1.95/2.17 tff(1529,plain,
% 1.95/2.17 (((~![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)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1530,plain,
% 1.95/2.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s2, s3)) | until2p29(s3) | (~xuntil2p30(s2)))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(1531,plain,
% 1.95/2.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s2, s3)) | until2p29(s3) | (~xuntil2p30(s2))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1530, 1529])).
% 1.95/2.17 tff(1532,plain,
% 1.95/2.17 (until2p29(s3) | (~xuntil2p30(s2))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1531, 565, 1508])).
% 1.95/2.17 tff(1533,plain,
% 1.95/2.17 (~xuntil2p30(s2)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1532, 1518])).
% 1.95/2.17 tff(1534,plain,
% 1.95/2.17 (((~![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)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1535,plain,
% 1.95/2.17 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s2) | xuntil2p30(s2) | (~until2p29(s2)))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(1536,plain,
% 1.95/2.17 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s2) | xuntil2p30(s2) | (~until2p29(s2))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1535, 1534])).
% 1.95/2.17 tff(1537,plain,
% 1.95/2.17 (xuntil2p30(s2) | (~until2p29(s2))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1536, 1493, 1356])).
% 1.95/2.17 tff(1538,plain,
% 1.95/2.17 (~until2p29(s2)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1537, 1533])).
% 1.95/2.17 tff(1539,plain,
% 1.95/2.17 (((~![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)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1540,plain,
% 1.95/2.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s1, s2)) | until2p29(s2) | (~xuntil2p30(s1)))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(1541,plain,
% 1.95/2.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s1, s2)) | until2p29(s2) | (~xuntil2p30(s1))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1540, 1539])).
% 1.95/2.17 tff(1542,plain,
% 1.95/2.17 (until2p29(s2) | (~xuntil2p30(s1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1541, 253, 1508])).
% 1.95/2.17 tff(1543,plain,
% 1.95/2.17 (~xuntil2p30(s1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1542, 1538])).
% 1.95/2.17 tff(1544,plain,
% 1.95/2.17 (((~![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)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1545,plain,
% 1.95/2.17 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s1) | xuntil2p30(s1) | (~until2p29(s1)))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(1546,plain,
% 1.95/2.17 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s1) | xuntil2p30(s1) | (~until2p29(s1))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1545, 1544])).
% 1.95/2.17 tff(1547,plain,
% 1.95/2.17 (xuntil2p30(s1) | (~until2p29(s1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1546, 1493, 1357])).
% 1.95/2.17 tff(1548,plain,
% 1.95/2.17 (~until2p29(s1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1547, 1543])).
% 1.95/2.17 tff(1549,assumption,(xuntil28(s4)), introduced(assumption)).
% 1.95/2.17 tff(1550,assumption,(~until2p29(s1)), introduced(assumption)).
% 1.95/2.17 tff(1551,assumption,(trans(s4, s1)), introduced(assumption)).
% 1.95/2.17 tff(1552,plain,
% 1.95/2.17 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s1) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s1)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s1) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s1)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1553,plain,
% 1.95/2.17 (((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s1)) | until2p29(s1)) <=> (until2p29(s1) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s1)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1554,plain,
% 1.95/2.17 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s1)) | until2p29(s1))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s1) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s1))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[1553])).
% 1.95/2.17 tff(1555,plain,
% 1.95/2.17 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s1)) | until2p29(s1))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s1) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s1)))),
% 1.95/2.17 inference(transitivity,[status(thm)],[1554, 1552])).
% 1.95/2.17 tff(1556,plain,
% 1.95/2.17 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s1)) | until2p29(s1))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(1557,plain,
% 1.95/2.17 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s1) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s1))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1556, 1555])).
% 1.95/2.17 tff(1558,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1557, 1479, 1551, 1528, 1550, 1549])).
% 1.95/2.17 tff(1559,plain,((~trans(s4, s1)) | until2p29(s1) | (~xuntil28(s4))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(1560,plain,
% 1.95/2.17 (~trans(s4, s1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1559, 1548, 1469])).
% 1.95/2.17 tff(1561,assumption,(~until2p29(s2)), introduced(assumption)).
% 1.95/2.17 tff(1562,assumption,(trans(s4, s2)), introduced(assumption)).
% 1.95/2.17 tff(1563,plain,
% 1.95/2.17 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s2) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s2)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s2) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s2)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1564,plain,
% 1.95/2.17 (((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s2)) | until2p29(s2)) <=> (until2p29(s2) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s2)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1565,plain,
% 1.95/2.17 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s2)) | until2p29(s2))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s2) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s2))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[1564])).
% 1.95/2.17 tff(1566,plain,
% 1.95/2.17 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s2)) | until2p29(s2))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s2) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s2)))),
% 1.95/2.17 inference(transitivity,[status(thm)],[1565, 1563])).
% 1.95/2.17 tff(1567,plain,
% 1.95/2.17 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s2)) | until2p29(s2))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(1568,plain,
% 1.95/2.17 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s2) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s2))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1567, 1566])).
% 1.95/2.17 tff(1569,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1568, 1479, 1562, 1528, 1561, 1549])).
% 1.95/2.17 tff(1570,plain,((~trans(s4, s2)) | until2p29(s2) | (~xuntil28(s4))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(1571,plain,
% 1.95/2.17 (~trans(s4, s2)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1570, 1538, 1469])).
% 1.95/2.17 tff(1572,assumption,(~until2p29(s4)), introduced(assumption)).
% 1.95/2.17 tff(1573,assumption,(trans(s4, s4)), introduced(assumption)).
% 1.95/2.17 tff(1574,plain,
% 1.95/2.17 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s4) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s4)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s4) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s4)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1575,plain,
% 1.95/2.17 (((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s4)) | until2p29(s4)) <=> (until2p29(s4) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s4)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1576,plain,
% 1.95/2.17 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s4)) | until2p29(s4))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s4) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s4))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[1575])).
% 1.95/2.17 tff(1577,plain,
% 1.95/2.17 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s4)) | until2p29(s4))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s4) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s4)))),
% 1.95/2.17 inference(transitivity,[status(thm)],[1576, 1574])).
% 1.95/2.17 tff(1578,plain,
% 1.95/2.17 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s4)) | until2p29(s4))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(1579,plain,
% 1.95/2.17 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s4) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s4))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1578, 1577])).
% 1.95/2.17 tff(1580,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1579, 1479, 1573, 1528, 1572, 1549])).
% 1.95/2.17 tff(1581,plain,((~trans(s4, s4)) | until2p29(s4) | (~xuntil28(s4))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(1582,plain,
% 1.95/2.17 (~trans(s4, s4)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1581, 1498, 1469])).
% 1.95/2.17 tff(1583,plain,
% 1.95/2.17 (^[X: $i] : refl((loop | (~last(X)) | (~xuntil28(X))) <=> (loop | (~last(X)) | (~xuntil28(X))))),
% 1.95/2.17 inference(bind,[status(th)],[])).
% 1.95/2.17 tff(1584,plain,
% 1.95/2.17 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 1.95/2.17 inference(quant_intro,[status(thm)],[1583])).
% 1.95/2.17 tff(1585,plain,
% 1.95/2.17 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1586,plain,
% 1.95/2.17 (^[X: $i] : rewrite(((loop | (~last(X))) | (~xuntil28(X))) <=> (loop | (~last(X)) | (~xuntil28(X))))),
% 1.95/2.17 inference(bind,[status(th)],[])).
% 1.95/2.17 tff(1587,plain,
% 1.95/2.17 (![X: $i] : ((loop | (~last(X))) | (~xuntil28(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 1.95/2.17 inference(quant_intro,[status(thm)],[1586])).
% 1.95/2.17 tff(1588,axiom,(![X: $i] : ((loop | (~last(X))) | (~xuntil28(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty10')).
% 1.95/2.17 tff(1589,plain,
% 1.95/2.17 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1588, 1587])).
% 1.95/2.17 tff(1590,plain,
% 1.95/2.17 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1589, 1585])).
% 1.95/2.17 tff(1591,plain,(
% 1.95/2.17 ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 1.95/2.17 inference(skolemize,[status(sab)],[1590])).
% 1.95/2.17 tff(1592,plain,
% 1.95/2.17 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1591, 1584])).
% 1.95/2.17 tff(1593,plain,
% 1.95/2.17 (((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | (loop | (~last(s4)) | (~xuntil28(s4)))) <=> ((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | loop | (~last(s4)) | (~xuntil28(s4)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1594,plain,
% 1.95/2.17 ((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | (loop | (~last(s4)) | (~xuntil28(s4)))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(1595,plain,
% 1.95/2.17 ((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | loop | (~last(s4)) | (~xuntil28(s4))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1594, 1593])).
% 1.95/2.17 tff(1596,plain,
% 1.95/2.17 (loop | (~xuntil28(s4))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1595, 1479, 1592])).
% 1.95/2.17 tff(1597,plain,
% 1.95/2.17 (loop),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1596, 1469])).
% 1.95/2.17 tff(1598,plain,
% 1.95/2.17 (((~![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)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1599,plain,
% 1.95/2.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s0, s1)) | until2p29(s1) | (~xuntil2p30(s0)))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(1600,plain,
% 1.95/2.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s0, s1)) | until2p29(s1) | (~xuntil2p30(s0))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1599, 1598])).
% 1.95/2.17 tff(1601,plain,
% 1.95/2.17 (until2p29(s1) | (~xuntil2p30(s0))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1600, 87, 1508])).
% 1.95/2.17 tff(1602,plain,
% 1.95/2.17 (~xuntil2p30(s0)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1601, 1548])).
% 1.95/2.17 tff(1603,plain,
% 1.95/2.17 (((~![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)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1604,plain,
% 1.95/2.17 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s0) | xuntil2p30(s0) | (~until2p29(s0)))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(1605,plain,
% 1.95/2.17 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s0) | xuntil2p30(s0) | (~until2p29(s0))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1604, 1603])).
% 1.95/2.17 tff(1606,plain,
% 1.95/2.17 (xuntil2p30(s0) | (~until2p29(s0))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1605, 1493, 1387])).
% 1.95/2.17 tff(1607,plain,
% 1.95/2.17 (~until2p29(s0)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1606, 1602])).
% 1.95/2.17 tff(1608,assumption,(~until2p29(s0)), introduced(assumption)).
% 1.95/2.17 tff(1609,assumption,(trans(s4, s0)), introduced(assumption)).
% 1.95/2.17 tff(1610,plain,
% 1.95/2.17 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | until2p29(s0) | (~trans(s4, s0)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (~last(s4)) | (~xuntil28(s4)) | until2p29(s0) | (~trans(s4, s0)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1611,plain,
% 1.95/2.17 (((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s0)) | until2p29(s0)) <=> ((~last(s4)) | (~xuntil28(s4)) | until2p29(s0) | (~trans(s4, s0)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1612,plain,
% 1.95/2.17 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s0)) | until2p29(s0))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | until2p29(s0) | (~trans(s4, s0))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[1611])).
% 1.95/2.17 tff(1613,plain,
% 1.95/2.17 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s0)) | until2p29(s0))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (~last(s4)) | (~xuntil28(s4)) | until2p29(s0) | (~trans(s4, s0)))),
% 1.95/2.17 inference(transitivity,[status(thm)],[1612, 1610])).
% 1.95/2.17 tff(1614,plain,
% 1.95/2.17 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s0)) | until2p29(s0))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(1615,plain,
% 1.95/2.17 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (~last(s4)) | (~xuntil28(s4)) | until2p29(s0) | (~trans(s4, s0))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1614, 1613])).
% 1.95/2.17 tff(1616,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1615, 1479, 1609, 1528, 1549, 1608])).
% 1.95/2.17 tff(1617,plain,((~trans(s4, s0)) | (~xuntil28(s4)) | until2p29(s0)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(1618,plain,
% 1.95/2.17 (~trans(s4, s0)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1617, 1469, 1607])).
% 1.95/2.17 tff(1619,plain,
% 1.95/2.17 (((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2) | trans(s4, s3) | trans(s4, s4)) <=> ((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2) | trans(s4, s3) | trans(s4, s4))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1620,plain,
% 1.95/2.17 ((((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2) | trans(s4, s3)) | trans(s4, s4)) <=> ((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2) | trans(s4, s3) | trans(s4, s4))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1621,plain,
% 1.95/2.17 ((((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2)) | trans(s4, s3)) <=> ((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2) | trans(s4, s3))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(1622,plain,
% 1.95/2.17 ((((~loop) | trans(s4, s0) | trans(s4, s1)) | trans(s4, s2)) <=> ((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(1623,plain,
% 1.95/2.18 ((((~loop) | trans(s4, s0)) | trans(s4, s1)) <=> ((~loop) | trans(s4, s0) | trans(s4, s1))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(1624,plain,
% 1.95/2.18 (((((~loop) | trans(s4, s0)) | trans(s4, s1)) | trans(s4, s2)) <=> (((~loop) | trans(s4, s0) | trans(s4, s1)) | trans(s4, s2))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[1623])).
% 1.95/2.18 tff(1625,plain,
% 1.95/2.18 (((((~loop) | trans(s4, s0)) | trans(s4, s1)) | trans(s4, s2)) <=> ((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2))),
% 1.95/2.18 inference(transitivity,[status(thm)],[1624, 1622])).
% 1.95/2.18 tff(1626,plain,
% 1.95/2.18 ((((((~loop) | trans(s4, s0)) | trans(s4, s1)) | trans(s4, s2)) | trans(s4, s3)) <=> (((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2)) | trans(s4, s3))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[1625])).
% 1.95/2.18 tff(1627,plain,
% 1.95/2.18 ((((((~loop) | trans(s4, s0)) | trans(s4, s1)) | trans(s4, s2)) | trans(s4, s3)) <=> ((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2) | trans(s4, s3))),
% 1.95/2.18 inference(transitivity,[status(thm)],[1626, 1621])).
% 1.95/2.18 tff(1628,plain,
% 1.95/2.18 (((((((~loop) | trans(s4, s0)) | trans(s4, s1)) | trans(s4, s2)) | trans(s4, s3)) | trans(s4, s4)) <=> (((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2) | trans(s4, s3)) | trans(s4, s4))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[1627])).
% 1.95/2.18 tff(1629,plain,
% 1.95/2.18 (((((((~loop) | trans(s4, s0)) | trans(s4, s1)) | trans(s4, s2)) | trans(s4, s3)) | trans(s4, s4)) <=> ((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2) | trans(s4, s3) | trans(s4, s4))),
% 1.95/2.18 inference(transitivity,[status(thm)],[1628, 1620])).
% 1.95/2.18 tff(1630,axiom,((((((~loop) | trans(s4, s0)) | trans(s4, s1)) | trans(s4, s2)) | trans(s4, s3)) | trans(s4, s4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound7')).
% 1.95/2.18 tff(1631,plain,
% 1.95/2.18 ((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2) | trans(s4, s3) | trans(s4, s4)),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[1630, 1629])).
% 1.95/2.18 tff(1632,plain,
% 1.95/2.18 ((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2) | trans(s4, s3) | trans(s4, s4)),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[1631, 1619])).
% 1.95/2.18 tff(1633,plain,
% 1.95/2.18 (trans(s4, s3)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1632, 1618, 1597, 1582, 1571, 1560])).
% 1.95/2.18 tff(1634,plain,
% 1.95/2.18 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s3) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s3)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s3) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s3)))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(1635,plain,
% 1.95/2.18 (((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s3)) | until2p29(s3)) <=> (until2p29(s3) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s3)))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(1636,plain,
% 1.95/2.18 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s3)) | until2p29(s3))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s3) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s3))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[1635])).
% 1.95/2.18 tff(1637,plain,
% 1.95/2.18 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s3)) | until2p29(s3))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s3) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s3)))),
% 1.95/2.18 inference(transitivity,[status(thm)],[1636, 1634])).
% 1.95/2.18 tff(1638,plain,
% 1.95/2.18 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s3)) | until2p29(s3))),
% 1.95/2.18 inference(quant_inst,[status(thm)],[])).
% 1.95/2.18 tff(1639,plain,
% 1.95/2.18 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s3) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s3))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[1638, 1637])).
% 1.95/2.18 tff(1640,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1639, 1479, 1633, 1528, 1518, 1469])).
% 1.95/2.18 tff(1641,plain,(m_and_h_gate_v_out(c_e_h_2, c_r, s3) | node26(s1) | node26(s2) | node24(s4) | node25(s4) | node20(c_e_h_2, c_r, s3) | node24(s3) | node25(s3)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(1642,plain,
% 1.95/2.18 (m_and_h_gate_v_out(c_e_h_2, c_r, s3) | node26(s2) | node24(s4) | node25(s4) | node24(s3) | node25(s3)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1641, 1320, 1156])).
% 1.95/2.18 tff(1643,plain,
% 1.95/2.18 (m_and_h_gate_v_out(c_e_h_2, c_r, s3) | node26(s2) | node24(s4) | node25(s4) | node25(s3)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1642, 1238])).
% 1.95/2.18 tff(1644,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1643, 1229, 1187, 1026, 575, 597])).
% 1.95/2.18 % SZS output end Proof
% 1.95/2.18 % E exiting
%------------------------------------------------------------------------------