%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV418-1.060 : TPTP v9.0.0. Released v3.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:32:25 AM UTC 2025
% Result : Unsatisfiable 13.02s 13.18s
% Output : Proof 13.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SWV418-1.060 : TPTP v9.0.0. Released v3.5.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.37 % Computer : n015.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Fri Jun 20 09:46:11 EDT 2025
% 0.14/0.37 % CPUTime :
% 13.02/13.18 % SZS status Unsatisfiable
% 13.02/13.18 % SZS output start Proof
% 13.02/13.18 tff(node3_type, type, (
% 13.02/13.18 node3: ( $i * $i * $i ) > $o)).
% 13.02/13.18 tff(s56_type, type, (
% 13.02/13.18 s56: $i)).
% 13.02/13.18 tff(s59_type, type, (
% 13.02/13.18 s59: $i)).
% 13.02/13.18 tff(c_bit2_type, type, (
% 13.02/13.18 c_bit2: $i)).
% 13.02/13.18 tff(trans_type, type, (
% 13.02/13.18 trans: ( $i * $i ) > $o)).
% 13.02/13.18 tff(s50_type, type, (
% 13.02/13.18 s50: $i)).
% 13.02/13.18 tff(always5_type, type, (
% 13.02/13.18 always5: $i > $o)).
% 13.02/13.18 tff(s51_type, type, (
% 13.02/13.18 s51: $i)).
% 13.02/13.18 tff(m_counter_cell_v_carry_in_type, type, (
% 13.02/13.18 m_counter_cell_v_carry_in: ( $i * $i ) > $o)).
% 13.02/13.18 tff(m_counter_cell_v_carry_out_type, type, (
% 13.02/13.18 m_counter_cell_v_carry_out: ( $i * $i ) > $o)).
% 13.02/13.18 tff(c_bit1_type, type, (
% 13.02/13.18 c_bit1: $i)).
% 13.02/13.18 tff(m_counter_cell_v_value_type, type, (
% 13.02/13.18 m_counter_cell_v_value: ( $i * $i ) > $o)).
% 13.02/13.18 tff(node1_type, type, (
% 13.02/13.18 node1: ( $i * $i ) > $o)).
% 13.02/13.18 tff(s49_type, type, (
% 13.02/13.18 s49: $i)).
% 13.02/13.18 tff(node2_type, type, (
% 13.02/13.18 node2: ( $i * $i ) > $o)).
% 13.02/13.18 tff(s48_type, type, (
% 13.02/13.18 s48: $i)).
% 13.02/13.18 tff(s47_type, type, (
% 13.02/13.18 s47: $i)).
% 13.02/13.18 tff(s46_type, type, (
% 13.02/13.18 s46: $i)).
% 13.02/13.18 tff(s45_type, type, (
% 13.02/13.18 s45: $i)).
% 13.02/13.18 tff(s44_type, type, (
% 13.02/13.18 s44: $i)).
% 13.02/13.18 tff(c_bit0_type, type, (
% 13.02/13.18 c_bit0: $i)).
% 13.02/13.18 tff(node4_type, type, (
% 13.02/13.18 node4: ( $i * $i ) > $o)).
% 13.02/13.18 tff(s43_type, type, (
% 13.02/13.18 s43: $i)).
% 13.02/13.18 tff(s42_type, type, (
% 13.02/13.18 s42: $i)).
% 13.02/13.18 tff(s41_type, type, (
% 13.02/13.18 s41: $i)).
% 13.02/13.18 tff(s40_type, type, (
% 13.02/13.18 s40: $i)).
% 13.02/13.18 tff(s39_type, type, (
% 13.02/13.18 s39: $i)).
% 13.02/13.18 tff(s38_type, type, (
% 13.02/13.18 s38: $i)).
% 13.02/13.18 tff(s37_type, type, (
% 13.02/13.18 s37: $i)).
% 13.02/13.18 tff(s36_type, type, (
% 13.02/13.18 s36: $i)).
% 13.02/13.18 tff(s35_type, type, (
% 13.02/13.18 s35: $i)).
% 13.02/13.18 tff(s34_type, type, (
% 13.02/13.18 s34: $i)).
% 13.02/13.18 tff(s33_type, type, (
% 13.02/13.18 s33: $i)).
% 13.02/13.18 tff(s32_type, type, (
% 13.02/13.18 s32: $i)).
% 13.02/13.18 tff(s31_type, type, (
% 13.02/13.18 s31: $i)).
% 13.02/13.18 tff(s30_type, type, (
% 13.02/13.18 s30: $i)).
% 13.02/13.18 tff(s29_type, type, (
% 13.02/13.18 s29: $i)).
% 13.02/13.18 tff(s28_type, type, (
% 13.02/13.18 s28: $i)).
% 13.02/13.18 tff(s27_type, type, (
% 13.02/13.18 s27: $i)).
% 13.02/13.18 tff(s26_type, type, (
% 13.02/13.18 s26: $i)).
% 13.02/13.18 tff(s25_type, type, (
% 13.02/13.18 s25: $i)).
% 13.02/13.18 tff(s24_type, type, (
% 13.02/13.18 s24: $i)).
% 13.02/13.18 tff(s23_type, type, (
% 13.02/13.18 s23: $i)).
% 13.02/13.18 tff(s22_type, type, (
% 13.02/13.18 s22: $i)).
% 13.02/13.18 tff(s21_type, type, (
% 13.02/13.18 s21: $i)).
% 13.02/13.18 tff(s20_type, type, (
% 13.02/13.18 s20: $i)).
% 13.02/13.18 tff(s19_type, type, (
% 13.02/13.18 s19: $i)).
% 13.02/13.18 tff(s18_type, type, (
% 13.02/13.18 s18: $i)).
% 13.02/13.18 tff(s17_type, type, (
% 13.02/13.18 s17: $i)).
% 13.02/13.18 tff(s16_type, type, (
% 13.02/13.18 s16: $i)).
% 13.02/13.18 tff(s15_type, type, (
% 13.02/13.18 s15: $i)).
% 13.02/13.18 tff(s14_type, type, (
% 13.02/13.18 s14: $i)).
% 13.02/13.18 tff(s13_type, type, (
% 13.02/13.18 s13: $i)).
% 13.02/13.18 tff(s12_type, type, (
% 13.02/13.18 s12: $i)).
% 13.02/13.18 tff(s11_type, type, (
% 13.02/13.18 s11: $i)).
% 13.02/13.18 tff(s10_type, type, (
% 13.02/13.18 s10: $i)).
% 13.02/13.18 tff(s9_type, type, (
% 13.02/13.18 s9: $i)).
% 13.02/13.18 tff(s8_type, type, (
% 13.02/13.18 s8: $i)).
% 13.02/13.18 tff(s7_type, type, (
% 13.02/13.18 s7: $i)).
% 13.02/13.18 tff(s6_type, type, (
% 13.02/13.18 s6: $i)).
% 13.02/13.18 tff(s5_type, type, (
% 13.02/13.18 s5: $i)).
% 13.02/13.18 tff(s4_type, type, (
% 13.02/13.18 s4: $i)).
% 13.02/13.18 tff(s3_type, type, (
% 13.02/13.18 s3: $i)).
% 13.02/13.18 tff(s2_type, type, (
% 13.02/13.18 s2: $i)).
% 13.02/13.18 tff(s1_type, type, (
% 13.02/13.18 s1: $i)).
% 13.02/13.18 tff(s0_type, type, (
% 13.02/13.18 s0: $i)).
% 13.02/13.18 tff(succ_type, type, (
% 13.02/13.18 succ: ( $i * $i ) > $o)).
% 13.02/13.18 tff(s55_type, type, (
% 13.02/13.18 s55: $i)).
% 13.02/13.18 tff(s54_type, type, (
% 13.02/13.18 s54: $i)).
% 13.02/13.18 tff(s53_type, type, (
% 13.02/13.18 s53: $i)).
% 13.02/13.18 tff(s52_type, type, (
% 13.02/13.18 s52: $i)).
% 13.02/13.18 tff(s57_type, type, (
% 13.02/13.18 s57: $i)).
% 13.02/13.18 tff(s58_type, type, (
% 13.02/13.18 s58: $i)).
% 13.02/13.18 tff(xuntil7_type, type, (
% 13.02/13.18 xuntil7: $i > $o)).
% 13.02/13.18 tff(until6_type, type, (
% 13.02/13.18 until6: $i > $o)).
% 13.02/13.18 tff(until2p8_type, type, (
% 13.02/13.18 until2p8: $i > $o)).
% 13.02/13.18 tff(xuntil2p9_type, type, (
% 13.02/13.18 xuntil2p9: $i > $o)).
% 13.02/13.18 tff(last_type, type, (
% 13.02/13.18 last: $i > $o)).
% 13.02/13.18 tff(loop_type, type, (
% 13.02/13.18 loop: $o)).
% 13.02/13.18 tff(1,assumption,(m_counter_cell_v_value(c_bit0, s0)), introduced(assumption)).
% 13.02/13.18 tff(2,plain,
% 13.02/13.18 (^[I0: $i] : refl((~m_counter_cell_v_value(I0, s0)) <=> (~m_counter_cell_v_value(I0, s0)))),
% 13.02/13.18 inference(bind,[status(th)],[])).
% 13.02/13.18 tff(3,plain,
% 13.02/13.18 (![I0: $i] : (~m_counter_cell_v_value(I0, s0)) <=> ![I0: $i] : (~m_counter_cell_v_value(I0, s0))),
% 13.02/13.18 inference(quant_intro,[status(thm)],[2])).
% 13.02/13.18 tff(4,plain,
% 13.02/13.18 (![I0: $i] : (~m_counter_cell_v_value(I0, s0)) <=> ![I0: $i] : (~m_counter_cell_v_value(I0, s0))),
% 13.02/13.18 inference(rewrite,[status(thm)],[])).
% 13.02/13.18 tff(5,axiom,(![I0: $i] : (~m_counter_cell_v_value(I0, s0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_counter_cell_1')).
% 13.02/13.18 tff(6,plain,
% 13.02/13.18 (![I0: $i] : (~m_counter_cell_v_value(I0, s0))),
% 13.02/13.18 inference(modus_ponens,[status(thm)],[5, 4])).
% 13.02/13.18 tff(7,plain,(
% 13.02/13.18 ![I0: $i] : (~m_counter_cell_v_value(I0, s0))),
% 13.02/13.18 inference(skolemize,[status(sab)],[6])).
% 13.02/13.18 tff(8,plain,
% 13.02/13.18 (![I0: $i] : (~m_counter_cell_v_value(I0, s0))),
% 13.02/13.18 inference(modus_ponens,[status(thm)],[7, 3])).
% 13.02/13.18 tff(9,plain,
% 13.02/13.18 ((~![I0: $i] : (~m_counter_cell_v_value(I0, s0))) | (~m_counter_cell_v_value(c_bit0, s0))),
% 13.02/13.18 inference(quant_inst,[status(thm)],[])).
% 13.02/13.18 tff(10,plain,
% 13.02/13.18 ($false),
% 13.02/13.18 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 13.02/13.18 tff(11,plain,(~m_counter_cell_v_value(c_bit0, s0)), inference(lemma,lemma(discharge,[]))).
% 13.02/13.18 tff(12,plain,
% 13.02/13.18 (^[X: $i] : refl(m_counter_cell_v_carry_in(c_bit0, X) <=> m_counter_cell_v_carry_in(c_bit0, X))),
% 13.02/13.18 inference(bind,[status(th)],[])).
% 13.02/13.18 tff(13,plain,
% 13.02/13.18 (![X: $i] : m_counter_cell_v_carry_in(c_bit0, X) <=> ![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)),
% 13.02/13.18 inference(quant_intro,[status(thm)],[12])).
% 13.02/13.18 tff(14,plain,
% 13.02/13.18 (![X: $i] : m_counter_cell_v_carry_in(c_bit0, X) <=> ![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)),
% 13.02/13.18 inference(rewrite,[status(thm)],[])).
% 13.02/13.18 tff(15,axiom,(![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_1')).
% 13.02/13.18 tff(16,plain,
% 13.02/13.18 (![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)),
% 13.02/13.18 inference(modus_ponens,[status(thm)],[15, 14])).
% 13.02/13.18 tff(17,plain,(
% 13.02/13.18 ![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)),
% 13.02/13.18 inference(skolemize,[status(sab)],[16])).
% 13.02/13.18 tff(18,plain,
% 13.02/13.18 (![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)),
% 13.02/13.18 inference(modus_ponens,[status(thm)],[17, 13])).
% 13.02/13.18 tff(19,plain,
% 13.02/13.18 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s0)),
% 13.02/13.18 inference(quant_inst,[status(thm)],[])).
% 13.02/13.18 tff(20,plain,
% 13.02/13.18 (m_counter_cell_v_carry_in(c_bit0, s0)),
% 13.02/13.18 inference(unit_resolution,[status(thm)],[19, 18])).
% 13.02/13.18 tff(21,plain,
% 13.02/13.18 (^[I0: $i, X: $i] : refl(((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X)) <=> ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X)))),
% 13.02/13.18 inference(bind,[status(th)],[])).
% 13.02/13.18 tff(22,plain,
% 13.02/13.18 (![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X)) <=> ![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))),
% 13.02/13.18 inference(quant_intro,[status(thm)],[21])).
% 13.02/13.18 tff(23,plain,
% 13.02/13.18 (![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X)) <=> ![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))),
% 13.02/13.18 inference(rewrite,[status(thm)],[])).
% 13.02/13.18 tff(24,plain,
% 13.02/13.18 (^[I0: $i, X: $i] : trans(monotonicity(rewrite((m_counter_cell_v_value(I0, X) | (~m_counter_cell_v_carry_in(I0, X))) <=> ((~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))), (((m_counter_cell_v_value(I0, X) | (~m_counter_cell_v_carry_in(I0, X))) | (~node1(I0, X))) <=> (((~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X)) | (~node1(I0, X))))), rewrite((((~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X)) | (~node1(I0, X))) <=> ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))), (((m_counter_cell_v_value(I0, X) | (~m_counter_cell_v_carry_in(I0, X))) | (~node1(I0, X))) <=> ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))))),
% 13.02/13.18 inference(bind,[status(th)],[])).
% 13.02/13.18 tff(25,plain,
% 13.02/13.18 (![I0: $i, X: $i] : ((m_counter_cell_v_value(I0, X) | (~m_counter_cell_v_carry_in(I0, X))) | (~node1(I0, X))) <=> ![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))),
% 13.02/13.18 inference(quant_intro,[status(thm)],[24])).
% 13.02/13.18 tff(26,axiom,(![I0: $i, X: $i] : ((m_counter_cell_v_value(I0, X) | (~m_counter_cell_v_carry_in(I0, X))) | (~node1(I0, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_counter_cell_2')).
% 13.02/13.18 tff(27,plain,
% 13.02/13.18 (![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))),
% 13.02/13.18 inference(modus_ponens,[status(thm)],[26, 25])).
% 13.02/13.18 tff(28,plain,
% 13.02/13.18 (![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))),
% 13.02/13.18 inference(modus_ponens,[status(thm)],[27, 23])).
% 13.02/13.18 tff(29,plain,(
% 13.02/13.18 ![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))),
% 13.02/13.18 inference(skolemize,[status(sab)],[28])).
% 13.02/13.18 tff(30,plain,
% 13.02/13.18 (![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))),
% 13.02/13.18 inference(modus_ponens,[status(thm)],[29, 22])).
% 13.02/13.18 tff(31,plain,
% 13.02/13.18 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s0)) | (~node1(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s0)) | (~node1(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0))),
% 13.02/13.18 inference(rewrite,[status(thm)],[])).
% 13.02/13.18 tff(32,plain,
% 13.02/13.18 (((~node1(c_bit0, s0)) | (~m_counter_cell_v_carry_in(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s0)) | (~node1(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0))),
% 13.02/13.18 inference(rewrite,[status(thm)],[])).
% 13.02/13.18 tff(33,plain,
% 13.02/13.18 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s0)) | (~m_counter_cell_v_carry_in(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s0)) | (~node1(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0)))),
% 13.02/13.18 inference(monotonicity,[status(thm)],[32])).
% 13.02/13.18 tff(34,plain,
% 13.02/13.18 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s0)) | (~m_counter_cell_v_carry_in(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s0)) | (~node1(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0))),
% 13.02/13.18 inference(transitivity,[status(thm)],[33, 31])).
% 13.02/13.18 tff(35,plain,
% 13.02/13.18 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s0)) | (~m_counter_cell_v_carry_in(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0))),
% 13.02/13.18 inference(quant_inst,[status(thm)],[])).
% 13.02/13.18 tff(36,plain,
% 13.02/13.18 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s0)) | (~node1(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0)),
% 13.02/13.18 inference(modus_ponens,[status(thm)],[35, 34])).
% 13.02/13.18 tff(37,plain,
% 13.02/13.18 ((~node1(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0)),
% 13.02/13.18 inference(unit_resolution,[status(thm)],[36, 30, 20])).
% 13.02/13.18 tff(38,plain,
% 13.02/13.18 (~node1(c_bit0, s0)),
% 13.02/13.18 inference(unit_resolution,[status(thm)],[37, 11])).
% 13.02/13.18 tff(39,plain,
% 13.02/13.18 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | trans(X, Y)) <=> ((~succ(X, Y)) | trans(X, Y)))),
% 13.02/13.18 inference(bind,[status(th)],[])).
% 13.02/13.18 tff(40,plain,
% 13.02/13.18 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 13.02/13.18 inference(quant_intro,[status(thm)],[39])).
% 13.02/13.18 tff(41,plain,
% 13.02/13.18 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 13.02/13.18 inference(rewrite,[status(thm)],[])).
% 13.02/13.18 tff(42,axiom,(![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound61')).
% 13.02/13.18 tff(43,plain,
% 13.02/13.18 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 13.02/13.18 inference(modus_ponens,[status(thm)],[42, 41])).
% 13.02/13.18 tff(44,plain,(
% 13.02/13.18 ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 13.02/13.18 inference(skolemize,[status(sab)],[43])).
% 13.02/13.18 tff(45,plain,
% 13.02/13.18 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 13.02/13.18 inference(modus_ponens,[status(thm)],[44, 40])).
% 13.02/13.18 tff(46,plain,
% 13.02/13.18 (succ(s0, s1) <=> succ(s0, s1)),
% 13.02/13.18 inference(rewrite,[status(thm)],[])).
% 13.02/13.18 tff(47,axiom,(succ(s0, s1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound1')).
% 13.02/13.18 tff(48,plain,
% 13.02/13.18 (succ(s0, s1)),
% 13.02/13.18 inference(modus_ponens,[status(thm)],[47, 46])).
% 13.02/13.18 tff(49,plain,
% 13.02/13.18 (((~![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))),
% 13.02/13.18 inference(rewrite,[status(thm)],[])).
% 13.02/13.18 tff(50,plain,
% 13.02/13.18 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s0, s1)) | trans(s0, s1))),
% 13.02/13.18 inference(quant_inst,[status(thm)],[])).
% 13.02/13.18 tff(51,plain,
% 13.02/13.18 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s0, s1)) | trans(s0, s1)),
% 13.02/13.18 inference(modus_ponens,[status(thm)],[50, 49])).
% 13.02/13.18 tff(52,plain,
% 13.02/13.18 (trans(s0, s1)),
% 13.02/13.18 inference(unit_resolution,[status(thm)],[51, 48, 45])).
% 13.02/13.18 tff(53,plain,
% 13.02/13.18 (^[Y: $i, I0: $i, X: $i] : refl(((~trans(X, Y)) | node3(I0, X, Y)) <=> ((~trans(X, Y)) | node3(I0, X, Y)))),
% 13.02/13.18 inference(bind,[status(th)],[])).
% 13.02/13.18 tff(54,plain,
% 13.02/13.18 (![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y)) <=> ![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))),
% 13.02/13.18 inference(quant_intro,[status(thm)],[53])).
% 13.02/13.18 tff(55,plain,
% 13.02/13.18 (![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y)) <=> ![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))),
% 13.02/13.18 inference(rewrite,[status(thm)],[])).
% 13.02/13.18 tff(56,axiom,(![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_counter_cell_8')).
% 13.02/13.18 tff(57,plain,
% 13.02/13.18 (![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))),
% 13.02/13.18 inference(modus_ponens,[status(thm)],[56, 55])).
% 13.02/13.18 tff(58,plain,(
% 13.02/13.18 ![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))),
% 13.02/13.18 inference(skolemize,[status(sab)],[57])).
% 13.02/13.18 tff(59,plain,
% 13.02/13.18 (![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))),
% 13.02/13.18 inference(modus_ponens,[status(thm)],[58, 54])).
% 13.02/13.18 tff(60,plain,
% 13.02/13.18 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s0, s1)) | node3(c_bit0, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s0, s1)) | node3(c_bit0, s0, s1))),
% 13.02/13.18 inference(rewrite,[status(thm)],[])).
% 13.02/13.18 tff(61,plain,
% 13.02/13.18 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s0, s1)) | node3(c_bit0, s0, s1))),
% 13.02/13.18 inference(quant_inst,[status(thm)],[])).
% 13.02/13.18 tff(62,plain,
% 13.02/13.18 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s0, s1)) | node3(c_bit0, s0, s1)),
% 13.02/13.18 inference(modus_ponens,[status(thm)],[61, 60])).
% 13.02/13.18 tff(63,plain,
% 13.02/13.18 (node3(c_bit0, s0, s1)),
% 13.02/13.18 inference(unit_resolution,[status(thm)],[62, 59, 52])).
% 13.02/13.18 tff(64,plain,
% 13.02/13.18 (^[Y: $i, I0: $i, X: $i] : refl((node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y)) <=> (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y)))),
% 13.02/13.18 inference(bind,[status(th)],[])).
% 13.02/13.18 tff(65,plain,
% 13.02/13.18 (![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y)) <=> ![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))),
% 13.02/13.18 inference(quant_intro,[status(thm)],[64])).
% 13.02/13.18 tff(66,plain,
% 13.02/13.18 (![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y)) <=> ![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))),
% 13.02/13.18 inference(rewrite,[status(thm)],[])).
% 13.02/13.18 tff(67,plain,
% 13.02/13.18 (^[Y: $i, I0: $i, X: $i] : rewrite(((m_counter_cell_v_value(I0, Y) | node1(I0, X)) | (~node3(I0, X, Y))) <=> (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y)))),
% 13.02/13.18 inference(bind,[status(th)],[])).
% 13.02/13.18 tff(68,plain,
% 13.02/13.18 (![Y: $i, I0: $i, X: $i] : ((m_counter_cell_v_value(I0, Y) | node1(I0, X)) | (~node3(I0, X, Y))) <=> ![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))),
% 13.02/13.18 inference(quant_intro,[status(thm)],[67])).
% 13.02/13.18 tff(69,axiom,(![Y: $i, I0: $i, X: $i] : ((m_counter_cell_v_value(I0, Y) | node1(I0, X)) | (~node3(I0, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_counter_cell_6')).
% 13.04/13.19 tff(70,plain,
% 13.04/13.19 (![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[69, 68])).
% 13.04/13.19 tff(71,plain,
% 13.04/13.19 (![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[70, 66])).
% 13.04/13.19 tff(72,plain,(
% 13.04/13.19 ![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))),
% 13.04/13.19 inference(skolemize,[status(sab)],[71])).
% 13.04/13.19 tff(73,plain,
% 13.04/13.19 (![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[72, 65])).
% 13.04/13.19 tff(74,plain,
% 13.04/13.19 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s0) | m_counter_cell_v_value(c_bit0, s1) | (~node3(c_bit0, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit0, s0) | m_counter_cell_v_value(c_bit0, s1) | (~node3(c_bit0, s0, s1)))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(75,plain,
% 13.04/13.19 ((node1(c_bit0, s0) | (~node3(c_bit0, s0, s1)) | m_counter_cell_v_value(c_bit0, s1)) <=> (node1(c_bit0, s0) | m_counter_cell_v_value(c_bit0, s1) | (~node3(c_bit0, s0, s1)))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(76,plain,
% 13.04/13.19 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s0) | (~node3(c_bit0, s0, s1)) | m_counter_cell_v_value(c_bit0, s1))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s0) | m_counter_cell_v_value(c_bit0, s1) | (~node3(c_bit0, s0, s1))))),
% 13.04/13.19 inference(monotonicity,[status(thm)],[75])).
% 13.04/13.19 tff(77,plain,
% 13.04/13.19 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s0) | (~node3(c_bit0, s0, s1)) | m_counter_cell_v_value(c_bit0, s1))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit0, s0) | m_counter_cell_v_value(c_bit0, s1) | (~node3(c_bit0, s0, s1)))),
% 13.04/13.19 inference(transitivity,[status(thm)],[76, 74])).
% 13.04/13.19 tff(78,plain,
% 13.04/13.19 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s0) | (~node3(c_bit0, s0, s1)) | m_counter_cell_v_value(c_bit0, s1))),
% 13.04/13.19 inference(quant_inst,[status(thm)],[])).
% 13.04/13.19 tff(79,plain,
% 13.04/13.19 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit0, s0) | m_counter_cell_v_value(c_bit0, s1) | (~node3(c_bit0, s0, s1))),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[78, 77])).
% 13.04/13.19 tff(80,plain,
% 13.04/13.19 (node1(c_bit0, s0) | m_counter_cell_v_value(c_bit0, s1)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[79, 73, 63])).
% 13.04/13.19 tff(81,plain,
% 13.04/13.19 (m_counter_cell_v_value(c_bit0, s1)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[80, 38])).
% 13.04/13.19 tff(82,plain,
% 13.04/13.19 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s1)),
% 13.04/13.19 inference(quant_inst,[status(thm)],[])).
% 13.04/13.19 tff(83,plain,
% 13.04/13.19 (m_counter_cell_v_carry_in(c_bit0, s1)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[82, 18])).
% 13.04/13.19 tff(84,plain,
% 13.04/13.19 (^[I0: $i, X: $i] : refl(((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X))) <=> ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X))))),
% 13.04/13.19 inference(bind,[status(th)],[])).
% 13.04/13.19 tff(85,plain,
% 13.04/13.19 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X))) <=> ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))),
% 13.04/13.19 inference(quant_intro,[status(thm)],[84])).
% 13.04/13.19 tff(86,plain,
% 13.04/13.19 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X))) <=> ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(87,plain,
% 13.04/13.19 (^[I0: $i, X: $i] : trans(monotonicity(rewrite(((~m_counter_cell_v_value(I0, X)) | (~m_counter_cell_v_carry_in(I0, X))) <=> ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)))), ((((~m_counter_cell_v_value(I0, X)) | (~m_counter_cell_v_carry_in(I0, X))) | (~node2(I0, X))) <=> (((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X))) | (~node2(I0, X))))), rewrite((((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X))) | (~node2(I0, X))) <=> ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))), ((((~m_counter_cell_v_value(I0, X)) | (~m_counter_cell_v_carry_in(I0, X))) | (~node2(I0, X))) <=> ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))))),
% 13.04/13.19 inference(bind,[status(th)],[])).
% 13.04/13.19 tff(88,plain,
% 13.04/13.19 (![I0: $i, X: $i] : (((~m_counter_cell_v_value(I0, X)) | (~m_counter_cell_v_carry_in(I0, X))) | (~node2(I0, X))) <=> ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))),
% 13.04/13.19 inference(quant_intro,[status(thm)],[87])).
% 13.04/13.19 tff(89,axiom,(![I0: $i, X: $i] : (((~m_counter_cell_v_value(I0, X)) | (~m_counter_cell_v_carry_in(I0, X))) | (~node2(I0, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_counter_cell_5')).
% 13.04/13.19 tff(90,plain,
% 13.04/13.19 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[89, 88])).
% 13.04/13.19 tff(91,plain,
% 13.04/13.19 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[90, 86])).
% 13.04/13.19 tff(92,plain,(
% 13.04/13.19 ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))),
% 13.04/13.19 inference(skolemize,[status(sab)],[91])).
% 13.04/13.19 tff(93,plain,
% 13.04/13.19 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[92, 85])).
% 13.04/13.19 tff(94,plain,
% 13.04/13.19 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s1)) | (~m_counter_cell_v_value(c_bit0, s1)) | (~node2(c_bit0, s1)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s1)) | (~m_counter_cell_v_value(c_bit0, s1)) | (~node2(c_bit0, s1)))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(95,plain,
% 13.04/13.19 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s1)) | (~m_counter_cell_v_value(c_bit0, s1)) | (~node2(c_bit0, s1)))),
% 13.04/13.19 inference(quant_inst,[status(thm)],[])).
% 13.04/13.19 tff(96,plain,
% 13.04/13.19 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s1)) | (~m_counter_cell_v_value(c_bit0, s1)) | (~node2(c_bit0, s1))),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[95, 94])).
% 13.04/13.19 tff(97,plain,
% 13.04/13.19 ((~m_counter_cell_v_value(c_bit0, s1)) | (~node2(c_bit0, s1))),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[96, 93, 83])).
% 13.04/13.19 tff(98,plain,
% 13.04/13.19 (~node2(c_bit0, s1)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[97, 81])).
% 13.04/13.19 tff(99,assumption,(~node3(c_bit0, s1, s2)), introduced(assumption)).
% 13.04/13.19 tff(100,plain,
% 13.04/13.19 (succ(s1, s2) <=> succ(s1, s2)),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(101,axiom,(succ(s1, s2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound2')).
% 13.04/13.19 tff(102,plain,
% 13.04/13.19 (succ(s1, s2)),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[101, 100])).
% 13.04/13.19 tff(103,plain,
% 13.04/13.19 (((~![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))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(104,plain,
% 13.04/13.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s1, s2)) | trans(s1, s2))),
% 13.04/13.19 inference(quant_inst,[status(thm)],[])).
% 13.04/13.19 tff(105,plain,
% 13.04/13.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s1, s2)) | trans(s1, s2)),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[104, 103])).
% 13.04/13.19 tff(106,plain,
% 13.04/13.19 (trans(s1, s2)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[105, 102, 45])).
% 13.04/13.19 tff(107,plain,
% 13.04/13.19 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s1, s2)) | node3(c_bit0, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s1, s2)) | node3(c_bit0, s1, s2))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(108,plain,
% 13.04/13.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s1, s2)) | node3(c_bit0, s1, s2))),
% 13.04/13.19 inference(quant_inst,[status(thm)],[])).
% 13.04/13.19 tff(109,plain,
% 13.04/13.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s1, s2)) | node3(c_bit0, s1, s2)),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[108, 107])).
% 13.04/13.19 tff(110,plain,
% 13.04/13.19 ($false),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[109, 59, 106, 99])).
% 13.04/13.19 tff(111,plain,(node3(c_bit0, s1, s2)), inference(lemma,lemma(discharge,[]))).
% 13.04/13.19 tff(112,plain,
% 13.04/13.19 (^[Y: $i, I0: $i, X: $i] : refl((node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y))) <=> (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y))))),
% 13.04/13.19 inference(bind,[status(th)],[])).
% 13.04/13.19 tff(113,plain,
% 13.04/13.19 (![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y))) <=> ![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))),
% 13.04/13.19 inference(quant_intro,[status(thm)],[112])).
% 13.04/13.19 tff(114,plain,
% 13.04/13.19 (![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y))) <=> ![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(115,plain,
% 13.04/13.19 (^[Y: $i, I0: $i, X: $i] : rewrite((((~m_counter_cell_v_value(I0, Y)) | node2(I0, X)) | (~node3(I0, X, Y))) <=> (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y))))),
% 13.04/13.19 inference(bind,[status(th)],[])).
% 13.04/13.19 tff(116,plain,
% 13.04/13.19 (![Y: $i, I0: $i, X: $i] : (((~m_counter_cell_v_value(I0, Y)) | node2(I0, X)) | (~node3(I0, X, Y))) <=> ![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))),
% 13.04/13.19 inference(quant_intro,[status(thm)],[115])).
% 13.04/13.19 tff(117,axiom,(![Y: $i, I0: $i, X: $i] : (((~m_counter_cell_v_value(I0, Y)) | node2(I0, X)) | (~node3(I0, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_counter_cell_7')).
% 13.04/13.19 tff(118,plain,
% 13.04/13.19 (![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[117, 116])).
% 13.04/13.19 tff(119,plain,
% 13.04/13.19 (![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[118, 114])).
% 13.04/13.19 tff(120,plain,(
% 13.04/13.19 ![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))),
% 13.04/13.19 inference(skolemize,[status(sab)],[119])).
% 13.04/13.19 tff(121,plain,
% 13.04/13.19 (![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[120, 113])).
% 13.04/13.19 tff(122,plain,
% 13.04/13.19 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s2)) | node2(c_bit0, s1) | (~node3(c_bit0, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s2)) | node2(c_bit0, s1) | (~node3(c_bit0, s1, s2)))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(123,plain,
% 13.04/13.19 ((node2(c_bit0, s1) | (~node3(c_bit0, s1, s2)) | (~m_counter_cell_v_value(c_bit0, s2))) <=> ((~m_counter_cell_v_value(c_bit0, s2)) | node2(c_bit0, s1) | (~node3(c_bit0, s1, s2)))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(124,plain,
% 13.04/13.19 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s1) | (~node3(c_bit0, s1, s2)) | (~m_counter_cell_v_value(c_bit0, s2)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s2)) | node2(c_bit0, s1) | (~node3(c_bit0, s1, s2))))),
% 13.04/13.19 inference(monotonicity,[status(thm)],[123])).
% 13.04/13.19 tff(125,plain,
% 13.04/13.19 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s1) | (~node3(c_bit0, s1, s2)) | (~m_counter_cell_v_value(c_bit0, s2)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s2)) | node2(c_bit0, s1) | (~node3(c_bit0, s1, s2)))),
% 13.04/13.19 inference(transitivity,[status(thm)],[124, 122])).
% 13.04/13.19 tff(126,plain,
% 13.04/13.19 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s1) | (~node3(c_bit0, s1, s2)) | (~m_counter_cell_v_value(c_bit0, s2)))),
% 13.04/13.19 inference(quant_inst,[status(thm)],[])).
% 13.04/13.19 tff(127,plain,
% 13.04/13.19 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s2)) | node2(c_bit0, s1) | (~node3(c_bit0, s1, s2))),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[126, 125])).
% 13.04/13.19 tff(128,plain,
% 13.04/13.19 ((~m_counter_cell_v_value(c_bit0, s2)) | node2(c_bit0, s1)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[127, 121, 111])).
% 13.04/13.19 tff(129,plain,
% 13.04/13.19 (~m_counter_cell_v_value(c_bit0, s2)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[128, 98])).
% 13.04/13.19 tff(130,plain,
% 13.04/13.19 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s2)),
% 13.04/13.19 inference(quant_inst,[status(thm)],[])).
% 13.04/13.19 tff(131,plain,
% 13.04/13.19 (m_counter_cell_v_carry_in(c_bit0, s2)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[130, 18])).
% 13.04/13.19 tff(132,plain,
% 13.04/13.19 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s2)) | (~m_counter_cell_v_carry_in(c_bit0, s2)) | m_counter_cell_v_value(c_bit0, s2))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~node1(c_bit0, s2)) | (~m_counter_cell_v_carry_in(c_bit0, s2)) | m_counter_cell_v_value(c_bit0, s2))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(133,plain,
% 13.04/13.19 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s2)) | (~m_counter_cell_v_carry_in(c_bit0, s2)) | m_counter_cell_v_value(c_bit0, s2))),
% 13.04/13.19 inference(quant_inst,[status(thm)],[])).
% 13.04/13.19 tff(134,plain,
% 13.04/13.19 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~node1(c_bit0, s2)) | (~m_counter_cell_v_carry_in(c_bit0, s2)) | m_counter_cell_v_value(c_bit0, s2)),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[133, 132])).
% 13.04/13.19 tff(135,plain,
% 13.04/13.19 ((~node1(c_bit0, s2)) | m_counter_cell_v_value(c_bit0, s2)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[134, 30, 131])).
% 13.04/13.19 tff(136,plain,
% 13.04/13.19 (~node1(c_bit0, s2)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[135, 129])).
% 13.04/13.19 tff(137,plain,
% 13.04/13.19 (succ(s2, s3) <=> succ(s2, s3)),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(138,axiom,(succ(s2, s3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound3')).
% 13.04/13.19 tff(139,plain,
% 13.04/13.19 (succ(s2, s3)),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[138, 137])).
% 13.04/13.19 tff(140,plain,
% 13.04/13.19 (((~![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))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(141,plain,
% 13.04/13.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s2, s3)) | trans(s2, s3))),
% 13.04/13.19 inference(quant_inst,[status(thm)],[])).
% 13.04/13.19 tff(142,plain,
% 13.04/13.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s2, s3)) | trans(s2, s3)),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[141, 140])).
% 13.04/13.19 tff(143,plain,
% 13.04/13.19 (trans(s2, s3)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[142, 139, 45])).
% 13.04/13.19 tff(144,plain,
% 13.04/13.19 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s2, s3)) | node3(c_bit0, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s2, s3)) | node3(c_bit0, s2, s3))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(145,plain,
% 13.04/13.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s2, s3)) | node3(c_bit0, s2, s3))),
% 13.04/13.19 inference(quant_inst,[status(thm)],[])).
% 13.04/13.19 tff(146,plain,
% 13.04/13.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s2, s3)) | node3(c_bit0, s2, s3)),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[145, 144])).
% 13.04/13.19 tff(147,plain,
% 13.04/13.19 (node3(c_bit0, s2, s3)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[146, 59, 143])).
% 13.04/13.19 tff(148,plain,
% 13.04/13.19 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s3) | node1(c_bit0, s2) | (~node3(c_bit0, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s3) | node1(c_bit0, s2) | (~node3(c_bit0, s2, s3)))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(149,plain,
% 13.04/13.19 ((node1(c_bit0, s2) | (~node3(c_bit0, s2, s3)) | m_counter_cell_v_value(c_bit0, s3)) <=> (m_counter_cell_v_value(c_bit0, s3) | node1(c_bit0, s2) | (~node3(c_bit0, s2, s3)))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(150,plain,
% 13.04/13.19 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s2) | (~node3(c_bit0, s2, s3)) | m_counter_cell_v_value(c_bit0, s3))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s3) | node1(c_bit0, s2) | (~node3(c_bit0, s2, s3))))),
% 13.04/13.19 inference(monotonicity,[status(thm)],[149])).
% 13.04/13.19 tff(151,plain,
% 13.04/13.19 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s2) | (~node3(c_bit0, s2, s3)) | m_counter_cell_v_value(c_bit0, s3))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s3) | node1(c_bit0, s2) | (~node3(c_bit0, s2, s3)))),
% 13.04/13.19 inference(transitivity,[status(thm)],[150, 148])).
% 13.04/13.19 tff(152,plain,
% 13.04/13.19 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s2) | (~node3(c_bit0, s2, s3)) | m_counter_cell_v_value(c_bit0, s3))),
% 13.04/13.19 inference(quant_inst,[status(thm)],[])).
% 13.04/13.19 tff(153,plain,
% 13.04/13.19 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s3) | node1(c_bit0, s2) | (~node3(c_bit0, s2, s3))),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[152, 151])).
% 13.04/13.19 tff(154,plain,
% 13.04/13.19 (m_counter_cell_v_value(c_bit0, s3) | node1(c_bit0, s2)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[153, 73, 147])).
% 13.04/13.19 tff(155,plain,
% 13.04/13.19 (m_counter_cell_v_value(c_bit0, s3)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[154, 136])).
% 13.04/13.19 tff(156,plain,
% 13.04/13.19 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s3)),
% 13.04/13.19 inference(quant_inst,[status(thm)],[])).
% 13.04/13.19 tff(157,plain,
% 13.04/13.19 (m_counter_cell_v_carry_in(c_bit0, s3)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[156, 18])).
% 13.04/13.19 tff(158,plain,
% 13.04/13.19 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s3)) | (~m_counter_cell_v_value(c_bit0, s3)) | (~node2(c_bit0, s3)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s3)) | (~m_counter_cell_v_value(c_bit0, s3)) | (~node2(c_bit0, s3)))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(159,plain,
% 13.04/13.19 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s3)) | (~m_counter_cell_v_value(c_bit0, s3)) | (~node2(c_bit0, s3)))),
% 13.04/13.19 inference(quant_inst,[status(thm)],[])).
% 13.04/13.19 tff(160,plain,
% 13.04/13.19 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s3)) | (~m_counter_cell_v_value(c_bit0, s3)) | (~node2(c_bit0, s3))),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[159, 158])).
% 13.04/13.19 tff(161,plain,
% 13.04/13.19 ((~m_counter_cell_v_value(c_bit0, s3)) | (~node2(c_bit0, s3))),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[160, 93, 157])).
% 13.04/13.19 tff(162,plain,
% 13.04/13.19 (~node2(c_bit0, s3)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[161, 155])).
% 13.04/13.19 tff(163,plain,
% 13.04/13.19 (succ(s3, s4) <=> succ(s3, s4)),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(164,axiom,(succ(s3, s4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound4')).
% 13.04/13.19 tff(165,plain,
% 13.04/13.19 (succ(s3, s4)),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[164, 163])).
% 13.04/13.19 tff(166,plain,
% 13.04/13.19 (((~![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))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(167,plain,
% 13.04/13.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s3, s4)) | trans(s3, s4))),
% 13.04/13.19 inference(quant_inst,[status(thm)],[])).
% 13.04/13.19 tff(168,plain,
% 13.04/13.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s3, s4)) | trans(s3, s4)),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[167, 166])).
% 13.04/13.19 tff(169,plain,
% 13.04/13.19 (trans(s3, s4)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[168, 165, 45])).
% 13.04/13.19 tff(170,plain,
% 13.04/13.19 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s3, s4)) | node3(c_bit0, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s3, s4)) | node3(c_bit0, s3, s4))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(171,plain,
% 13.04/13.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s3, s4)) | node3(c_bit0, s3, s4))),
% 13.04/13.19 inference(quant_inst,[status(thm)],[])).
% 13.04/13.19 tff(172,plain,
% 13.04/13.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s3, s4)) | node3(c_bit0, s3, s4)),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[171, 170])).
% 13.04/13.19 tff(173,plain,
% 13.04/13.19 (node3(c_bit0, s3, s4)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[172, 59, 169])).
% 13.04/13.19 tff(174,plain,
% 13.04/13.19 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s3) | (~m_counter_cell_v_value(c_bit0, s4)) | (~node3(c_bit0, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s3) | (~m_counter_cell_v_value(c_bit0, s4)) | (~node3(c_bit0, s3, s4)))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(175,plain,
% 13.04/13.19 ((node2(c_bit0, s3) | (~node3(c_bit0, s3, s4)) | (~m_counter_cell_v_value(c_bit0, s4))) <=> (node2(c_bit0, s3) | (~m_counter_cell_v_value(c_bit0, s4)) | (~node3(c_bit0, s3, s4)))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(176,plain,
% 13.04/13.19 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s3) | (~node3(c_bit0, s3, s4)) | (~m_counter_cell_v_value(c_bit0, s4)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s3) | (~m_counter_cell_v_value(c_bit0, s4)) | (~node3(c_bit0, s3, s4))))),
% 13.04/13.19 inference(monotonicity,[status(thm)],[175])).
% 13.04/13.19 tff(177,plain,
% 13.04/13.19 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s3) | (~node3(c_bit0, s3, s4)) | (~m_counter_cell_v_value(c_bit0, s4)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s3) | (~m_counter_cell_v_value(c_bit0, s4)) | (~node3(c_bit0, s3, s4)))),
% 13.04/13.19 inference(transitivity,[status(thm)],[176, 174])).
% 13.04/13.19 tff(178,plain,
% 13.04/13.19 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s3) | (~node3(c_bit0, s3, s4)) | (~m_counter_cell_v_value(c_bit0, s4)))),
% 13.04/13.19 inference(quant_inst,[status(thm)],[])).
% 13.04/13.19 tff(179,plain,
% 13.04/13.19 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s3) | (~m_counter_cell_v_value(c_bit0, s4)) | (~node3(c_bit0, s3, s4))),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[178, 177])).
% 13.04/13.19 tff(180,plain,
% 13.04/13.19 (node2(c_bit0, s3) | (~m_counter_cell_v_value(c_bit0, s4))),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[179, 121, 173])).
% 13.04/13.19 tff(181,plain,
% 13.04/13.19 (~m_counter_cell_v_value(c_bit0, s4)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[180, 162])).
% 13.04/13.19 tff(182,plain,
% 13.04/13.19 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s4)),
% 13.04/13.19 inference(quant_inst,[status(thm)],[])).
% 13.04/13.19 tff(183,plain,
% 13.04/13.19 (m_counter_cell_v_carry_in(c_bit0, s4)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[182, 18])).
% 13.04/13.19 tff(184,plain,
% 13.04/13.19 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (m_counter_cell_v_value(c_bit0, s4) | (~node1(c_bit0, s4)) | (~m_counter_cell_v_carry_in(c_bit0, s4)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | m_counter_cell_v_value(c_bit0, s4) | (~node1(c_bit0, s4)) | (~m_counter_cell_v_carry_in(c_bit0, s4)))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(185,plain,
% 13.04/13.19 (((~node1(c_bit0, s4)) | (~m_counter_cell_v_carry_in(c_bit0, s4)) | m_counter_cell_v_value(c_bit0, s4)) <=> (m_counter_cell_v_value(c_bit0, s4) | (~node1(c_bit0, s4)) | (~m_counter_cell_v_carry_in(c_bit0, s4)))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(186,plain,
% 13.04/13.19 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s4)) | (~m_counter_cell_v_carry_in(c_bit0, s4)) | m_counter_cell_v_value(c_bit0, s4))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (m_counter_cell_v_value(c_bit0, s4) | (~node1(c_bit0, s4)) | (~m_counter_cell_v_carry_in(c_bit0, s4))))),
% 13.04/13.19 inference(monotonicity,[status(thm)],[185])).
% 13.04/13.19 tff(187,plain,
% 13.04/13.19 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s4)) | (~m_counter_cell_v_carry_in(c_bit0, s4)) | m_counter_cell_v_value(c_bit0, s4))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | m_counter_cell_v_value(c_bit0, s4) | (~node1(c_bit0, s4)) | (~m_counter_cell_v_carry_in(c_bit0, s4)))),
% 13.04/13.19 inference(transitivity,[status(thm)],[186, 184])).
% 13.04/13.19 tff(188,plain,
% 13.04/13.19 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s4)) | (~m_counter_cell_v_carry_in(c_bit0, s4)) | m_counter_cell_v_value(c_bit0, s4))),
% 13.04/13.19 inference(quant_inst,[status(thm)],[])).
% 13.04/13.19 tff(189,plain,
% 13.04/13.19 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | m_counter_cell_v_value(c_bit0, s4) | (~node1(c_bit0, s4)) | (~m_counter_cell_v_carry_in(c_bit0, s4))),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[188, 187])).
% 13.04/13.19 tff(190,plain,
% 13.04/13.19 (m_counter_cell_v_value(c_bit0, s4) | (~node1(c_bit0, s4))),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[189, 30, 183])).
% 13.04/13.19 tff(191,plain,
% 13.04/13.19 (~node1(c_bit0, s4)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[190, 181])).
% 13.04/13.19 tff(192,plain,
% 13.04/13.19 (succ(s4, s5) <=> succ(s4, s5)),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(193,axiom,(succ(s4, s5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound5')).
% 13.04/13.19 tff(194,plain,
% 13.04/13.19 (succ(s4, s5)),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[193, 192])).
% 13.04/13.19 tff(195,plain,
% 13.04/13.19 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s4, s5)) | trans(s4, s5))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s4, s5)) | trans(s4, s5))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(196,plain,
% 13.04/13.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s4, s5)) | trans(s4, s5))),
% 13.04/13.19 inference(quant_inst,[status(thm)],[])).
% 13.04/13.19 tff(197,plain,
% 13.04/13.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s4, s5)) | trans(s4, s5)),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[196, 195])).
% 13.04/13.19 tff(198,plain,
% 13.04/13.19 (trans(s4, s5)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[197, 194, 45])).
% 13.04/13.19 tff(199,plain,
% 13.04/13.19 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s4, s5)) | node3(c_bit0, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s4, s5)) | node3(c_bit0, s4, s5))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(200,plain,
% 13.04/13.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s4, s5)) | node3(c_bit0, s4, s5))),
% 13.04/13.19 inference(quant_inst,[status(thm)],[])).
% 13.04/13.19 tff(201,plain,
% 13.04/13.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s4, s5)) | node3(c_bit0, s4, s5)),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[200, 199])).
% 13.04/13.19 tff(202,plain,
% 13.04/13.19 (node3(c_bit0, s4, s5)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[201, 59, 198])).
% 13.04/13.19 tff(203,plain,
% 13.04/13.19 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s5) | node1(c_bit0, s4) | (~node3(c_bit0, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s5) | node1(c_bit0, s4) | (~node3(c_bit0, s4, s5)))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(204,plain,
% 13.04/13.19 ((node1(c_bit0, s4) | (~node3(c_bit0, s4, s5)) | m_counter_cell_v_value(c_bit0, s5)) <=> (m_counter_cell_v_value(c_bit0, s5) | node1(c_bit0, s4) | (~node3(c_bit0, s4, s5)))),
% 13.04/13.19 inference(rewrite,[status(thm)],[])).
% 13.04/13.19 tff(205,plain,
% 13.04/13.19 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s4) | (~node3(c_bit0, s4, s5)) | m_counter_cell_v_value(c_bit0, s5))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s5) | node1(c_bit0, s4) | (~node3(c_bit0, s4, s5))))),
% 13.04/13.19 inference(monotonicity,[status(thm)],[204])).
% 13.04/13.19 tff(206,plain,
% 13.04/13.19 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s4) | (~node3(c_bit0, s4, s5)) | m_counter_cell_v_value(c_bit0, s5))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s5) | node1(c_bit0, s4) | (~node3(c_bit0, s4, s5)))),
% 13.04/13.19 inference(transitivity,[status(thm)],[205, 203])).
% 13.04/13.19 tff(207,plain,
% 13.04/13.19 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s4) | (~node3(c_bit0, s4, s5)) | m_counter_cell_v_value(c_bit0, s5))),
% 13.04/13.19 inference(quant_inst,[status(thm)],[])).
% 13.04/13.19 tff(208,plain,
% 13.04/13.19 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s5) | node1(c_bit0, s4) | (~node3(c_bit0, s4, s5))),
% 13.04/13.19 inference(modus_ponens,[status(thm)],[207, 206])).
% 13.04/13.19 tff(209,plain,
% 13.04/13.19 (m_counter_cell_v_value(c_bit0, s5) | node1(c_bit0, s4)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[208, 73, 202])).
% 13.04/13.19 tff(210,plain,
% 13.04/13.19 (m_counter_cell_v_value(c_bit0, s5)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[209, 191])).
% 13.04/13.19 tff(211,plain,
% 13.04/13.19 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s5)),
% 13.04/13.19 inference(quant_inst,[status(thm)],[])).
% 13.04/13.19 tff(212,plain,
% 13.04/13.19 (m_counter_cell_v_carry_in(c_bit0, s5)),
% 13.04/13.19 inference(unit_resolution,[status(thm)],[211, 18])).
% 13.04/13.19 tff(213,plain,
% 13.04/13.19 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s5)) | (~m_counter_cell_v_value(c_bit0, s5)) | (~node2(c_bit0, s5)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s5)) | (~m_counter_cell_v_value(c_bit0, s5)) | (~node2(c_bit0, s5)))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(214,plain,
% 13.04/13.20 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s5)) | (~m_counter_cell_v_value(c_bit0, s5)) | (~node2(c_bit0, s5)))),
% 13.04/13.20 inference(quant_inst,[status(thm)],[])).
% 13.04/13.20 tff(215,plain,
% 13.04/13.20 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s5)) | (~m_counter_cell_v_value(c_bit0, s5)) | (~node2(c_bit0, s5))),
% 13.04/13.20 inference(modus_ponens,[status(thm)],[214, 213])).
% 13.04/13.20 tff(216,plain,
% 13.04/13.20 ((~m_counter_cell_v_value(c_bit0, s5)) | (~node2(c_bit0, s5))),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[215, 93, 212])).
% 13.04/13.20 tff(217,plain,
% 13.04/13.20 (~node2(c_bit0, s5)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[216, 210])).
% 13.04/13.20 tff(218,plain,
% 13.04/13.20 (succ(s5, s6) <=> succ(s5, s6)),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(219,axiom,(succ(s5, s6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound6')).
% 13.04/13.20 tff(220,plain,
% 13.04/13.20 (succ(s5, s6)),
% 13.04/13.20 inference(modus_ponens,[status(thm)],[219, 218])).
% 13.04/13.20 tff(221,plain,
% 13.04/13.20 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s5, s6)) | trans(s5, s6))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s5, s6)) | trans(s5, s6))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(222,plain,
% 13.04/13.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s5, s6)) | trans(s5, s6))),
% 13.04/13.20 inference(quant_inst,[status(thm)],[])).
% 13.04/13.20 tff(223,plain,
% 13.04/13.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s5, s6)) | trans(s5, s6)),
% 13.04/13.20 inference(modus_ponens,[status(thm)],[222, 221])).
% 13.04/13.20 tff(224,plain,
% 13.04/13.20 (trans(s5, s6)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[223, 220, 45])).
% 13.04/13.20 tff(225,plain,
% 13.04/13.20 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s5, s6)) | node3(c_bit0, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s5, s6)) | node3(c_bit0, s5, s6))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(226,plain,
% 13.04/13.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s5, s6)) | node3(c_bit0, s5, s6))),
% 13.04/13.20 inference(quant_inst,[status(thm)],[])).
% 13.04/13.20 tff(227,plain,
% 13.04/13.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s5, s6)) | node3(c_bit0, s5, s6)),
% 13.04/13.20 inference(modus_ponens,[status(thm)],[226, 225])).
% 13.04/13.20 tff(228,plain,
% 13.04/13.20 (node3(c_bit0, s5, s6)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[227, 59, 224])).
% 13.04/13.20 tff(229,plain,
% 13.04/13.20 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s5) | (~m_counter_cell_v_value(c_bit0, s6)) | (~node3(c_bit0, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s5) | (~m_counter_cell_v_value(c_bit0, s6)) | (~node3(c_bit0, s5, s6)))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(230,plain,
% 13.04/13.20 ((node2(c_bit0, s5) | (~node3(c_bit0, s5, s6)) | (~m_counter_cell_v_value(c_bit0, s6))) <=> (node2(c_bit0, s5) | (~m_counter_cell_v_value(c_bit0, s6)) | (~node3(c_bit0, s5, s6)))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(231,plain,
% 13.04/13.20 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s5) | (~node3(c_bit0, s5, s6)) | (~m_counter_cell_v_value(c_bit0, s6)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s5) | (~m_counter_cell_v_value(c_bit0, s6)) | (~node3(c_bit0, s5, s6))))),
% 13.04/13.20 inference(monotonicity,[status(thm)],[230])).
% 13.04/13.20 tff(232,plain,
% 13.04/13.20 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s5) | (~node3(c_bit0, s5, s6)) | (~m_counter_cell_v_value(c_bit0, s6)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s5) | (~m_counter_cell_v_value(c_bit0, s6)) | (~node3(c_bit0, s5, s6)))),
% 13.04/13.20 inference(transitivity,[status(thm)],[231, 229])).
% 13.04/13.20 tff(233,plain,
% 13.04/13.20 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s5) | (~node3(c_bit0, s5, s6)) | (~m_counter_cell_v_value(c_bit0, s6)))),
% 13.04/13.20 inference(quant_inst,[status(thm)],[])).
% 13.04/13.20 tff(234,plain,
% 13.04/13.20 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s5) | (~m_counter_cell_v_value(c_bit0, s6)) | (~node3(c_bit0, s5, s6))),
% 13.04/13.20 inference(modus_ponens,[status(thm)],[233, 232])).
% 13.04/13.20 tff(235,plain,
% 13.04/13.20 (node2(c_bit0, s5) | (~m_counter_cell_v_value(c_bit0, s6))),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[234, 121, 228])).
% 13.04/13.20 tff(236,plain,
% 13.04/13.20 (~m_counter_cell_v_value(c_bit0, s6)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[235, 217])).
% 13.04/13.20 tff(237,plain,
% 13.04/13.20 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s6)),
% 13.04/13.20 inference(quant_inst,[status(thm)],[])).
% 13.04/13.20 tff(238,plain,
% 13.04/13.20 (m_counter_cell_v_carry_in(c_bit0, s6)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[237, 18])).
% 13.04/13.20 tff(239,plain,
% 13.04/13.20 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6) | (~node1(c_bit0, s6)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6) | (~node1(c_bit0, s6)))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(240,plain,
% 13.04/13.20 (((~node1(c_bit0, s6)) | (~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6) | (~node1(c_bit0, s6)))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(241,plain,
% 13.04/13.20 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s6)) | (~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6) | (~node1(c_bit0, s6))))),
% 13.04/13.20 inference(monotonicity,[status(thm)],[240])).
% 13.04/13.20 tff(242,plain,
% 13.04/13.20 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s6)) | (~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6) | (~node1(c_bit0, s6)))),
% 13.04/13.20 inference(transitivity,[status(thm)],[241, 239])).
% 13.04/13.20 tff(243,plain,
% 13.04/13.20 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s6)) | (~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6))),
% 13.04/13.20 inference(quant_inst,[status(thm)],[])).
% 13.04/13.20 tff(244,plain,
% 13.04/13.20 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6) | (~node1(c_bit0, s6))),
% 13.04/13.20 inference(modus_ponens,[status(thm)],[243, 242])).
% 13.04/13.20 tff(245,plain,
% 13.04/13.20 (m_counter_cell_v_value(c_bit0, s6) | (~node1(c_bit0, s6))),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[244, 30, 238])).
% 13.04/13.20 tff(246,plain,
% 13.04/13.20 (~node1(c_bit0, s6)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[245, 236])).
% 13.04/13.20 tff(247,plain,
% 13.04/13.20 (succ(s6, s7) <=> succ(s6, s7)),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(248,axiom,(succ(s6, s7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound7')).
% 13.04/13.20 tff(249,plain,
% 13.04/13.20 (succ(s6, s7)),
% 13.04/13.20 inference(modus_ponens,[status(thm)],[248, 247])).
% 13.04/13.20 tff(250,plain,
% 13.04/13.20 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s6, s7)) | trans(s6, s7))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s6, s7)) | trans(s6, s7))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(251,plain,
% 13.04/13.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s6, s7)) | trans(s6, s7))),
% 13.04/13.20 inference(quant_inst,[status(thm)],[])).
% 13.04/13.20 tff(252,plain,
% 13.04/13.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s6, s7)) | trans(s6, s7)),
% 13.04/13.20 inference(modus_ponens,[status(thm)],[251, 250])).
% 13.04/13.20 tff(253,plain,
% 13.04/13.20 (trans(s6, s7)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[252, 249, 45])).
% 13.04/13.20 tff(254,plain,
% 13.04/13.20 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s6, s7)) | node3(c_bit0, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s6, s7)) | node3(c_bit0, s6, s7))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(255,plain,
% 13.04/13.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s6, s7)) | node3(c_bit0, s6, s7))),
% 13.04/13.20 inference(quant_inst,[status(thm)],[])).
% 13.04/13.20 tff(256,plain,
% 13.04/13.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s6, s7)) | node3(c_bit0, s6, s7)),
% 13.04/13.20 inference(modus_ponens,[status(thm)],[255, 254])).
% 13.04/13.20 tff(257,plain,
% 13.04/13.20 (node3(c_bit0, s6, s7)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[256, 59, 253])).
% 13.04/13.20 tff(258,plain,
% 13.04/13.20 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s6) | m_counter_cell_v_value(c_bit0, s7) | (~node3(c_bit0, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit0, s6) | m_counter_cell_v_value(c_bit0, s7) | (~node3(c_bit0, s6, s7)))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(259,plain,
% 13.04/13.20 ((node1(c_bit0, s6) | (~node3(c_bit0, s6, s7)) | m_counter_cell_v_value(c_bit0, s7)) <=> (node1(c_bit0, s6) | m_counter_cell_v_value(c_bit0, s7) | (~node3(c_bit0, s6, s7)))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(260,plain,
% 13.04/13.20 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s6) | (~node3(c_bit0, s6, s7)) | m_counter_cell_v_value(c_bit0, s7))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s6) | m_counter_cell_v_value(c_bit0, s7) | (~node3(c_bit0, s6, s7))))),
% 13.04/13.20 inference(monotonicity,[status(thm)],[259])).
% 13.04/13.20 tff(261,plain,
% 13.04/13.20 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s6) | (~node3(c_bit0, s6, s7)) | m_counter_cell_v_value(c_bit0, s7))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit0, s6) | m_counter_cell_v_value(c_bit0, s7) | (~node3(c_bit0, s6, s7)))),
% 13.04/13.20 inference(transitivity,[status(thm)],[260, 258])).
% 13.04/13.20 tff(262,plain,
% 13.04/13.20 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s6) | (~node3(c_bit0, s6, s7)) | m_counter_cell_v_value(c_bit0, s7))),
% 13.04/13.20 inference(quant_inst,[status(thm)],[])).
% 13.04/13.20 tff(263,plain,
% 13.04/13.20 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit0, s6) | m_counter_cell_v_value(c_bit0, s7) | (~node3(c_bit0, s6, s7))),
% 13.04/13.20 inference(modus_ponens,[status(thm)],[262, 261])).
% 13.04/13.20 tff(264,plain,
% 13.04/13.20 (node1(c_bit0, s6) | m_counter_cell_v_value(c_bit0, s7)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[263, 73, 257])).
% 13.04/13.20 tff(265,plain,
% 13.04/13.20 (m_counter_cell_v_value(c_bit0, s7)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[264, 246])).
% 13.04/13.20 tff(266,plain,
% 13.04/13.20 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s7)),
% 13.04/13.20 inference(quant_inst,[status(thm)],[])).
% 13.04/13.20 tff(267,plain,
% 13.04/13.20 (m_counter_cell_v_carry_in(c_bit0, s7)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[266, 18])).
% 13.04/13.20 tff(268,plain,
% 13.04/13.20 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s7)) | (~m_counter_cell_v_value(c_bit0, s7)) | (~node2(c_bit0, s7)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s7)) | (~m_counter_cell_v_value(c_bit0, s7)) | (~node2(c_bit0, s7)))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(269,plain,
% 13.04/13.20 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s7)) | (~m_counter_cell_v_value(c_bit0, s7)) | (~node2(c_bit0, s7)))),
% 13.04/13.20 inference(quant_inst,[status(thm)],[])).
% 13.04/13.20 tff(270,plain,
% 13.04/13.20 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s7)) | (~m_counter_cell_v_value(c_bit0, s7)) | (~node2(c_bit0, s7))),
% 13.04/13.20 inference(modus_ponens,[status(thm)],[269, 268])).
% 13.04/13.20 tff(271,plain,
% 13.04/13.20 ((~m_counter_cell_v_value(c_bit0, s7)) | (~node2(c_bit0, s7))),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[270, 93, 267])).
% 13.04/13.20 tff(272,plain,
% 13.04/13.20 (~node2(c_bit0, s7)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[271, 265])).
% 13.04/13.20 tff(273,plain,
% 13.04/13.20 (succ(s7, s8) <=> succ(s7, s8)),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(274,axiom,(succ(s7, s8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound8')).
% 13.04/13.20 tff(275,plain,
% 13.04/13.20 (succ(s7, s8)),
% 13.04/13.20 inference(modus_ponens,[status(thm)],[274, 273])).
% 13.04/13.20 tff(276,plain,
% 13.04/13.20 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s7, s8)) | trans(s7, s8))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s7, s8)) | trans(s7, s8))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(277,plain,
% 13.04/13.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s7, s8)) | trans(s7, s8))),
% 13.04/13.20 inference(quant_inst,[status(thm)],[])).
% 13.04/13.20 tff(278,plain,
% 13.04/13.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s7, s8)) | trans(s7, s8)),
% 13.04/13.20 inference(modus_ponens,[status(thm)],[277, 276])).
% 13.04/13.20 tff(279,plain,
% 13.04/13.20 (trans(s7, s8)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[278, 275, 45])).
% 13.04/13.20 tff(280,plain,
% 13.04/13.20 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s7, s8)) | node3(c_bit0, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s7, s8)) | node3(c_bit0, s7, s8))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(281,plain,
% 13.04/13.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s7, s8)) | node3(c_bit0, s7, s8))),
% 13.04/13.20 inference(quant_inst,[status(thm)],[])).
% 13.04/13.20 tff(282,plain,
% 13.04/13.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s7, s8)) | node3(c_bit0, s7, s8)),
% 13.04/13.20 inference(modus_ponens,[status(thm)],[281, 280])).
% 13.04/13.20 tff(283,plain,
% 13.04/13.20 (node3(c_bit0, s7, s8)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[282, 59, 279])).
% 13.04/13.20 tff(284,plain,
% 13.04/13.20 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s8)) | node2(c_bit0, s7) | (~node3(c_bit0, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s8)) | node2(c_bit0, s7) | (~node3(c_bit0, s7, s8)))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(285,plain,
% 13.04/13.20 ((node2(c_bit0, s7) | (~node3(c_bit0, s7, s8)) | (~m_counter_cell_v_value(c_bit0, s8))) <=> ((~m_counter_cell_v_value(c_bit0, s8)) | node2(c_bit0, s7) | (~node3(c_bit0, s7, s8)))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(286,plain,
% 13.04/13.20 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s7) | (~node3(c_bit0, s7, s8)) | (~m_counter_cell_v_value(c_bit0, s8)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s8)) | node2(c_bit0, s7) | (~node3(c_bit0, s7, s8))))),
% 13.04/13.20 inference(monotonicity,[status(thm)],[285])).
% 13.04/13.20 tff(287,plain,
% 13.04/13.20 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s7) | (~node3(c_bit0, s7, s8)) | (~m_counter_cell_v_value(c_bit0, s8)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s8)) | node2(c_bit0, s7) | (~node3(c_bit0, s7, s8)))),
% 13.04/13.20 inference(transitivity,[status(thm)],[286, 284])).
% 13.04/13.20 tff(288,plain,
% 13.04/13.20 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s7) | (~node3(c_bit0, s7, s8)) | (~m_counter_cell_v_value(c_bit0, s8)))),
% 13.04/13.20 inference(quant_inst,[status(thm)],[])).
% 13.04/13.20 tff(289,plain,
% 13.04/13.20 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s8)) | node2(c_bit0, s7) | (~node3(c_bit0, s7, s8))),
% 13.04/13.20 inference(modus_ponens,[status(thm)],[288, 287])).
% 13.04/13.20 tff(290,plain,
% 13.04/13.20 ((~m_counter_cell_v_value(c_bit0, s8)) | node2(c_bit0, s7)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[289, 121, 283])).
% 13.04/13.20 tff(291,plain,
% 13.04/13.20 (~m_counter_cell_v_value(c_bit0, s8)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[290, 272])).
% 13.04/13.20 tff(292,plain,
% 13.04/13.20 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s8)),
% 13.04/13.20 inference(quant_inst,[status(thm)],[])).
% 13.04/13.20 tff(293,plain,
% 13.04/13.20 (m_counter_cell_v_carry_in(c_bit0, s8)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[292, 18])).
% 13.04/13.20 tff(294,plain,
% 13.04/13.20 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s8)) | (~node1(c_bit0, s8)) | m_counter_cell_v_value(c_bit0, s8))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s8)) | (~node1(c_bit0, s8)) | m_counter_cell_v_value(c_bit0, s8))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(295,plain,
% 13.04/13.20 (((~node1(c_bit0, s8)) | (~m_counter_cell_v_carry_in(c_bit0, s8)) | m_counter_cell_v_value(c_bit0, s8)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s8)) | (~node1(c_bit0, s8)) | m_counter_cell_v_value(c_bit0, s8))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(296,plain,
% 13.04/13.20 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s8)) | (~m_counter_cell_v_carry_in(c_bit0, s8)) | m_counter_cell_v_value(c_bit0, s8))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s8)) | (~node1(c_bit0, s8)) | m_counter_cell_v_value(c_bit0, s8)))),
% 13.04/13.20 inference(monotonicity,[status(thm)],[295])).
% 13.04/13.20 tff(297,plain,
% 13.04/13.20 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s8)) | (~m_counter_cell_v_carry_in(c_bit0, s8)) | m_counter_cell_v_value(c_bit0, s8))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s8)) | (~node1(c_bit0, s8)) | m_counter_cell_v_value(c_bit0, s8))),
% 13.04/13.20 inference(transitivity,[status(thm)],[296, 294])).
% 13.04/13.20 tff(298,plain,
% 13.04/13.20 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s8)) | (~m_counter_cell_v_carry_in(c_bit0, s8)) | m_counter_cell_v_value(c_bit0, s8))),
% 13.04/13.20 inference(quant_inst,[status(thm)],[])).
% 13.04/13.20 tff(299,plain,
% 13.04/13.20 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s8)) | (~node1(c_bit0, s8)) | m_counter_cell_v_value(c_bit0, s8)),
% 13.04/13.20 inference(modus_ponens,[status(thm)],[298, 297])).
% 13.04/13.20 tff(300,plain,
% 13.04/13.20 ((~node1(c_bit0, s8)) | m_counter_cell_v_value(c_bit0, s8)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[299, 30, 293])).
% 13.04/13.20 tff(301,plain,
% 13.04/13.20 (~node1(c_bit0, s8)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[300, 291])).
% 13.04/13.20 tff(302,plain,
% 13.04/13.20 (succ(s8, s9) <=> succ(s8, s9)),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(303,axiom,(succ(s8, s9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound9')).
% 13.04/13.20 tff(304,plain,
% 13.04/13.20 (succ(s8, s9)),
% 13.04/13.20 inference(modus_ponens,[status(thm)],[303, 302])).
% 13.04/13.20 tff(305,plain,
% 13.04/13.20 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s8, s9)) | trans(s8, s9))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s8, s9)) | trans(s8, s9))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(306,plain,
% 13.04/13.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s8, s9)) | trans(s8, s9))),
% 13.04/13.20 inference(quant_inst,[status(thm)],[])).
% 13.04/13.20 tff(307,plain,
% 13.04/13.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s8, s9)) | trans(s8, s9)),
% 13.04/13.20 inference(modus_ponens,[status(thm)],[306, 305])).
% 13.04/13.20 tff(308,plain,
% 13.04/13.20 (trans(s8, s9)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[307, 304, 45])).
% 13.04/13.20 tff(309,plain,
% 13.04/13.20 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s8, s9)) | node3(c_bit0, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s8, s9)) | node3(c_bit0, s8, s9))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(310,plain,
% 13.04/13.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s8, s9)) | node3(c_bit0, s8, s9))),
% 13.04/13.20 inference(quant_inst,[status(thm)],[])).
% 13.04/13.20 tff(311,plain,
% 13.04/13.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s8, s9)) | node3(c_bit0, s8, s9)),
% 13.04/13.20 inference(modus_ponens,[status(thm)],[310, 309])).
% 13.04/13.20 tff(312,plain,
% 13.04/13.20 (node3(c_bit0, s8, s9)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[311, 59, 308])).
% 13.04/13.20 tff(313,plain,
% 13.04/13.20 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s9) | node1(c_bit0, s8) | (~node3(c_bit0, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s9) | node1(c_bit0, s8) | (~node3(c_bit0, s8, s9)))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(314,plain,
% 13.04/13.20 ((node1(c_bit0, s8) | (~node3(c_bit0, s8, s9)) | m_counter_cell_v_value(c_bit0, s9)) <=> (m_counter_cell_v_value(c_bit0, s9) | node1(c_bit0, s8) | (~node3(c_bit0, s8, s9)))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(315,plain,
% 13.04/13.20 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s8) | (~node3(c_bit0, s8, s9)) | m_counter_cell_v_value(c_bit0, s9))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s9) | node1(c_bit0, s8) | (~node3(c_bit0, s8, s9))))),
% 13.04/13.20 inference(monotonicity,[status(thm)],[314])).
% 13.04/13.20 tff(316,plain,
% 13.04/13.20 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s8) | (~node3(c_bit0, s8, s9)) | m_counter_cell_v_value(c_bit0, s9))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s9) | node1(c_bit0, s8) | (~node3(c_bit0, s8, s9)))),
% 13.04/13.20 inference(transitivity,[status(thm)],[315, 313])).
% 13.04/13.20 tff(317,plain,
% 13.04/13.20 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s8) | (~node3(c_bit0, s8, s9)) | m_counter_cell_v_value(c_bit0, s9))),
% 13.04/13.20 inference(quant_inst,[status(thm)],[])).
% 13.04/13.20 tff(318,plain,
% 13.04/13.20 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s9) | node1(c_bit0, s8) | (~node3(c_bit0, s8, s9))),
% 13.04/13.20 inference(modus_ponens,[status(thm)],[317, 316])).
% 13.04/13.20 tff(319,plain,
% 13.04/13.20 (m_counter_cell_v_value(c_bit0, s9) | node1(c_bit0, s8)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[318, 73, 312])).
% 13.04/13.20 tff(320,plain,
% 13.04/13.20 (m_counter_cell_v_value(c_bit0, s9)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[319, 301])).
% 13.04/13.20 tff(321,plain,
% 13.04/13.20 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s9)),
% 13.04/13.20 inference(quant_inst,[status(thm)],[])).
% 13.04/13.20 tff(322,plain,
% 13.04/13.20 (m_counter_cell_v_carry_in(c_bit0, s9)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[321, 18])).
% 13.04/13.20 tff(323,plain,
% 13.04/13.20 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s9)) | (~m_counter_cell_v_value(c_bit0, s9)) | (~node2(c_bit0, s9)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s9)) | (~m_counter_cell_v_value(c_bit0, s9)) | (~node2(c_bit0, s9)))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(324,plain,
% 13.04/13.20 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s9)) | (~m_counter_cell_v_value(c_bit0, s9)) | (~node2(c_bit0, s9)))),
% 13.04/13.20 inference(quant_inst,[status(thm)],[])).
% 13.04/13.20 tff(325,plain,
% 13.04/13.20 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s9)) | (~m_counter_cell_v_value(c_bit0, s9)) | (~node2(c_bit0, s9))),
% 13.04/13.20 inference(modus_ponens,[status(thm)],[324, 323])).
% 13.04/13.20 tff(326,plain,
% 13.04/13.20 ((~m_counter_cell_v_value(c_bit0, s9)) | (~node2(c_bit0, s9))),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[325, 93, 322])).
% 13.04/13.20 tff(327,plain,
% 13.04/13.20 (~node2(c_bit0, s9)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[326, 320])).
% 13.04/13.20 tff(328,plain,
% 13.04/13.20 (succ(s9, s10) <=> succ(s9, s10)),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(329,axiom,(succ(s9, s10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound10')).
% 13.04/13.20 tff(330,plain,
% 13.04/13.20 (succ(s9, s10)),
% 13.04/13.20 inference(modus_ponens,[status(thm)],[329, 328])).
% 13.04/13.20 tff(331,plain,
% 13.04/13.20 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s9, s10)) | trans(s9, s10))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s9, s10)) | trans(s9, s10))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(332,plain,
% 13.04/13.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s9, s10)) | trans(s9, s10))),
% 13.04/13.20 inference(quant_inst,[status(thm)],[])).
% 13.04/13.20 tff(333,plain,
% 13.04/13.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s9, s10)) | trans(s9, s10)),
% 13.04/13.20 inference(modus_ponens,[status(thm)],[332, 331])).
% 13.04/13.20 tff(334,plain,
% 13.04/13.20 (trans(s9, s10)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[333, 330, 45])).
% 13.04/13.20 tff(335,plain,
% 13.04/13.20 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s9, s10)) | node3(c_bit0, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s9, s10)) | node3(c_bit0, s9, s10))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(336,plain,
% 13.04/13.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s9, s10)) | node3(c_bit0, s9, s10))),
% 13.04/13.20 inference(quant_inst,[status(thm)],[])).
% 13.04/13.20 tff(337,plain,
% 13.04/13.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s9, s10)) | node3(c_bit0, s9, s10)),
% 13.04/13.20 inference(modus_ponens,[status(thm)],[336, 335])).
% 13.04/13.20 tff(338,plain,
% 13.04/13.20 (node3(c_bit0, s9, s10)),
% 13.04/13.20 inference(unit_resolution,[status(thm)],[337, 59, 334])).
% 13.04/13.20 tff(339,plain,
% 13.04/13.20 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s10)) | node2(c_bit0, s9) | (~node3(c_bit0, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s10)) | node2(c_bit0, s9) | (~node3(c_bit0, s9, s10)))),
% 13.04/13.20 inference(rewrite,[status(thm)],[])).
% 13.04/13.20 tff(340,plain,
% 13.04/13.20 ((node2(c_bit0, s9) | (~node3(c_bit0, s9, s10)) | (~m_counter_cell_v_value(c_bit0, s10))) <=> ((~m_counter_cell_v_value(c_bit0, s10)) | node2(c_bit0, s9) | (~node3(c_bit0, s9, s10)))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(341,plain,
% 13.04/13.21 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s9) | (~node3(c_bit0, s9, s10)) | (~m_counter_cell_v_value(c_bit0, s10)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s10)) | node2(c_bit0, s9) | (~node3(c_bit0, s9, s10))))),
% 13.04/13.21 inference(monotonicity,[status(thm)],[340])).
% 13.04/13.21 tff(342,plain,
% 13.04/13.21 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s9) | (~node3(c_bit0, s9, s10)) | (~m_counter_cell_v_value(c_bit0, s10)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s10)) | node2(c_bit0, s9) | (~node3(c_bit0, s9, s10)))),
% 13.04/13.21 inference(transitivity,[status(thm)],[341, 339])).
% 13.04/13.21 tff(343,plain,
% 13.04/13.21 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s9) | (~node3(c_bit0, s9, s10)) | (~m_counter_cell_v_value(c_bit0, s10)))),
% 13.04/13.21 inference(quant_inst,[status(thm)],[])).
% 13.04/13.21 tff(344,plain,
% 13.04/13.21 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s10)) | node2(c_bit0, s9) | (~node3(c_bit0, s9, s10))),
% 13.04/13.21 inference(modus_ponens,[status(thm)],[343, 342])).
% 13.04/13.21 tff(345,plain,
% 13.04/13.21 ((~m_counter_cell_v_value(c_bit0, s10)) | node2(c_bit0, s9)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[344, 121, 338])).
% 13.04/13.21 tff(346,plain,
% 13.04/13.21 (~m_counter_cell_v_value(c_bit0, s10)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[345, 327])).
% 13.04/13.21 tff(347,plain,
% 13.04/13.21 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s10)),
% 13.04/13.21 inference(quant_inst,[status(thm)],[])).
% 13.04/13.21 tff(348,plain,
% 13.04/13.21 (m_counter_cell_v_carry_in(c_bit0, s10)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[347, 18])).
% 13.04/13.21 tff(349,plain,
% 13.04/13.21 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s10)) | m_counter_cell_v_value(c_bit0, s10) | (~node1(c_bit0, s10)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s10)) | m_counter_cell_v_value(c_bit0, s10) | (~node1(c_bit0, s10)))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(350,plain,
% 13.04/13.21 (((~node1(c_bit0, s10)) | (~m_counter_cell_v_carry_in(c_bit0, s10)) | m_counter_cell_v_value(c_bit0, s10)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s10)) | m_counter_cell_v_value(c_bit0, s10) | (~node1(c_bit0, s10)))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(351,plain,
% 13.04/13.21 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s10)) | (~m_counter_cell_v_carry_in(c_bit0, s10)) | m_counter_cell_v_value(c_bit0, s10))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s10)) | m_counter_cell_v_value(c_bit0, s10) | (~node1(c_bit0, s10))))),
% 13.04/13.21 inference(monotonicity,[status(thm)],[350])).
% 13.04/13.21 tff(352,plain,
% 13.04/13.21 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s10)) | (~m_counter_cell_v_carry_in(c_bit0, s10)) | m_counter_cell_v_value(c_bit0, s10))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s10)) | m_counter_cell_v_value(c_bit0, s10) | (~node1(c_bit0, s10)))),
% 13.04/13.21 inference(transitivity,[status(thm)],[351, 349])).
% 13.04/13.21 tff(353,plain,
% 13.04/13.21 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s10)) | (~m_counter_cell_v_carry_in(c_bit0, s10)) | m_counter_cell_v_value(c_bit0, s10))),
% 13.04/13.21 inference(quant_inst,[status(thm)],[])).
% 13.04/13.21 tff(354,plain,
% 13.04/13.21 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s10)) | m_counter_cell_v_value(c_bit0, s10) | (~node1(c_bit0, s10))),
% 13.04/13.21 inference(modus_ponens,[status(thm)],[353, 352])).
% 13.04/13.21 tff(355,plain,
% 13.04/13.21 (m_counter_cell_v_value(c_bit0, s10) | (~node1(c_bit0, s10))),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[354, 30, 348])).
% 13.04/13.21 tff(356,plain,
% 13.04/13.21 (~node1(c_bit0, s10)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[355, 346])).
% 13.04/13.21 tff(357,plain,
% 13.04/13.21 (succ(s10, s11) <=> succ(s10, s11)),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(358,axiom,(succ(s10, s11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound11')).
% 13.04/13.21 tff(359,plain,
% 13.04/13.21 (succ(s10, s11)),
% 13.04/13.21 inference(modus_ponens,[status(thm)],[358, 357])).
% 13.04/13.21 tff(360,plain,
% 13.04/13.21 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s10, s11)) | trans(s10, s11))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s10, s11)) | trans(s10, s11))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(361,plain,
% 13.04/13.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s10, s11)) | trans(s10, s11))),
% 13.04/13.21 inference(quant_inst,[status(thm)],[])).
% 13.04/13.21 tff(362,plain,
% 13.04/13.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s10, s11)) | trans(s10, s11)),
% 13.04/13.21 inference(modus_ponens,[status(thm)],[361, 360])).
% 13.04/13.21 tff(363,plain,
% 13.04/13.21 (trans(s10, s11)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[362, 359, 45])).
% 13.04/13.21 tff(364,plain,
% 13.04/13.21 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s10, s11)) | node3(c_bit0, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s10, s11)) | node3(c_bit0, s10, s11))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(365,plain,
% 13.04/13.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s10, s11)) | node3(c_bit0, s10, s11))),
% 13.04/13.21 inference(quant_inst,[status(thm)],[])).
% 13.04/13.21 tff(366,plain,
% 13.04/13.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s10, s11)) | node3(c_bit0, s10, s11)),
% 13.04/13.21 inference(modus_ponens,[status(thm)],[365, 364])).
% 13.04/13.21 tff(367,plain,
% 13.04/13.21 (node3(c_bit0, s10, s11)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[366, 59, 363])).
% 13.04/13.21 tff(368,plain,
% 13.04/13.21 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s11) | node1(c_bit0, s10) | (~node3(c_bit0, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s11) | node1(c_bit0, s10) | (~node3(c_bit0, s10, s11)))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(369,plain,
% 13.04/13.21 ((node1(c_bit0, s10) | (~node3(c_bit0, s10, s11)) | m_counter_cell_v_value(c_bit0, s11)) <=> (m_counter_cell_v_value(c_bit0, s11) | node1(c_bit0, s10) | (~node3(c_bit0, s10, s11)))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(370,plain,
% 13.04/13.21 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s10) | (~node3(c_bit0, s10, s11)) | m_counter_cell_v_value(c_bit0, s11))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s11) | node1(c_bit0, s10) | (~node3(c_bit0, s10, s11))))),
% 13.04/13.21 inference(monotonicity,[status(thm)],[369])).
% 13.04/13.21 tff(371,plain,
% 13.04/13.21 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s10) | (~node3(c_bit0, s10, s11)) | m_counter_cell_v_value(c_bit0, s11))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s11) | node1(c_bit0, s10) | (~node3(c_bit0, s10, s11)))),
% 13.04/13.21 inference(transitivity,[status(thm)],[370, 368])).
% 13.04/13.21 tff(372,plain,
% 13.04/13.21 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s10) | (~node3(c_bit0, s10, s11)) | m_counter_cell_v_value(c_bit0, s11))),
% 13.04/13.21 inference(quant_inst,[status(thm)],[])).
% 13.04/13.21 tff(373,plain,
% 13.04/13.21 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s11) | node1(c_bit0, s10) | (~node3(c_bit0, s10, s11))),
% 13.04/13.21 inference(modus_ponens,[status(thm)],[372, 371])).
% 13.04/13.21 tff(374,plain,
% 13.04/13.21 (m_counter_cell_v_value(c_bit0, s11) | node1(c_bit0, s10)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[373, 73, 367])).
% 13.04/13.21 tff(375,plain,
% 13.04/13.21 (m_counter_cell_v_value(c_bit0, s11)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[374, 356])).
% 13.04/13.21 tff(376,plain,
% 13.04/13.21 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s11)),
% 13.04/13.21 inference(quant_inst,[status(thm)],[])).
% 13.04/13.21 tff(377,plain,
% 13.04/13.21 (m_counter_cell_v_carry_in(c_bit0, s11)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[376, 18])).
% 13.04/13.21 tff(378,plain,
% 13.04/13.21 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s11)) | (~m_counter_cell_v_value(c_bit0, s11)) | (~node2(c_bit0, s11)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s11)) | (~m_counter_cell_v_value(c_bit0, s11)) | (~node2(c_bit0, s11)))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(379,plain,
% 13.04/13.21 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s11)) | (~m_counter_cell_v_value(c_bit0, s11)) | (~node2(c_bit0, s11)))),
% 13.04/13.21 inference(quant_inst,[status(thm)],[])).
% 13.04/13.21 tff(380,plain,
% 13.04/13.21 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s11)) | (~m_counter_cell_v_value(c_bit0, s11)) | (~node2(c_bit0, s11))),
% 13.04/13.21 inference(modus_ponens,[status(thm)],[379, 378])).
% 13.04/13.21 tff(381,plain,
% 13.04/13.21 ((~m_counter_cell_v_value(c_bit0, s11)) | (~node2(c_bit0, s11))),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[380, 93, 377])).
% 13.04/13.21 tff(382,plain,
% 13.04/13.21 (~node2(c_bit0, s11)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[381, 375])).
% 13.04/13.21 tff(383,plain,
% 13.04/13.21 (succ(s11, s12) <=> succ(s11, s12)),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(384,axiom,(succ(s11, s12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound12')).
% 13.04/13.21 tff(385,plain,
% 13.04/13.21 (succ(s11, s12)),
% 13.04/13.21 inference(modus_ponens,[status(thm)],[384, 383])).
% 13.04/13.21 tff(386,plain,
% 13.04/13.21 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s11, s12)) | trans(s11, s12))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s11, s12)) | trans(s11, s12))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(387,plain,
% 13.04/13.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s11, s12)) | trans(s11, s12))),
% 13.04/13.21 inference(quant_inst,[status(thm)],[])).
% 13.04/13.21 tff(388,plain,
% 13.04/13.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s11, s12)) | trans(s11, s12)),
% 13.04/13.21 inference(modus_ponens,[status(thm)],[387, 386])).
% 13.04/13.21 tff(389,plain,
% 13.04/13.21 (trans(s11, s12)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[388, 385, 45])).
% 13.04/13.21 tff(390,plain,
% 13.04/13.21 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s11, s12)) | node3(c_bit0, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s11, s12)) | node3(c_bit0, s11, s12))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(391,plain,
% 13.04/13.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s11, s12)) | node3(c_bit0, s11, s12))),
% 13.04/13.21 inference(quant_inst,[status(thm)],[])).
% 13.04/13.21 tff(392,plain,
% 13.04/13.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s11, s12)) | node3(c_bit0, s11, s12)),
% 13.04/13.21 inference(modus_ponens,[status(thm)],[391, 390])).
% 13.04/13.21 tff(393,plain,
% 13.04/13.21 (node3(c_bit0, s11, s12)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[392, 59, 389])).
% 13.04/13.21 tff(394,plain,
% 13.04/13.21 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s12)) | node2(c_bit0, s11) | (~node3(c_bit0, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s12)) | node2(c_bit0, s11) | (~node3(c_bit0, s11, s12)))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(395,plain,
% 13.04/13.21 ((node2(c_bit0, s11) | (~node3(c_bit0, s11, s12)) | (~m_counter_cell_v_value(c_bit0, s12))) <=> ((~m_counter_cell_v_value(c_bit0, s12)) | node2(c_bit0, s11) | (~node3(c_bit0, s11, s12)))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(396,plain,
% 13.04/13.21 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s11) | (~node3(c_bit0, s11, s12)) | (~m_counter_cell_v_value(c_bit0, s12)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s12)) | node2(c_bit0, s11) | (~node3(c_bit0, s11, s12))))),
% 13.04/13.21 inference(monotonicity,[status(thm)],[395])).
% 13.04/13.21 tff(397,plain,
% 13.04/13.21 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s11) | (~node3(c_bit0, s11, s12)) | (~m_counter_cell_v_value(c_bit0, s12)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s12)) | node2(c_bit0, s11) | (~node3(c_bit0, s11, s12)))),
% 13.04/13.21 inference(transitivity,[status(thm)],[396, 394])).
% 13.04/13.21 tff(398,plain,
% 13.04/13.21 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s11) | (~node3(c_bit0, s11, s12)) | (~m_counter_cell_v_value(c_bit0, s12)))),
% 13.04/13.21 inference(quant_inst,[status(thm)],[])).
% 13.04/13.21 tff(399,plain,
% 13.04/13.21 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s12)) | node2(c_bit0, s11) | (~node3(c_bit0, s11, s12))),
% 13.04/13.21 inference(modus_ponens,[status(thm)],[398, 397])).
% 13.04/13.21 tff(400,plain,
% 13.04/13.21 ((~m_counter_cell_v_value(c_bit0, s12)) | node2(c_bit0, s11)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[399, 121, 393])).
% 13.04/13.21 tff(401,plain,
% 13.04/13.21 (~m_counter_cell_v_value(c_bit0, s12)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[400, 382])).
% 13.04/13.21 tff(402,plain,
% 13.04/13.21 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s12)),
% 13.04/13.21 inference(quant_inst,[status(thm)],[])).
% 13.04/13.21 tff(403,plain,
% 13.04/13.21 (m_counter_cell_v_carry_in(c_bit0, s12)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[402, 18])).
% 13.04/13.21 tff(404,plain,
% 13.04/13.21 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s12)) | m_counter_cell_v_value(c_bit0, s12) | (~node1(c_bit0, s12)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s12)) | m_counter_cell_v_value(c_bit0, s12) | (~node1(c_bit0, s12)))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(405,plain,
% 13.04/13.21 (((~node1(c_bit0, s12)) | (~m_counter_cell_v_carry_in(c_bit0, s12)) | m_counter_cell_v_value(c_bit0, s12)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s12)) | m_counter_cell_v_value(c_bit0, s12) | (~node1(c_bit0, s12)))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(406,plain,
% 13.04/13.21 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s12)) | (~m_counter_cell_v_carry_in(c_bit0, s12)) | m_counter_cell_v_value(c_bit0, s12))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s12)) | m_counter_cell_v_value(c_bit0, s12) | (~node1(c_bit0, s12))))),
% 13.04/13.21 inference(monotonicity,[status(thm)],[405])).
% 13.04/13.21 tff(407,plain,
% 13.04/13.21 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s12)) | (~m_counter_cell_v_carry_in(c_bit0, s12)) | m_counter_cell_v_value(c_bit0, s12))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s12)) | m_counter_cell_v_value(c_bit0, s12) | (~node1(c_bit0, s12)))),
% 13.04/13.21 inference(transitivity,[status(thm)],[406, 404])).
% 13.04/13.21 tff(408,plain,
% 13.04/13.21 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s12)) | (~m_counter_cell_v_carry_in(c_bit0, s12)) | m_counter_cell_v_value(c_bit0, s12))),
% 13.04/13.21 inference(quant_inst,[status(thm)],[])).
% 13.04/13.21 tff(409,plain,
% 13.04/13.21 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s12)) | m_counter_cell_v_value(c_bit0, s12) | (~node1(c_bit0, s12))),
% 13.04/13.21 inference(modus_ponens,[status(thm)],[408, 407])).
% 13.04/13.21 tff(410,plain,
% 13.04/13.21 (m_counter_cell_v_value(c_bit0, s12) | (~node1(c_bit0, s12))),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[409, 30, 403])).
% 13.04/13.21 tff(411,plain,
% 13.04/13.21 (~node1(c_bit0, s12)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[410, 401])).
% 13.04/13.21 tff(412,plain,
% 13.04/13.21 (succ(s12, s13) <=> succ(s12, s13)),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(413,axiom,(succ(s12, s13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound13')).
% 13.04/13.21 tff(414,plain,
% 13.04/13.21 (succ(s12, s13)),
% 13.04/13.21 inference(modus_ponens,[status(thm)],[413, 412])).
% 13.04/13.21 tff(415,plain,
% 13.04/13.21 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s12, s13)) | trans(s12, s13))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s12, s13)) | trans(s12, s13))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(416,plain,
% 13.04/13.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s12, s13)) | trans(s12, s13))),
% 13.04/13.21 inference(quant_inst,[status(thm)],[])).
% 13.04/13.21 tff(417,plain,
% 13.04/13.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s12, s13)) | trans(s12, s13)),
% 13.04/13.21 inference(modus_ponens,[status(thm)],[416, 415])).
% 13.04/13.21 tff(418,plain,
% 13.04/13.21 (trans(s12, s13)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[417, 414, 45])).
% 13.04/13.21 tff(419,plain,
% 13.04/13.21 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s12, s13)) | node3(c_bit0, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s12, s13)) | node3(c_bit0, s12, s13))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(420,plain,
% 13.04/13.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s12, s13)) | node3(c_bit0, s12, s13))),
% 13.04/13.21 inference(quant_inst,[status(thm)],[])).
% 13.04/13.21 tff(421,plain,
% 13.04/13.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s12, s13)) | node3(c_bit0, s12, s13)),
% 13.04/13.21 inference(modus_ponens,[status(thm)],[420, 419])).
% 13.04/13.21 tff(422,plain,
% 13.04/13.21 (node3(c_bit0, s12, s13)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[421, 59, 418])).
% 13.04/13.21 tff(423,plain,
% 13.04/13.21 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s13) | node1(c_bit0, s12) | (~node3(c_bit0, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s13) | node1(c_bit0, s12) | (~node3(c_bit0, s12, s13)))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(424,plain,
% 13.04/13.21 ((node1(c_bit0, s12) | (~node3(c_bit0, s12, s13)) | m_counter_cell_v_value(c_bit0, s13)) <=> (m_counter_cell_v_value(c_bit0, s13) | node1(c_bit0, s12) | (~node3(c_bit0, s12, s13)))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(425,plain,
% 13.04/13.21 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s12) | (~node3(c_bit0, s12, s13)) | m_counter_cell_v_value(c_bit0, s13))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s13) | node1(c_bit0, s12) | (~node3(c_bit0, s12, s13))))),
% 13.04/13.21 inference(monotonicity,[status(thm)],[424])).
% 13.04/13.21 tff(426,plain,
% 13.04/13.21 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s12) | (~node3(c_bit0, s12, s13)) | m_counter_cell_v_value(c_bit0, s13))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s13) | node1(c_bit0, s12) | (~node3(c_bit0, s12, s13)))),
% 13.04/13.21 inference(transitivity,[status(thm)],[425, 423])).
% 13.04/13.21 tff(427,plain,
% 13.04/13.21 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s12) | (~node3(c_bit0, s12, s13)) | m_counter_cell_v_value(c_bit0, s13))),
% 13.04/13.21 inference(quant_inst,[status(thm)],[])).
% 13.04/13.21 tff(428,plain,
% 13.04/13.21 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s13) | node1(c_bit0, s12) | (~node3(c_bit0, s12, s13))),
% 13.04/13.21 inference(modus_ponens,[status(thm)],[427, 426])).
% 13.04/13.21 tff(429,plain,
% 13.04/13.21 (m_counter_cell_v_value(c_bit0, s13) | node1(c_bit0, s12)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[428, 73, 422])).
% 13.04/13.21 tff(430,plain,
% 13.04/13.21 (m_counter_cell_v_value(c_bit0, s13)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[429, 411])).
% 13.04/13.21 tff(431,plain,
% 13.04/13.21 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s13)),
% 13.04/13.21 inference(quant_inst,[status(thm)],[])).
% 13.04/13.21 tff(432,plain,
% 13.04/13.21 (m_counter_cell_v_carry_in(c_bit0, s13)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[431, 18])).
% 13.04/13.21 tff(433,plain,
% 13.04/13.21 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s13)) | (~m_counter_cell_v_value(c_bit0, s13)) | (~node2(c_bit0, s13)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s13)) | (~m_counter_cell_v_value(c_bit0, s13)) | (~node2(c_bit0, s13)))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(434,plain,
% 13.04/13.21 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s13)) | (~m_counter_cell_v_value(c_bit0, s13)) | (~node2(c_bit0, s13)))),
% 13.04/13.21 inference(quant_inst,[status(thm)],[])).
% 13.04/13.21 tff(435,plain,
% 13.04/13.21 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s13)) | (~m_counter_cell_v_value(c_bit0, s13)) | (~node2(c_bit0, s13))),
% 13.04/13.21 inference(modus_ponens,[status(thm)],[434, 433])).
% 13.04/13.21 tff(436,plain,
% 13.04/13.21 ((~m_counter_cell_v_value(c_bit0, s13)) | (~node2(c_bit0, s13))),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[435, 93, 432])).
% 13.04/13.21 tff(437,plain,
% 13.04/13.21 (~node2(c_bit0, s13)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[436, 430])).
% 13.04/13.21 tff(438,plain,
% 13.04/13.21 (succ(s13, s14) <=> succ(s13, s14)),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(439,axiom,(succ(s13, s14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound14')).
% 13.04/13.21 tff(440,plain,
% 13.04/13.21 (succ(s13, s14)),
% 13.04/13.21 inference(modus_ponens,[status(thm)],[439, 438])).
% 13.04/13.21 tff(441,plain,
% 13.04/13.21 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s13, s14)) | trans(s13, s14))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s13, s14)) | trans(s13, s14))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(442,plain,
% 13.04/13.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s13, s14)) | trans(s13, s14))),
% 13.04/13.21 inference(quant_inst,[status(thm)],[])).
% 13.04/13.21 tff(443,plain,
% 13.04/13.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s13, s14)) | trans(s13, s14)),
% 13.04/13.21 inference(modus_ponens,[status(thm)],[442, 441])).
% 13.04/13.21 tff(444,plain,
% 13.04/13.21 (trans(s13, s14)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[443, 440, 45])).
% 13.04/13.21 tff(445,plain,
% 13.04/13.21 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s13, s14)) | node3(c_bit0, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s13, s14)) | node3(c_bit0, s13, s14))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(446,plain,
% 13.04/13.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s13, s14)) | node3(c_bit0, s13, s14))),
% 13.04/13.21 inference(quant_inst,[status(thm)],[])).
% 13.04/13.21 tff(447,plain,
% 13.04/13.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s13, s14)) | node3(c_bit0, s13, s14)),
% 13.04/13.21 inference(modus_ponens,[status(thm)],[446, 445])).
% 13.04/13.21 tff(448,plain,
% 13.04/13.21 (node3(c_bit0, s13, s14)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[447, 59, 444])).
% 13.04/13.21 tff(449,plain,
% 13.04/13.21 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s14)) | node2(c_bit0, s13) | (~node3(c_bit0, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s14)) | node2(c_bit0, s13) | (~node3(c_bit0, s13, s14)))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(450,plain,
% 13.04/13.21 ((node2(c_bit0, s13) | (~node3(c_bit0, s13, s14)) | (~m_counter_cell_v_value(c_bit0, s14))) <=> ((~m_counter_cell_v_value(c_bit0, s14)) | node2(c_bit0, s13) | (~node3(c_bit0, s13, s14)))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(451,plain,
% 13.04/13.21 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s13) | (~node3(c_bit0, s13, s14)) | (~m_counter_cell_v_value(c_bit0, s14)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s14)) | node2(c_bit0, s13) | (~node3(c_bit0, s13, s14))))),
% 13.04/13.21 inference(monotonicity,[status(thm)],[450])).
% 13.04/13.21 tff(452,plain,
% 13.04/13.21 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s13) | (~node3(c_bit0, s13, s14)) | (~m_counter_cell_v_value(c_bit0, s14)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s14)) | node2(c_bit0, s13) | (~node3(c_bit0, s13, s14)))),
% 13.04/13.21 inference(transitivity,[status(thm)],[451, 449])).
% 13.04/13.21 tff(453,plain,
% 13.04/13.21 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s13) | (~node3(c_bit0, s13, s14)) | (~m_counter_cell_v_value(c_bit0, s14)))),
% 13.04/13.21 inference(quant_inst,[status(thm)],[])).
% 13.04/13.21 tff(454,plain,
% 13.04/13.21 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s14)) | node2(c_bit0, s13) | (~node3(c_bit0, s13, s14))),
% 13.04/13.21 inference(modus_ponens,[status(thm)],[453, 452])).
% 13.04/13.21 tff(455,plain,
% 13.04/13.21 ((~m_counter_cell_v_value(c_bit0, s14)) | node2(c_bit0, s13)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[454, 121, 448])).
% 13.04/13.21 tff(456,plain,
% 13.04/13.21 (~m_counter_cell_v_value(c_bit0, s14)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[455, 437])).
% 13.04/13.21 tff(457,plain,
% 13.04/13.21 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s14)),
% 13.04/13.21 inference(quant_inst,[status(thm)],[])).
% 13.04/13.21 tff(458,plain,
% 13.04/13.21 (m_counter_cell_v_carry_in(c_bit0, s14)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[457, 18])).
% 13.04/13.21 tff(459,plain,
% 13.04/13.21 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s14)) | m_counter_cell_v_value(c_bit0, s14) | (~node1(c_bit0, s14)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s14)) | m_counter_cell_v_value(c_bit0, s14) | (~node1(c_bit0, s14)))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(460,plain,
% 13.04/13.21 (((~node1(c_bit0, s14)) | (~m_counter_cell_v_carry_in(c_bit0, s14)) | m_counter_cell_v_value(c_bit0, s14)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s14)) | m_counter_cell_v_value(c_bit0, s14) | (~node1(c_bit0, s14)))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(461,plain,
% 13.04/13.21 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s14)) | (~m_counter_cell_v_carry_in(c_bit0, s14)) | m_counter_cell_v_value(c_bit0, s14))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s14)) | m_counter_cell_v_value(c_bit0, s14) | (~node1(c_bit0, s14))))),
% 13.04/13.21 inference(monotonicity,[status(thm)],[460])).
% 13.04/13.21 tff(462,plain,
% 13.04/13.21 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s14)) | (~m_counter_cell_v_carry_in(c_bit0, s14)) | m_counter_cell_v_value(c_bit0, s14))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s14)) | m_counter_cell_v_value(c_bit0, s14) | (~node1(c_bit0, s14)))),
% 13.04/13.21 inference(transitivity,[status(thm)],[461, 459])).
% 13.04/13.21 tff(463,plain,
% 13.04/13.21 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s14)) | (~m_counter_cell_v_carry_in(c_bit0, s14)) | m_counter_cell_v_value(c_bit0, s14))),
% 13.04/13.21 inference(quant_inst,[status(thm)],[])).
% 13.04/13.21 tff(464,plain,
% 13.04/13.21 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s14)) | m_counter_cell_v_value(c_bit0, s14) | (~node1(c_bit0, s14))),
% 13.04/13.21 inference(modus_ponens,[status(thm)],[463, 462])).
% 13.04/13.21 tff(465,plain,
% 13.04/13.21 (m_counter_cell_v_value(c_bit0, s14) | (~node1(c_bit0, s14))),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[464, 30, 458])).
% 13.04/13.21 tff(466,plain,
% 13.04/13.21 (~node1(c_bit0, s14)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[465, 456])).
% 13.04/13.21 tff(467,plain,
% 13.04/13.21 (succ(s14, s15) <=> succ(s14, s15)),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(468,axiom,(succ(s14, s15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound15')).
% 13.04/13.21 tff(469,plain,
% 13.04/13.21 (succ(s14, s15)),
% 13.04/13.21 inference(modus_ponens,[status(thm)],[468, 467])).
% 13.04/13.21 tff(470,plain,
% 13.04/13.21 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s14, s15)) | trans(s14, s15))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s14, s15)) | trans(s14, s15))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(471,plain,
% 13.04/13.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s14, s15)) | trans(s14, s15))),
% 13.04/13.21 inference(quant_inst,[status(thm)],[])).
% 13.04/13.21 tff(472,plain,
% 13.04/13.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s14, s15)) | trans(s14, s15)),
% 13.04/13.21 inference(modus_ponens,[status(thm)],[471, 470])).
% 13.04/13.21 tff(473,plain,
% 13.04/13.21 (trans(s14, s15)),
% 13.04/13.21 inference(unit_resolution,[status(thm)],[472, 469, 45])).
% 13.04/13.21 tff(474,plain,
% 13.04/13.21 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s14, s15)) | node3(c_bit0, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s14, s15)) | node3(c_bit0, s14, s15))),
% 13.04/13.21 inference(rewrite,[status(thm)],[])).
% 13.04/13.21 tff(475,plain,
% 13.04/13.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s14, s15)) | node3(c_bit0, s14, s15))),
% 13.04/13.22 inference(quant_inst,[status(thm)],[])).
% 13.04/13.22 tff(476,plain,
% 13.04/13.22 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s14, s15)) | node3(c_bit0, s14, s15)),
% 13.04/13.22 inference(modus_ponens,[status(thm)],[475, 474])).
% 13.04/13.22 tff(477,plain,
% 13.04/13.22 (node3(c_bit0, s14, s15)),
% 13.04/13.22 inference(unit_resolution,[status(thm)],[476, 59, 473])).
% 13.04/13.22 tff(478,plain,
% 13.04/13.22 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s14) | m_counter_cell_v_value(c_bit0, s15) | (~node3(c_bit0, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit0, s14) | m_counter_cell_v_value(c_bit0, s15) | (~node3(c_bit0, s14, s15)))),
% 13.04/13.22 inference(rewrite,[status(thm)],[])).
% 13.04/13.22 tff(479,plain,
% 13.04/13.22 ((node1(c_bit0, s14) | (~node3(c_bit0, s14, s15)) | m_counter_cell_v_value(c_bit0, s15)) <=> (node1(c_bit0, s14) | m_counter_cell_v_value(c_bit0, s15) | (~node3(c_bit0, s14, s15)))),
% 13.04/13.22 inference(rewrite,[status(thm)],[])).
% 13.04/13.22 tff(480,plain,
% 13.04/13.22 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s14) | (~node3(c_bit0, s14, s15)) | m_counter_cell_v_value(c_bit0, s15))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s14) | m_counter_cell_v_value(c_bit0, s15) | (~node3(c_bit0, s14, s15))))),
% 13.04/13.22 inference(monotonicity,[status(thm)],[479])).
% 13.04/13.22 tff(481,plain,
% 13.04/13.22 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s14) | (~node3(c_bit0, s14, s15)) | m_counter_cell_v_value(c_bit0, s15))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit0, s14) | m_counter_cell_v_value(c_bit0, s15) | (~node3(c_bit0, s14, s15)))),
% 13.04/13.22 inference(transitivity,[status(thm)],[480, 478])).
% 13.04/13.22 tff(482,plain,
% 13.04/13.22 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s14) | (~node3(c_bit0, s14, s15)) | m_counter_cell_v_value(c_bit0, s15))),
% 13.04/13.22 inference(quant_inst,[status(thm)],[])).
% 13.04/13.22 tff(483,plain,
% 13.04/13.22 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit0, s14) | m_counter_cell_v_value(c_bit0, s15) | (~node3(c_bit0, s14, s15))),
% 13.04/13.22 inference(modus_ponens,[status(thm)],[482, 481])).
% 13.04/13.22 tff(484,plain,
% 13.04/13.22 (node1(c_bit0, s14) | m_counter_cell_v_value(c_bit0, s15)),
% 13.04/13.22 inference(unit_resolution,[status(thm)],[483, 73, 477])).
% 13.04/13.22 tff(485,plain,
% 13.04/13.22 (m_counter_cell_v_value(c_bit0, s15)),
% 13.04/13.22 inference(unit_resolution,[status(thm)],[484, 466])).
% 13.04/13.22 tff(486,plain,
% 13.04/13.22 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s15)),
% 13.04/13.22 inference(quant_inst,[status(thm)],[])).
% 13.04/13.22 tff(487,plain,
% 13.04/13.22 (m_counter_cell_v_carry_in(c_bit0, s15)),
% 13.04/13.22 inference(unit_resolution,[status(thm)],[486, 18])).
% 13.04/13.22 tff(488,plain,
% 13.04/13.22 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s15)) | (~m_counter_cell_v_value(c_bit0, s15)) | (~node2(c_bit0, s15)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s15)) | (~m_counter_cell_v_value(c_bit0, s15)) | (~node2(c_bit0, s15)))),
% 13.04/13.22 inference(rewrite,[status(thm)],[])).
% 13.04/13.22 tff(489,plain,
% 13.04/13.22 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s15)) | (~m_counter_cell_v_value(c_bit0, s15)) | (~node2(c_bit0, s15)))),
% 13.04/13.22 inference(quant_inst,[status(thm)],[])).
% 13.04/13.22 tff(490,plain,
% 13.04/13.22 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s15)) | (~m_counter_cell_v_value(c_bit0, s15)) | (~node2(c_bit0, s15))),
% 13.04/13.22 inference(modus_ponens,[status(thm)],[489, 488])).
% 13.04/13.22 tff(491,plain,
% 13.04/13.22 ((~m_counter_cell_v_value(c_bit0, s15)) | (~node2(c_bit0, s15))),
% 13.04/13.22 inference(unit_resolution,[status(thm)],[490, 93, 487])).
% 13.04/13.22 tff(492,plain,
% 13.04/13.22 (~node2(c_bit0, s15)),
% 13.04/13.22 inference(unit_resolution,[status(thm)],[491, 485])).
% 13.04/13.22 tff(493,plain,
% 13.04/13.22 (succ(s15, s16) <=> succ(s15, s16)),
% 13.04/13.22 inference(rewrite,[status(thm)],[])).
% 13.04/13.22 tff(494,axiom,(succ(s15, s16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound16')).
% 13.04/13.22 tff(495,plain,
% 13.04/13.22 (succ(s15, s16)),
% 13.04/13.22 inference(modus_ponens,[status(thm)],[494, 493])).
% 13.04/13.22 tff(496,plain,
% 13.04/13.22 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s15, s16)) | trans(s15, s16))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s15, s16)) | trans(s15, s16))),
% 13.04/13.22 inference(rewrite,[status(thm)],[])).
% 13.04/13.22 tff(497,plain,
% 13.04/13.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s15, s16)) | trans(s15, s16))),
% 13.04/13.22 inference(quant_inst,[status(thm)],[])).
% 13.04/13.22 tff(498,plain,
% 13.04/13.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s15, s16)) | trans(s15, s16)),
% 13.04/13.22 inference(modus_ponens,[status(thm)],[497, 496])).
% 13.04/13.22 tff(499,plain,
% 13.04/13.22 (trans(s15, s16)),
% 13.04/13.22 inference(unit_resolution,[status(thm)],[498, 495, 45])).
% 13.04/13.22 tff(500,plain,
% 13.04/13.22 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s15, s16)) | node3(c_bit0, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s15, s16)) | node3(c_bit0, s15, s16))),
% 13.04/13.22 inference(rewrite,[status(thm)],[])).
% 13.04/13.22 tff(501,plain,
% 13.04/13.22 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s15, s16)) | node3(c_bit0, s15, s16))),
% 13.04/13.22 inference(quant_inst,[status(thm)],[])).
% 13.04/13.22 tff(502,plain,
% 13.04/13.22 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s15, s16)) | node3(c_bit0, s15, s16)),
% 13.04/13.22 inference(modus_ponens,[status(thm)],[501, 500])).
% 13.04/13.22 tff(503,plain,
% 13.04/13.22 (node3(c_bit0, s15, s16)),
% 13.04/13.22 inference(unit_resolution,[status(thm)],[502, 59, 499])).
% 13.04/13.22 tff(504,plain,
% 13.04/13.22 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s16)) | node2(c_bit0, s15) | (~node3(c_bit0, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s16)) | node2(c_bit0, s15) | (~node3(c_bit0, s15, s16)))),
% 13.04/13.22 inference(rewrite,[status(thm)],[])).
% 13.04/13.22 tff(505,plain,
% 13.04/13.22 ((node2(c_bit0, s15) | (~node3(c_bit0, s15, s16)) | (~m_counter_cell_v_value(c_bit0, s16))) <=> ((~m_counter_cell_v_value(c_bit0, s16)) | node2(c_bit0, s15) | (~node3(c_bit0, s15, s16)))),
% 13.04/13.22 inference(rewrite,[status(thm)],[])).
% 13.04/13.22 tff(506,plain,
% 13.04/13.22 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s15) | (~node3(c_bit0, s15, s16)) | (~m_counter_cell_v_value(c_bit0, s16)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s16)) | node2(c_bit0, s15) | (~node3(c_bit0, s15, s16))))),
% 13.04/13.22 inference(monotonicity,[status(thm)],[505])).
% 13.04/13.22 tff(507,plain,
% 13.04/13.22 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s15) | (~node3(c_bit0, s15, s16)) | (~m_counter_cell_v_value(c_bit0, s16)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s16)) | node2(c_bit0, s15) | (~node3(c_bit0, s15, s16)))),
% 13.04/13.22 inference(transitivity,[status(thm)],[506, 504])).
% 13.04/13.22 tff(508,plain,
% 13.04/13.22 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s15) | (~node3(c_bit0, s15, s16)) | (~m_counter_cell_v_value(c_bit0, s16)))),
% 13.04/13.22 inference(quant_inst,[status(thm)],[])).
% 13.04/13.22 tff(509,plain,
% 13.04/13.22 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s16)) | node2(c_bit0, s15) | (~node3(c_bit0, s15, s16))),
% 13.07/13.22 inference(modus_ponens,[status(thm)],[508, 507])).
% 13.07/13.22 tff(510,plain,
% 13.07/13.22 ((~m_counter_cell_v_value(c_bit0, s16)) | node2(c_bit0, s15)),
% 13.07/13.22 inference(unit_resolution,[status(thm)],[509, 121, 503])).
% 13.07/13.22 tff(511,plain,
% 13.07/13.22 (~m_counter_cell_v_value(c_bit0, s16)),
% 13.07/13.22 inference(unit_resolution,[status(thm)],[510, 492])).
% 13.07/13.22 tff(512,plain,
% 13.07/13.22 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s16)),
% 13.07/13.22 inference(quant_inst,[status(thm)],[])).
% 13.07/13.22 tff(513,plain,
% 13.07/13.22 (m_counter_cell_v_carry_in(c_bit0, s16)),
% 13.07/13.22 inference(unit_resolution,[status(thm)],[512, 18])).
% 13.07/13.22 tff(514,plain,
% 13.07/13.22 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s16)) | m_counter_cell_v_value(c_bit0, s16) | (~node1(c_bit0, s16)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s16)) | m_counter_cell_v_value(c_bit0, s16) | (~node1(c_bit0, s16)))),
% 13.07/13.22 inference(rewrite,[status(thm)],[])).
% 13.07/13.22 tff(515,plain,
% 13.07/13.22 (((~node1(c_bit0, s16)) | (~m_counter_cell_v_carry_in(c_bit0, s16)) | m_counter_cell_v_value(c_bit0, s16)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s16)) | m_counter_cell_v_value(c_bit0, s16) | (~node1(c_bit0, s16)))),
% 13.07/13.22 inference(rewrite,[status(thm)],[])).
% 13.07/13.22 tff(516,plain,
% 13.07/13.22 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s16)) | (~m_counter_cell_v_carry_in(c_bit0, s16)) | m_counter_cell_v_value(c_bit0, s16))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s16)) | m_counter_cell_v_value(c_bit0, s16) | (~node1(c_bit0, s16))))),
% 13.07/13.22 inference(monotonicity,[status(thm)],[515])).
% 13.07/13.22 tff(517,plain,
% 13.07/13.22 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s16)) | (~m_counter_cell_v_carry_in(c_bit0, s16)) | m_counter_cell_v_value(c_bit0, s16))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s16)) | m_counter_cell_v_value(c_bit0, s16) | (~node1(c_bit0, s16)))),
% 13.07/13.22 inference(transitivity,[status(thm)],[516, 514])).
% 13.07/13.22 tff(518,plain,
% 13.07/13.22 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s16)) | (~m_counter_cell_v_carry_in(c_bit0, s16)) | m_counter_cell_v_value(c_bit0, s16))),
% 13.07/13.22 inference(quant_inst,[status(thm)],[])).
% 13.07/13.22 tff(519,plain,
% 13.07/13.22 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s16)) | m_counter_cell_v_value(c_bit0, s16) | (~node1(c_bit0, s16))),
% 13.07/13.22 inference(modus_ponens,[status(thm)],[518, 517])).
% 13.07/13.22 tff(520,plain,
% 13.07/13.22 (m_counter_cell_v_value(c_bit0, s16) | (~node1(c_bit0, s16))),
% 13.07/13.22 inference(unit_resolution,[status(thm)],[519, 30, 513])).
% 13.07/13.22 tff(521,plain,
% 13.07/13.22 (~node1(c_bit0, s16)),
% 13.07/13.22 inference(unit_resolution,[status(thm)],[520, 511])).
% 13.07/13.22 tff(522,plain,
% 13.07/13.22 (succ(s16, s17) <=> succ(s16, s17)),
% 13.07/13.22 inference(rewrite,[status(thm)],[])).
% 13.07/13.22 tff(523,axiom,(succ(s16, s17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound17')).
% 13.07/13.22 tff(524,plain,
% 13.07/13.22 (succ(s16, s17)),
% 13.07/13.22 inference(modus_ponens,[status(thm)],[523, 522])).
% 13.07/13.22 tff(525,plain,
% 13.07/13.22 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s16, s17)) | trans(s16, s17))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s16, s17)) | trans(s16, s17))),
% 13.07/13.22 inference(rewrite,[status(thm)],[])).
% 13.07/13.22 tff(526,plain,
% 13.07/13.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s16, s17)) | trans(s16, s17))),
% 13.07/13.22 inference(quant_inst,[status(thm)],[])).
% 13.07/13.22 tff(527,plain,
% 13.07/13.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s16, s17)) | trans(s16, s17)),
% 13.07/13.22 inference(modus_ponens,[status(thm)],[526, 525])).
% 13.07/13.22 tff(528,plain,
% 13.07/13.22 (trans(s16, s17)),
% 13.07/13.22 inference(unit_resolution,[status(thm)],[527, 524, 45])).
% 13.07/13.22 tff(529,plain,
% 13.07/13.22 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s16, s17)) | node3(c_bit0, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s16, s17)) | node3(c_bit0, s16, s17))),
% 13.07/13.22 inference(rewrite,[status(thm)],[])).
% 13.07/13.22 tff(530,plain,
% 13.07/13.22 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s16, s17)) | node3(c_bit0, s16, s17))),
% 13.07/13.22 inference(quant_inst,[status(thm)],[])).
% 13.07/13.22 tff(531,plain,
% 13.07/13.22 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s16, s17)) | node3(c_bit0, s16, s17)),
% 13.07/13.22 inference(modus_ponens,[status(thm)],[530, 529])).
% 13.07/13.22 tff(532,plain,
% 13.07/13.22 (node3(c_bit0, s16, s17)),
% 13.07/13.22 inference(unit_resolution,[status(thm)],[531, 59, 528])).
% 13.07/13.22 tff(533,plain,
% 13.07/13.22 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s17) | node1(c_bit0, s16) | (~node3(c_bit0, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s17) | node1(c_bit0, s16) | (~node3(c_bit0, s16, s17)))),
% 13.07/13.22 inference(rewrite,[status(thm)],[])).
% 13.07/13.22 tff(534,plain,
% 13.07/13.22 ((node1(c_bit0, s16) | (~node3(c_bit0, s16, s17)) | m_counter_cell_v_value(c_bit0, s17)) <=> (m_counter_cell_v_value(c_bit0, s17) | node1(c_bit0, s16) | (~node3(c_bit0, s16, s17)))),
% 13.07/13.22 inference(rewrite,[status(thm)],[])).
% 13.07/13.22 tff(535,plain,
% 13.07/13.22 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s16) | (~node3(c_bit0, s16, s17)) | m_counter_cell_v_value(c_bit0, s17))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s17) | node1(c_bit0, s16) | (~node3(c_bit0, s16, s17))))),
% 13.07/13.22 inference(monotonicity,[status(thm)],[534])).
% 13.07/13.22 tff(536,plain,
% 13.07/13.22 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s16) | (~node3(c_bit0, s16, s17)) | m_counter_cell_v_value(c_bit0, s17))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s17) | node1(c_bit0, s16) | (~node3(c_bit0, s16, s17)))),
% 13.07/13.22 inference(transitivity,[status(thm)],[535, 533])).
% 13.07/13.22 tff(537,plain,
% 13.07/13.22 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s16) | (~node3(c_bit0, s16, s17)) | m_counter_cell_v_value(c_bit0, s17))),
% 13.07/13.22 inference(quant_inst,[status(thm)],[])).
% 13.07/13.22 tff(538,plain,
% 13.07/13.22 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s17) | node1(c_bit0, s16) | (~node3(c_bit0, s16, s17))),
% 13.07/13.22 inference(modus_ponens,[status(thm)],[537, 536])).
% 13.07/13.22 tff(539,plain,
% 13.07/13.22 (m_counter_cell_v_value(c_bit0, s17) | node1(c_bit0, s16)),
% 13.07/13.22 inference(unit_resolution,[status(thm)],[538, 73, 532])).
% 13.07/13.22 tff(540,plain,
% 13.07/13.22 (m_counter_cell_v_value(c_bit0, s17)),
% 13.07/13.22 inference(unit_resolution,[status(thm)],[539, 521])).
% 13.07/13.22 tff(541,assumption,(~m_counter_cell_v_carry_in(c_bit0, s17)), introduced(assumption)).
% 13.07/13.22 tff(542,plain,
% 13.07/13.22 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s17)),
% 13.07/13.22 inference(quant_inst,[status(thm)],[])).
% 13.07/13.22 tff(543,plain,
% 13.07/13.22 ($false),
% 13.07/13.22 inference(unit_resolution,[status(thm)],[542, 18, 541])).
% 13.07/13.22 tff(544,plain,(m_counter_cell_v_carry_in(c_bit0, s17)), inference(lemma,lemma(discharge,[]))).
% 13.07/13.22 tff(545,plain,
% 13.07/13.22 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s17)) | (~m_counter_cell_v_value(c_bit0, s17)) | (~node2(c_bit0, s17)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s17)) | (~m_counter_cell_v_value(c_bit0, s17)) | (~node2(c_bit0, s17)))),
% 13.07/13.22 inference(rewrite,[status(thm)],[])).
% 13.07/13.22 tff(546,plain,
% 13.07/13.22 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s17)) | (~m_counter_cell_v_value(c_bit0, s17)) | (~node2(c_bit0, s17)))),
% 13.07/13.22 inference(quant_inst,[status(thm)],[])).
% 13.07/13.22 tff(547,plain,
% 13.07/13.22 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s17)) | (~m_counter_cell_v_value(c_bit0, s17)) | (~node2(c_bit0, s17))),
% 13.07/13.22 inference(modus_ponens,[status(thm)],[546, 545])).
% 13.07/13.22 tff(548,plain,
% 13.07/13.22 ((~m_counter_cell_v_value(c_bit0, s17)) | (~node2(c_bit0, s17))),
% 13.07/13.22 inference(unit_resolution,[status(thm)],[547, 93, 544])).
% 13.07/13.22 tff(549,plain,
% 13.07/13.22 (~node2(c_bit0, s17)),
% 13.07/13.22 inference(unit_resolution,[status(thm)],[548, 540])).
% 13.07/13.22 tff(550,plain,
% 13.07/13.22 (succ(s17, s18) <=> succ(s17, s18)),
% 13.07/13.22 inference(rewrite,[status(thm)],[])).
% 13.07/13.22 tff(551,axiom,(succ(s17, s18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound18')).
% 13.07/13.22 tff(552,plain,
% 13.07/13.22 (succ(s17, s18)),
% 13.07/13.22 inference(modus_ponens,[status(thm)],[551, 550])).
% 13.07/13.22 tff(553,plain,
% 13.07/13.22 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s17, s18)) | trans(s17, s18))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s17, s18)) | trans(s17, s18))),
% 13.07/13.22 inference(rewrite,[status(thm)],[])).
% 13.07/13.22 tff(554,plain,
% 13.07/13.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s17, s18)) | trans(s17, s18))),
% 13.07/13.22 inference(quant_inst,[status(thm)],[])).
% 13.07/13.22 tff(555,plain,
% 13.07/13.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s17, s18)) | trans(s17, s18)),
% 13.07/13.22 inference(modus_ponens,[status(thm)],[554, 553])).
% 13.07/13.22 tff(556,plain,
% 13.07/13.22 (trans(s17, s18)),
% 13.07/13.22 inference(unit_resolution,[status(thm)],[555, 552, 45])).
% 13.07/13.22 tff(557,plain,
% 13.07/13.22 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s17, s18)) | node3(c_bit0, s17, s18))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s17, s18)) | node3(c_bit0, s17, s18))),
% 13.07/13.22 inference(rewrite,[status(thm)],[])).
% 13.07/13.22 tff(558,plain,
% 13.07/13.22 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s17, s18)) | node3(c_bit0, s17, s18))),
% 13.07/13.22 inference(quant_inst,[status(thm)],[])).
% 13.07/13.22 tff(559,plain,
% 13.07/13.22 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s17, s18)) | node3(c_bit0, s17, s18)),
% 13.07/13.22 inference(modus_ponens,[status(thm)],[558, 557])).
% 13.07/13.22 tff(560,plain,
% 13.07/13.22 (node3(c_bit0, s17, s18)),
% 13.07/13.22 inference(unit_resolution,[status(thm)],[559, 59, 556])).
% 13.07/13.22 tff(561,plain,
% 13.07/13.22 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s18)) | node2(c_bit0, s17) | (~node3(c_bit0, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s18)) | node2(c_bit0, s17) | (~node3(c_bit0, s17, s18)))),
% 13.07/13.22 inference(rewrite,[status(thm)],[])).
% 13.07/13.22 tff(562,plain,
% 13.07/13.22 ((node2(c_bit0, s17) | (~node3(c_bit0, s17, s18)) | (~m_counter_cell_v_value(c_bit0, s18))) <=> ((~m_counter_cell_v_value(c_bit0, s18)) | node2(c_bit0, s17) | (~node3(c_bit0, s17, s18)))),
% 13.07/13.22 inference(rewrite,[status(thm)],[])).
% 13.07/13.22 tff(563,plain,
% 13.07/13.22 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s17) | (~node3(c_bit0, s17, s18)) | (~m_counter_cell_v_value(c_bit0, s18)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s18)) | node2(c_bit0, s17) | (~node3(c_bit0, s17, s18))))),
% 13.07/13.22 inference(monotonicity,[status(thm)],[562])).
% 13.07/13.22 tff(564,plain,
% 13.07/13.22 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s17) | (~node3(c_bit0, s17, s18)) | (~m_counter_cell_v_value(c_bit0, s18)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s18)) | node2(c_bit0, s17) | (~node3(c_bit0, s17, s18)))),
% 13.07/13.22 inference(transitivity,[status(thm)],[563, 561])).
% 13.07/13.22 tff(565,plain,
% 13.07/13.22 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s17) | (~node3(c_bit0, s17, s18)) | (~m_counter_cell_v_value(c_bit0, s18)))),
% 13.07/13.22 inference(quant_inst,[status(thm)],[])).
% 13.07/13.22 tff(566,plain,
% 13.07/13.22 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s18)) | node2(c_bit0, s17) | (~node3(c_bit0, s17, s18))),
% 13.07/13.22 inference(modus_ponens,[status(thm)],[565, 564])).
% 13.07/13.22 tff(567,plain,
% 13.07/13.22 ((~m_counter_cell_v_value(c_bit0, s18)) | node2(c_bit0, s17)),
% 13.07/13.22 inference(unit_resolution,[status(thm)],[566, 121, 560])).
% 13.07/13.22 tff(568,plain,
% 13.07/13.22 (~m_counter_cell_v_value(c_bit0, s18)),
% 13.07/13.22 inference(unit_resolution,[status(thm)],[567, 549])).
% 13.07/13.22 tff(569,assumption,(~m_counter_cell_v_carry_in(c_bit0, s18)), introduced(assumption)).
% 13.07/13.22 tff(570,plain,
% 13.07/13.22 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s18)),
% 13.07/13.22 inference(quant_inst,[status(thm)],[])).
% 13.07/13.22 tff(571,plain,
% 13.07/13.22 ($false),
% 13.07/13.22 inference(unit_resolution,[status(thm)],[570, 18, 569])).
% 13.07/13.22 tff(572,plain,(m_counter_cell_v_carry_in(c_bit0, s18)), inference(lemma,lemma(discharge,[]))).
% 13.07/13.22 tff(573,plain,
% 13.07/13.22 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s18)) | m_counter_cell_v_value(c_bit0, s18) | (~node1(c_bit0, s18)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s18)) | m_counter_cell_v_value(c_bit0, s18) | (~node1(c_bit0, s18)))),
% 13.07/13.22 inference(rewrite,[status(thm)],[])).
% 13.07/13.22 tff(574,plain,
% 13.07/13.22 (((~node1(c_bit0, s18)) | (~m_counter_cell_v_carry_in(c_bit0, s18)) | m_counter_cell_v_value(c_bit0, s18)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s18)) | m_counter_cell_v_value(c_bit0, s18) | (~node1(c_bit0, s18)))),
% 13.07/13.22 inference(rewrite,[status(thm)],[])).
% 13.07/13.22 tff(575,plain,
% 13.07/13.22 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s18)) | (~m_counter_cell_v_carry_in(c_bit0, s18)) | m_counter_cell_v_value(c_bit0, s18))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s18)) | m_counter_cell_v_value(c_bit0, s18) | (~node1(c_bit0, s18))))),
% 13.07/13.22 inference(monotonicity,[status(thm)],[574])).
% 13.07/13.22 tff(576,plain,
% 13.07/13.22 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s18)) | (~m_counter_cell_v_carry_in(c_bit0, s18)) | m_counter_cell_v_value(c_bit0, s18))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s18)) | m_counter_cell_v_value(c_bit0, s18) | (~node1(c_bit0, s18)))),
% 13.07/13.22 inference(transitivity,[status(thm)],[575, 573])).
% 13.07/13.22 tff(577,plain,
% 13.07/13.22 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s18)) | (~m_counter_cell_v_carry_in(c_bit0, s18)) | m_counter_cell_v_value(c_bit0, s18))),
% 13.07/13.22 inference(quant_inst,[status(thm)],[])).
% 13.07/13.22 tff(578,plain,
% 13.07/13.22 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s18)) | m_counter_cell_v_value(c_bit0, s18) | (~node1(c_bit0, s18))),
% 13.07/13.22 inference(modus_ponens,[status(thm)],[577, 576])).
% 13.07/13.22 tff(579,plain,
% 13.07/13.22 (m_counter_cell_v_value(c_bit0, s18) | (~node1(c_bit0, s18))),
% 13.07/13.22 inference(unit_resolution,[status(thm)],[578, 30, 572])).
% 13.07/13.22 tff(580,plain,
% 13.07/13.22 (~node1(c_bit0, s18)),
% 13.07/13.22 inference(unit_resolution,[status(thm)],[579, 568])).
% 13.07/13.22 tff(581,plain,
% 13.07/13.22 (succ(s18, s19) <=> succ(s18, s19)),
% 13.07/13.22 inference(rewrite,[status(thm)],[])).
% 13.07/13.22 tff(582,axiom,(succ(s18, s19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound19')).
% 13.07/13.22 tff(583,plain,
% 13.07/13.22 (succ(s18, s19)),
% 13.07/13.22 inference(modus_ponens,[status(thm)],[582, 581])).
% 13.07/13.22 tff(584,plain,
% 13.07/13.22 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s18, s19)) | trans(s18, s19))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s18, s19)) | trans(s18, s19))),
% 13.07/13.22 inference(rewrite,[status(thm)],[])).
% 13.07/13.22 tff(585,plain,
% 13.07/13.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s18, s19)) | trans(s18, s19))),
% 13.07/13.22 inference(quant_inst,[status(thm)],[])).
% 13.07/13.22 tff(586,plain,
% 13.07/13.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s18, s19)) | trans(s18, s19)),
% 13.07/13.22 inference(modus_ponens,[status(thm)],[585, 584])).
% 13.07/13.22 tff(587,plain,
% 13.07/13.22 (trans(s18, s19)),
% 13.07/13.22 inference(unit_resolution,[status(thm)],[586, 583, 45])).
% 13.07/13.22 tff(588,plain,
% 13.07/13.22 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s18, s19)) | node3(c_bit0, s18, s19))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s18, s19)) | node3(c_bit0, s18, s19))),
% 13.07/13.22 inference(rewrite,[status(thm)],[])).
% 13.07/13.22 tff(589,plain,
% 13.07/13.22 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s18, s19)) | node3(c_bit0, s18, s19))),
% 13.07/13.22 inference(quant_inst,[status(thm)],[])).
% 13.07/13.22 tff(590,plain,
% 13.07/13.22 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s18, s19)) | node3(c_bit0, s18, s19)),
% 13.07/13.22 inference(modus_ponens,[status(thm)],[589, 588])).
% 13.07/13.22 tff(591,plain,
% 13.07/13.22 (node3(c_bit0, s18, s19)),
% 13.07/13.22 inference(unit_resolution,[status(thm)],[590, 59, 587])).
% 13.07/13.22 tff(592,plain,
% 13.07/13.22 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s19) | node1(c_bit0, s18) | (~node3(c_bit0, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s19) | node1(c_bit0, s18) | (~node3(c_bit0, s18, s19)))),
% 13.07/13.22 inference(rewrite,[status(thm)],[])).
% 13.07/13.22 tff(593,plain,
% 13.07/13.22 ((node1(c_bit0, s18) | (~node3(c_bit0, s18, s19)) | m_counter_cell_v_value(c_bit0, s19)) <=> (m_counter_cell_v_value(c_bit0, s19) | node1(c_bit0, s18) | (~node3(c_bit0, s18, s19)))),
% 13.07/13.22 inference(rewrite,[status(thm)],[])).
% 13.07/13.22 tff(594,plain,
% 13.07/13.22 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s18) | (~node3(c_bit0, s18, s19)) | m_counter_cell_v_value(c_bit0, s19))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s19) | node1(c_bit0, s18) | (~node3(c_bit0, s18, s19))))),
% 13.07/13.22 inference(monotonicity,[status(thm)],[593])).
% 13.07/13.22 tff(595,plain,
% 13.07/13.22 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s18) | (~node3(c_bit0, s18, s19)) | m_counter_cell_v_value(c_bit0, s19))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s19) | node1(c_bit0, s18) | (~node3(c_bit0, s18, s19)))),
% 13.07/13.22 inference(transitivity,[status(thm)],[594, 592])).
% 13.07/13.22 tff(596,plain,
% 13.07/13.22 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s18) | (~node3(c_bit0, s18, s19)) | m_counter_cell_v_value(c_bit0, s19))),
% 13.07/13.22 inference(quant_inst,[status(thm)],[])).
% 13.07/13.22 tff(597,plain,
% 13.07/13.22 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s19) | node1(c_bit0, s18) | (~node3(c_bit0, s18, s19))),
% 13.07/13.22 inference(modus_ponens,[status(thm)],[596, 595])).
% 13.07/13.22 tff(598,plain,
% 13.07/13.22 (m_counter_cell_v_value(c_bit0, s19) | node1(c_bit0, s18)),
% 13.07/13.22 inference(unit_resolution,[status(thm)],[597, 73, 591])).
% 13.07/13.22 tff(599,plain,
% 13.07/13.22 (m_counter_cell_v_value(c_bit0, s19)),
% 13.07/13.22 inference(unit_resolution,[status(thm)],[598, 580])).
% 13.07/13.22 tff(600,assumption,(~m_counter_cell_v_carry_in(c_bit0, s19)), introduced(assumption)).
% 13.07/13.22 tff(601,plain,
% 13.07/13.22 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s19)),
% 13.07/13.22 inference(quant_inst,[status(thm)],[])).
% 13.07/13.22 tff(602,plain,
% 13.07/13.22 ($false),
% 13.07/13.22 inference(unit_resolution,[status(thm)],[601, 18, 600])).
% 13.07/13.22 tff(603,plain,(m_counter_cell_v_carry_in(c_bit0, s19)), inference(lemma,lemma(discharge,[]))).
% 13.07/13.22 tff(604,plain,
% 13.07/13.22 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s19)) | (~m_counter_cell_v_value(c_bit0, s19)) | (~node2(c_bit0, s19)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s19)) | (~m_counter_cell_v_value(c_bit0, s19)) | (~node2(c_bit0, s19)))),
% 13.07/13.22 inference(rewrite,[status(thm)],[])).
% 13.07/13.22 tff(605,plain,
% 13.07/13.22 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s19)) | (~m_counter_cell_v_value(c_bit0, s19)) | (~node2(c_bit0, s19)))),
% 13.07/13.23 inference(quant_inst,[status(thm)],[])).
% 13.07/13.23 tff(606,plain,
% 13.07/13.23 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s19)) | (~m_counter_cell_v_value(c_bit0, s19)) | (~node2(c_bit0, s19))),
% 13.07/13.23 inference(modus_ponens,[status(thm)],[605, 604])).
% 13.07/13.23 tff(607,plain,
% 13.07/13.23 ((~m_counter_cell_v_value(c_bit0, s19)) | (~node2(c_bit0, s19))),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[606, 93, 603])).
% 13.07/13.23 tff(608,plain,
% 13.07/13.23 (~node2(c_bit0, s19)),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[607, 599])).
% 13.07/13.23 tff(609,plain,
% 13.07/13.23 (succ(s19, s20) <=> succ(s19, s20)),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(610,axiom,(succ(s19, s20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound20')).
% 13.07/13.23 tff(611,plain,
% 13.07/13.23 (succ(s19, s20)),
% 13.07/13.23 inference(modus_ponens,[status(thm)],[610, 609])).
% 13.07/13.23 tff(612,plain,
% 13.07/13.23 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s19, s20)) | trans(s19, s20))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s19, s20)) | trans(s19, s20))),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(613,plain,
% 13.07/13.23 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s19, s20)) | trans(s19, s20))),
% 13.07/13.23 inference(quant_inst,[status(thm)],[])).
% 13.07/13.23 tff(614,plain,
% 13.07/13.23 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s19, s20)) | trans(s19, s20)),
% 13.07/13.23 inference(modus_ponens,[status(thm)],[613, 612])).
% 13.07/13.23 tff(615,plain,
% 13.07/13.23 (trans(s19, s20)),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[614, 611, 45])).
% 13.07/13.23 tff(616,plain,
% 13.07/13.23 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s19, s20)) | node3(c_bit0, s19, s20))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s19, s20)) | node3(c_bit0, s19, s20))),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(617,plain,
% 13.07/13.23 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s19, s20)) | node3(c_bit0, s19, s20))),
% 13.07/13.23 inference(quant_inst,[status(thm)],[])).
% 13.07/13.23 tff(618,plain,
% 13.07/13.23 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s19, s20)) | node3(c_bit0, s19, s20)),
% 13.07/13.23 inference(modus_ponens,[status(thm)],[617, 616])).
% 13.07/13.23 tff(619,plain,
% 13.07/13.23 (node3(c_bit0, s19, s20)),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[618, 59, 615])).
% 13.07/13.23 tff(620,plain,
% 13.07/13.23 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s20)) | node2(c_bit0, s19) | (~node3(c_bit0, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s20)) | node2(c_bit0, s19) | (~node3(c_bit0, s19, s20)))),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(621,plain,
% 13.07/13.23 ((node2(c_bit0, s19) | (~node3(c_bit0, s19, s20)) | (~m_counter_cell_v_value(c_bit0, s20))) <=> ((~m_counter_cell_v_value(c_bit0, s20)) | node2(c_bit0, s19) | (~node3(c_bit0, s19, s20)))),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(622,plain,
% 13.07/13.23 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s19) | (~node3(c_bit0, s19, s20)) | (~m_counter_cell_v_value(c_bit0, s20)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s20)) | node2(c_bit0, s19) | (~node3(c_bit0, s19, s20))))),
% 13.07/13.23 inference(monotonicity,[status(thm)],[621])).
% 13.07/13.23 tff(623,plain,
% 13.07/13.23 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s19) | (~node3(c_bit0, s19, s20)) | (~m_counter_cell_v_value(c_bit0, s20)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s20)) | node2(c_bit0, s19) | (~node3(c_bit0, s19, s20)))),
% 13.07/13.23 inference(transitivity,[status(thm)],[622, 620])).
% 13.07/13.23 tff(624,plain,
% 13.07/13.23 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s19) | (~node3(c_bit0, s19, s20)) | (~m_counter_cell_v_value(c_bit0, s20)))),
% 13.07/13.23 inference(quant_inst,[status(thm)],[])).
% 13.07/13.23 tff(625,plain,
% 13.07/13.23 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s20)) | node2(c_bit0, s19) | (~node3(c_bit0, s19, s20))),
% 13.07/13.23 inference(modus_ponens,[status(thm)],[624, 623])).
% 13.07/13.23 tff(626,plain,
% 13.07/13.23 ((~m_counter_cell_v_value(c_bit0, s20)) | node2(c_bit0, s19)),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[625, 121, 619])).
% 13.07/13.23 tff(627,plain,
% 13.07/13.23 (~m_counter_cell_v_value(c_bit0, s20)),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[626, 608])).
% 13.07/13.23 tff(628,assumption,(~m_counter_cell_v_carry_in(c_bit0, s20)), introduced(assumption)).
% 13.07/13.23 tff(629,plain,
% 13.07/13.23 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s20)),
% 13.07/13.23 inference(quant_inst,[status(thm)],[])).
% 13.07/13.23 tff(630,plain,
% 13.07/13.23 ($false),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[629, 18, 628])).
% 13.07/13.23 tff(631,plain,(m_counter_cell_v_carry_in(c_bit0, s20)), inference(lemma,lemma(discharge,[]))).
% 13.07/13.23 tff(632,plain,
% 13.07/13.23 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s20)) | m_counter_cell_v_value(c_bit0, s20) | (~node1(c_bit0, s20)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s20)) | m_counter_cell_v_value(c_bit0, s20) | (~node1(c_bit0, s20)))),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(633,plain,
% 13.07/13.23 (((~node1(c_bit0, s20)) | (~m_counter_cell_v_carry_in(c_bit0, s20)) | m_counter_cell_v_value(c_bit0, s20)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s20)) | m_counter_cell_v_value(c_bit0, s20) | (~node1(c_bit0, s20)))),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(634,plain,
% 13.07/13.23 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s20)) | (~m_counter_cell_v_carry_in(c_bit0, s20)) | m_counter_cell_v_value(c_bit0, s20))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s20)) | m_counter_cell_v_value(c_bit0, s20) | (~node1(c_bit0, s20))))),
% 13.07/13.23 inference(monotonicity,[status(thm)],[633])).
% 13.07/13.23 tff(635,plain,
% 13.07/13.23 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s20)) | (~m_counter_cell_v_carry_in(c_bit0, s20)) | m_counter_cell_v_value(c_bit0, s20))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s20)) | m_counter_cell_v_value(c_bit0, s20) | (~node1(c_bit0, s20)))),
% 13.07/13.23 inference(transitivity,[status(thm)],[634, 632])).
% 13.07/13.23 tff(636,plain,
% 13.07/13.23 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s20)) | (~m_counter_cell_v_carry_in(c_bit0, s20)) | m_counter_cell_v_value(c_bit0, s20))),
% 13.07/13.23 inference(quant_inst,[status(thm)],[])).
% 13.07/13.23 tff(637,plain,
% 13.07/13.23 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s20)) | m_counter_cell_v_value(c_bit0, s20) | (~node1(c_bit0, s20))),
% 13.07/13.23 inference(modus_ponens,[status(thm)],[636, 635])).
% 13.07/13.23 tff(638,plain,
% 13.07/13.23 (m_counter_cell_v_value(c_bit0, s20) | (~node1(c_bit0, s20))),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[637, 30, 631])).
% 13.07/13.23 tff(639,plain,
% 13.07/13.23 (~node1(c_bit0, s20)),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[638, 627])).
% 13.07/13.23 tff(640,plain,
% 13.07/13.23 (succ(s20, s21) <=> succ(s20, s21)),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(641,axiom,(succ(s20, s21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound21')).
% 13.07/13.23 tff(642,plain,
% 13.07/13.23 (succ(s20, s21)),
% 13.07/13.23 inference(modus_ponens,[status(thm)],[641, 640])).
% 13.07/13.23 tff(643,plain,
% 13.07/13.23 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s20, s21)) | trans(s20, s21))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s20, s21)) | trans(s20, s21))),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(644,plain,
% 13.07/13.23 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s20, s21)) | trans(s20, s21))),
% 13.07/13.23 inference(quant_inst,[status(thm)],[])).
% 13.07/13.23 tff(645,plain,
% 13.07/13.23 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s20, s21)) | trans(s20, s21)),
% 13.07/13.23 inference(modus_ponens,[status(thm)],[644, 643])).
% 13.07/13.23 tff(646,plain,
% 13.07/13.23 (trans(s20, s21)),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[645, 642, 45])).
% 13.07/13.23 tff(647,plain,
% 13.07/13.23 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s20, s21)) | node3(c_bit0, s20, s21))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s20, s21)) | node3(c_bit0, s20, s21))),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(648,plain,
% 13.07/13.23 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s20, s21)) | node3(c_bit0, s20, s21))),
% 13.07/13.23 inference(quant_inst,[status(thm)],[])).
% 13.07/13.23 tff(649,plain,
% 13.07/13.23 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s20, s21)) | node3(c_bit0, s20, s21)),
% 13.07/13.23 inference(modus_ponens,[status(thm)],[648, 647])).
% 13.07/13.23 tff(650,plain,
% 13.07/13.23 (node3(c_bit0, s20, s21)),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[649, 59, 646])).
% 13.07/13.23 tff(651,plain,
% 13.07/13.23 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s21) | node1(c_bit0, s20) | (~node3(c_bit0, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s21) | node1(c_bit0, s20) | (~node3(c_bit0, s20, s21)))),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(652,plain,
% 13.07/13.23 ((node1(c_bit0, s20) | (~node3(c_bit0, s20, s21)) | m_counter_cell_v_value(c_bit0, s21)) <=> (m_counter_cell_v_value(c_bit0, s21) | node1(c_bit0, s20) | (~node3(c_bit0, s20, s21)))),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(653,plain,
% 13.07/13.23 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s20) | (~node3(c_bit0, s20, s21)) | m_counter_cell_v_value(c_bit0, s21))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s21) | node1(c_bit0, s20) | (~node3(c_bit0, s20, s21))))),
% 13.07/13.23 inference(monotonicity,[status(thm)],[652])).
% 13.07/13.23 tff(654,plain,
% 13.07/13.23 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s20) | (~node3(c_bit0, s20, s21)) | m_counter_cell_v_value(c_bit0, s21))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s21) | node1(c_bit0, s20) | (~node3(c_bit0, s20, s21)))),
% 13.07/13.23 inference(transitivity,[status(thm)],[653, 651])).
% 13.07/13.23 tff(655,plain,
% 13.07/13.23 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s20) | (~node3(c_bit0, s20, s21)) | m_counter_cell_v_value(c_bit0, s21))),
% 13.07/13.23 inference(quant_inst,[status(thm)],[])).
% 13.07/13.23 tff(656,plain,
% 13.07/13.23 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s21) | node1(c_bit0, s20) | (~node3(c_bit0, s20, s21))),
% 13.07/13.23 inference(modus_ponens,[status(thm)],[655, 654])).
% 13.07/13.23 tff(657,plain,
% 13.07/13.23 (m_counter_cell_v_value(c_bit0, s21) | node1(c_bit0, s20)),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[656, 73, 650])).
% 13.07/13.23 tff(658,plain,
% 13.07/13.23 (m_counter_cell_v_value(c_bit0, s21)),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[657, 639])).
% 13.07/13.23 tff(659,assumption,(~m_counter_cell_v_carry_in(c_bit0, s21)), introduced(assumption)).
% 13.07/13.23 tff(660,plain,
% 13.07/13.23 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s21)),
% 13.07/13.23 inference(quant_inst,[status(thm)],[])).
% 13.07/13.23 tff(661,plain,
% 13.07/13.23 ($false),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[660, 18, 659])).
% 13.07/13.23 tff(662,plain,(m_counter_cell_v_carry_in(c_bit0, s21)), inference(lemma,lemma(discharge,[]))).
% 13.07/13.23 tff(663,plain,
% 13.07/13.23 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s21)) | (~m_counter_cell_v_value(c_bit0, s21)) | (~node2(c_bit0, s21)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s21)) | (~m_counter_cell_v_value(c_bit0, s21)) | (~node2(c_bit0, s21)))),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(664,plain,
% 13.07/13.23 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s21)) | (~m_counter_cell_v_value(c_bit0, s21)) | (~node2(c_bit0, s21)))),
% 13.07/13.23 inference(quant_inst,[status(thm)],[])).
% 13.07/13.23 tff(665,plain,
% 13.07/13.23 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s21)) | (~m_counter_cell_v_value(c_bit0, s21)) | (~node2(c_bit0, s21))),
% 13.07/13.23 inference(modus_ponens,[status(thm)],[664, 663])).
% 13.07/13.23 tff(666,plain,
% 13.07/13.23 ((~m_counter_cell_v_value(c_bit0, s21)) | (~node2(c_bit0, s21))),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[665, 93, 662])).
% 13.07/13.23 tff(667,plain,
% 13.07/13.23 (~node2(c_bit0, s21)),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[666, 658])).
% 13.07/13.23 tff(668,plain,
% 13.07/13.23 (succ(s21, s22) <=> succ(s21, s22)),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(669,axiom,(succ(s21, s22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound22')).
% 13.07/13.23 tff(670,plain,
% 13.07/13.23 (succ(s21, s22)),
% 13.07/13.23 inference(modus_ponens,[status(thm)],[669, 668])).
% 13.07/13.23 tff(671,plain,
% 13.07/13.23 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s21, s22)) | trans(s21, s22))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s21, s22)) | trans(s21, s22))),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(672,plain,
% 13.07/13.23 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s21, s22)) | trans(s21, s22))),
% 13.07/13.23 inference(quant_inst,[status(thm)],[])).
% 13.07/13.23 tff(673,plain,
% 13.07/13.23 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s21, s22)) | trans(s21, s22)),
% 13.07/13.23 inference(modus_ponens,[status(thm)],[672, 671])).
% 13.07/13.23 tff(674,plain,
% 13.07/13.23 (trans(s21, s22)),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[673, 670, 45])).
% 13.07/13.23 tff(675,plain,
% 13.07/13.23 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s21, s22)) | node3(c_bit0, s21, s22))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s21, s22)) | node3(c_bit0, s21, s22))),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(676,plain,
% 13.07/13.23 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s21, s22)) | node3(c_bit0, s21, s22))),
% 13.07/13.23 inference(quant_inst,[status(thm)],[])).
% 13.07/13.23 tff(677,plain,
% 13.07/13.23 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s21, s22)) | node3(c_bit0, s21, s22)),
% 13.07/13.23 inference(modus_ponens,[status(thm)],[676, 675])).
% 13.07/13.23 tff(678,plain,
% 13.07/13.23 (node3(c_bit0, s21, s22)),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[677, 59, 674])).
% 13.07/13.23 tff(679,plain,
% 13.07/13.23 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s22)) | node2(c_bit0, s21) | (~node3(c_bit0, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s22)) | node2(c_bit0, s21) | (~node3(c_bit0, s21, s22)))),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(680,plain,
% 13.07/13.23 ((node2(c_bit0, s21) | (~node3(c_bit0, s21, s22)) | (~m_counter_cell_v_value(c_bit0, s22))) <=> ((~m_counter_cell_v_value(c_bit0, s22)) | node2(c_bit0, s21) | (~node3(c_bit0, s21, s22)))),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(681,plain,
% 13.07/13.23 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s21) | (~node3(c_bit0, s21, s22)) | (~m_counter_cell_v_value(c_bit0, s22)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s22)) | node2(c_bit0, s21) | (~node3(c_bit0, s21, s22))))),
% 13.07/13.23 inference(monotonicity,[status(thm)],[680])).
% 13.07/13.23 tff(682,plain,
% 13.07/13.23 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s21) | (~node3(c_bit0, s21, s22)) | (~m_counter_cell_v_value(c_bit0, s22)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s22)) | node2(c_bit0, s21) | (~node3(c_bit0, s21, s22)))),
% 13.07/13.23 inference(transitivity,[status(thm)],[681, 679])).
% 13.07/13.23 tff(683,plain,
% 13.07/13.23 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s21) | (~node3(c_bit0, s21, s22)) | (~m_counter_cell_v_value(c_bit0, s22)))),
% 13.07/13.23 inference(quant_inst,[status(thm)],[])).
% 13.07/13.23 tff(684,plain,
% 13.07/13.23 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s22)) | node2(c_bit0, s21) | (~node3(c_bit0, s21, s22))),
% 13.07/13.23 inference(modus_ponens,[status(thm)],[683, 682])).
% 13.07/13.23 tff(685,plain,
% 13.07/13.23 ((~m_counter_cell_v_value(c_bit0, s22)) | node2(c_bit0, s21)),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[684, 121, 678])).
% 13.07/13.23 tff(686,plain,
% 13.07/13.23 (~m_counter_cell_v_value(c_bit0, s22)),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[685, 667])).
% 13.07/13.23 tff(687,assumption,(~m_counter_cell_v_carry_in(c_bit0, s22)), introduced(assumption)).
% 13.07/13.23 tff(688,plain,
% 13.07/13.23 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s22)),
% 13.07/13.23 inference(quant_inst,[status(thm)],[])).
% 13.07/13.23 tff(689,plain,
% 13.07/13.23 ($false),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[688, 18, 687])).
% 13.07/13.23 tff(690,plain,(m_counter_cell_v_carry_in(c_bit0, s22)), inference(lemma,lemma(discharge,[]))).
% 13.07/13.23 tff(691,plain,
% 13.07/13.23 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s22)) | m_counter_cell_v_value(c_bit0, s22) | (~node1(c_bit0, s22)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s22)) | m_counter_cell_v_value(c_bit0, s22) | (~node1(c_bit0, s22)))),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(692,plain,
% 13.07/13.23 (((~node1(c_bit0, s22)) | (~m_counter_cell_v_carry_in(c_bit0, s22)) | m_counter_cell_v_value(c_bit0, s22)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s22)) | m_counter_cell_v_value(c_bit0, s22) | (~node1(c_bit0, s22)))),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(693,plain,
% 13.07/13.23 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s22)) | (~m_counter_cell_v_carry_in(c_bit0, s22)) | m_counter_cell_v_value(c_bit0, s22))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s22)) | m_counter_cell_v_value(c_bit0, s22) | (~node1(c_bit0, s22))))),
% 13.07/13.23 inference(monotonicity,[status(thm)],[692])).
% 13.07/13.23 tff(694,plain,
% 13.07/13.23 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s22)) | (~m_counter_cell_v_carry_in(c_bit0, s22)) | m_counter_cell_v_value(c_bit0, s22))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s22)) | m_counter_cell_v_value(c_bit0, s22) | (~node1(c_bit0, s22)))),
% 13.07/13.23 inference(transitivity,[status(thm)],[693, 691])).
% 13.07/13.23 tff(695,plain,
% 13.07/13.23 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s22)) | (~m_counter_cell_v_carry_in(c_bit0, s22)) | m_counter_cell_v_value(c_bit0, s22))),
% 13.07/13.23 inference(quant_inst,[status(thm)],[])).
% 13.07/13.23 tff(696,plain,
% 13.07/13.23 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s22)) | m_counter_cell_v_value(c_bit0, s22) | (~node1(c_bit0, s22))),
% 13.07/13.23 inference(modus_ponens,[status(thm)],[695, 694])).
% 13.07/13.23 tff(697,plain,
% 13.07/13.23 (m_counter_cell_v_value(c_bit0, s22) | (~node1(c_bit0, s22))),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[696, 30, 690])).
% 13.07/13.23 tff(698,plain,
% 13.07/13.23 (~node1(c_bit0, s22)),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[697, 686])).
% 13.07/13.23 tff(699,plain,
% 13.07/13.23 (succ(s22, s23) <=> succ(s22, s23)),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(700,axiom,(succ(s22, s23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound23')).
% 13.07/13.23 tff(701,plain,
% 13.07/13.23 (succ(s22, s23)),
% 13.07/13.23 inference(modus_ponens,[status(thm)],[700, 699])).
% 13.07/13.23 tff(702,plain,
% 13.07/13.23 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s22, s23)) | trans(s22, s23))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s22, s23)) | trans(s22, s23))),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(703,plain,
% 13.07/13.23 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s22, s23)) | trans(s22, s23))),
% 13.07/13.23 inference(quant_inst,[status(thm)],[])).
% 13.07/13.23 tff(704,plain,
% 13.07/13.23 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s22, s23)) | trans(s22, s23)),
% 13.07/13.23 inference(modus_ponens,[status(thm)],[703, 702])).
% 13.07/13.23 tff(705,plain,
% 13.07/13.23 (trans(s22, s23)),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[704, 701, 45])).
% 13.07/13.23 tff(706,plain,
% 13.07/13.23 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s22, s23)) | node3(c_bit0, s22, s23))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s22, s23)) | node3(c_bit0, s22, s23))),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(707,plain,
% 13.07/13.23 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s22, s23)) | node3(c_bit0, s22, s23))),
% 13.07/13.23 inference(quant_inst,[status(thm)],[])).
% 13.07/13.23 tff(708,plain,
% 13.07/13.23 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s22, s23)) | node3(c_bit0, s22, s23)),
% 13.07/13.23 inference(modus_ponens,[status(thm)],[707, 706])).
% 13.07/13.23 tff(709,plain,
% 13.07/13.23 (node3(c_bit0, s22, s23)),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[708, 59, 705])).
% 13.07/13.23 tff(710,plain,
% 13.07/13.23 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s23) | node1(c_bit0, s22) | (~node3(c_bit0, s22, s23)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s23) | node1(c_bit0, s22) | (~node3(c_bit0, s22, s23)))),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(711,plain,
% 13.07/13.23 ((node1(c_bit0, s22) | (~node3(c_bit0, s22, s23)) | m_counter_cell_v_value(c_bit0, s23)) <=> (m_counter_cell_v_value(c_bit0, s23) | node1(c_bit0, s22) | (~node3(c_bit0, s22, s23)))),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(712,plain,
% 13.07/13.23 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s22) | (~node3(c_bit0, s22, s23)) | m_counter_cell_v_value(c_bit0, s23))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s23) | node1(c_bit0, s22) | (~node3(c_bit0, s22, s23))))),
% 13.07/13.23 inference(monotonicity,[status(thm)],[711])).
% 13.07/13.23 tff(713,plain,
% 13.07/13.23 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s22) | (~node3(c_bit0, s22, s23)) | m_counter_cell_v_value(c_bit0, s23))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s23) | node1(c_bit0, s22) | (~node3(c_bit0, s22, s23)))),
% 13.07/13.23 inference(transitivity,[status(thm)],[712, 710])).
% 13.07/13.23 tff(714,plain,
% 13.07/13.23 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s22) | (~node3(c_bit0, s22, s23)) | m_counter_cell_v_value(c_bit0, s23))),
% 13.07/13.23 inference(quant_inst,[status(thm)],[])).
% 13.07/13.23 tff(715,plain,
% 13.07/13.23 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s23) | node1(c_bit0, s22) | (~node3(c_bit0, s22, s23))),
% 13.07/13.23 inference(modus_ponens,[status(thm)],[714, 713])).
% 13.07/13.23 tff(716,plain,
% 13.07/13.23 (m_counter_cell_v_value(c_bit0, s23) | node1(c_bit0, s22)),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[715, 73, 709])).
% 13.07/13.23 tff(717,plain,
% 13.07/13.23 (m_counter_cell_v_value(c_bit0, s23)),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[716, 698])).
% 13.07/13.23 tff(718,assumption,(~m_counter_cell_v_carry_in(c_bit0, s23)), introduced(assumption)).
% 13.07/13.23 tff(719,plain,
% 13.07/13.23 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s23)),
% 13.07/13.23 inference(quant_inst,[status(thm)],[])).
% 13.07/13.23 tff(720,plain,
% 13.07/13.23 ($false),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[719, 18, 718])).
% 13.07/13.23 tff(721,plain,(m_counter_cell_v_carry_in(c_bit0, s23)), inference(lemma,lemma(discharge,[]))).
% 13.07/13.23 tff(722,plain,
% 13.07/13.23 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s23)) | (~m_counter_cell_v_value(c_bit0, s23)) | (~node2(c_bit0, s23)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s23)) | (~m_counter_cell_v_value(c_bit0, s23)) | (~node2(c_bit0, s23)))),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(723,plain,
% 13.07/13.23 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s23)) | (~m_counter_cell_v_value(c_bit0, s23)) | (~node2(c_bit0, s23)))),
% 13.07/13.23 inference(quant_inst,[status(thm)],[])).
% 13.07/13.23 tff(724,plain,
% 13.07/13.23 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s23)) | (~m_counter_cell_v_value(c_bit0, s23)) | (~node2(c_bit0, s23))),
% 13.07/13.23 inference(modus_ponens,[status(thm)],[723, 722])).
% 13.07/13.23 tff(725,plain,
% 13.07/13.23 ((~m_counter_cell_v_value(c_bit0, s23)) | (~node2(c_bit0, s23))),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[724, 93, 721])).
% 13.07/13.23 tff(726,plain,
% 13.07/13.23 (~node2(c_bit0, s23)),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[725, 717])).
% 13.07/13.23 tff(727,plain,
% 13.07/13.23 (succ(s23, s24) <=> succ(s23, s24)),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(728,axiom,(succ(s23, s24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound24')).
% 13.07/13.23 tff(729,plain,
% 13.07/13.23 (succ(s23, s24)),
% 13.07/13.23 inference(modus_ponens,[status(thm)],[728, 727])).
% 13.07/13.23 tff(730,plain,
% 13.07/13.23 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s23, s24)) | trans(s23, s24))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s23, s24)) | trans(s23, s24))),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(731,plain,
% 13.07/13.23 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s23, s24)) | trans(s23, s24))),
% 13.07/13.23 inference(quant_inst,[status(thm)],[])).
% 13.07/13.23 tff(732,plain,
% 13.07/13.23 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s23, s24)) | trans(s23, s24)),
% 13.07/13.23 inference(modus_ponens,[status(thm)],[731, 730])).
% 13.07/13.23 tff(733,plain,
% 13.07/13.23 (trans(s23, s24)),
% 13.07/13.23 inference(unit_resolution,[status(thm)],[732, 729, 45])).
% 13.07/13.23 tff(734,plain,
% 13.07/13.23 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s23, s24)) | node3(c_bit0, s23, s24))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s23, s24)) | node3(c_bit0, s23, s24))),
% 13.07/13.23 inference(rewrite,[status(thm)],[])).
% 13.07/13.23 tff(735,plain,
% 13.07/13.23 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s23, s24)) | node3(c_bit0, s23, s24))),
% 13.07/13.23 inference(quant_inst,[status(thm)],[])).
% 13.07/13.23 tff(736,plain,
% 13.07/13.23 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s23, s24)) | node3(c_bit0, s23, s24)),
% 13.07/13.23 inference(modus_ponens,[status(thm)],[735, 734])).
% 13.07/13.24 tff(737,plain,
% 13.07/13.24 (node3(c_bit0, s23, s24)),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[736, 59, 733])).
% 13.07/13.24 tff(738,plain,
% 13.07/13.24 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s24)) | node2(c_bit0, s23) | (~node3(c_bit0, s23, s24)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s24)) | node2(c_bit0, s23) | (~node3(c_bit0, s23, s24)))),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(739,plain,
% 13.07/13.24 ((node2(c_bit0, s23) | (~node3(c_bit0, s23, s24)) | (~m_counter_cell_v_value(c_bit0, s24))) <=> ((~m_counter_cell_v_value(c_bit0, s24)) | node2(c_bit0, s23) | (~node3(c_bit0, s23, s24)))),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(740,plain,
% 13.07/13.24 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s23) | (~node3(c_bit0, s23, s24)) | (~m_counter_cell_v_value(c_bit0, s24)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s24)) | node2(c_bit0, s23) | (~node3(c_bit0, s23, s24))))),
% 13.07/13.24 inference(monotonicity,[status(thm)],[739])).
% 13.07/13.24 tff(741,plain,
% 13.07/13.24 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s23) | (~node3(c_bit0, s23, s24)) | (~m_counter_cell_v_value(c_bit0, s24)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s24)) | node2(c_bit0, s23) | (~node3(c_bit0, s23, s24)))),
% 13.07/13.24 inference(transitivity,[status(thm)],[740, 738])).
% 13.07/13.24 tff(742,plain,
% 13.07/13.24 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s23) | (~node3(c_bit0, s23, s24)) | (~m_counter_cell_v_value(c_bit0, s24)))),
% 13.07/13.24 inference(quant_inst,[status(thm)],[])).
% 13.07/13.24 tff(743,plain,
% 13.07/13.24 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s24)) | node2(c_bit0, s23) | (~node3(c_bit0, s23, s24))),
% 13.07/13.24 inference(modus_ponens,[status(thm)],[742, 741])).
% 13.07/13.24 tff(744,plain,
% 13.07/13.24 ((~m_counter_cell_v_value(c_bit0, s24)) | node2(c_bit0, s23)),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[743, 121, 737])).
% 13.07/13.24 tff(745,plain,
% 13.07/13.24 (~m_counter_cell_v_value(c_bit0, s24)),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[744, 726])).
% 13.07/13.24 tff(746,assumption,(~m_counter_cell_v_carry_in(c_bit0, s24)), introduced(assumption)).
% 13.07/13.24 tff(747,plain,
% 13.07/13.24 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s24)),
% 13.07/13.24 inference(quant_inst,[status(thm)],[])).
% 13.07/13.24 tff(748,plain,
% 13.07/13.24 ($false),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[747, 18, 746])).
% 13.07/13.24 tff(749,plain,(m_counter_cell_v_carry_in(c_bit0, s24)), inference(lemma,lemma(discharge,[]))).
% 13.07/13.24 tff(750,plain,
% 13.07/13.24 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s24)) | m_counter_cell_v_value(c_bit0, s24) | (~node1(c_bit0, s24)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s24)) | m_counter_cell_v_value(c_bit0, s24) | (~node1(c_bit0, s24)))),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(751,plain,
% 13.07/13.24 (((~node1(c_bit0, s24)) | (~m_counter_cell_v_carry_in(c_bit0, s24)) | m_counter_cell_v_value(c_bit0, s24)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s24)) | m_counter_cell_v_value(c_bit0, s24) | (~node1(c_bit0, s24)))),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(752,plain,
% 13.07/13.24 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s24)) | (~m_counter_cell_v_carry_in(c_bit0, s24)) | m_counter_cell_v_value(c_bit0, s24))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s24)) | m_counter_cell_v_value(c_bit0, s24) | (~node1(c_bit0, s24))))),
% 13.07/13.24 inference(monotonicity,[status(thm)],[751])).
% 13.07/13.24 tff(753,plain,
% 13.07/13.24 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s24)) | (~m_counter_cell_v_carry_in(c_bit0, s24)) | m_counter_cell_v_value(c_bit0, s24))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s24)) | m_counter_cell_v_value(c_bit0, s24) | (~node1(c_bit0, s24)))),
% 13.07/13.24 inference(transitivity,[status(thm)],[752, 750])).
% 13.07/13.24 tff(754,plain,
% 13.07/13.24 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s24)) | (~m_counter_cell_v_carry_in(c_bit0, s24)) | m_counter_cell_v_value(c_bit0, s24))),
% 13.07/13.24 inference(quant_inst,[status(thm)],[])).
% 13.07/13.24 tff(755,plain,
% 13.07/13.24 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s24)) | m_counter_cell_v_value(c_bit0, s24) | (~node1(c_bit0, s24))),
% 13.07/13.24 inference(modus_ponens,[status(thm)],[754, 753])).
% 13.07/13.24 tff(756,plain,
% 13.07/13.24 (m_counter_cell_v_value(c_bit0, s24) | (~node1(c_bit0, s24))),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[755, 30, 749])).
% 13.07/13.24 tff(757,plain,
% 13.07/13.24 (~node1(c_bit0, s24)),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[756, 745])).
% 13.07/13.24 tff(758,plain,
% 13.07/13.24 (succ(s24, s25) <=> succ(s24, s25)),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(759,axiom,(succ(s24, s25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound25')).
% 13.07/13.24 tff(760,plain,
% 13.07/13.24 (succ(s24, s25)),
% 13.07/13.24 inference(modus_ponens,[status(thm)],[759, 758])).
% 13.07/13.24 tff(761,plain,
% 13.07/13.24 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s24, s25)) | trans(s24, s25))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s24, s25)) | trans(s24, s25))),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(762,plain,
% 13.07/13.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s24, s25)) | trans(s24, s25))),
% 13.07/13.24 inference(quant_inst,[status(thm)],[])).
% 13.07/13.24 tff(763,plain,
% 13.07/13.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s24, s25)) | trans(s24, s25)),
% 13.07/13.24 inference(modus_ponens,[status(thm)],[762, 761])).
% 13.07/13.24 tff(764,plain,
% 13.07/13.24 (trans(s24, s25)),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[763, 760, 45])).
% 13.07/13.24 tff(765,plain,
% 13.07/13.24 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s24, s25)) | node3(c_bit0, s24, s25))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s24, s25)) | node3(c_bit0, s24, s25))),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(766,plain,
% 13.07/13.24 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s24, s25)) | node3(c_bit0, s24, s25))),
% 13.07/13.24 inference(quant_inst,[status(thm)],[])).
% 13.07/13.24 tff(767,plain,
% 13.07/13.24 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s24, s25)) | node3(c_bit0, s24, s25)),
% 13.07/13.24 inference(modus_ponens,[status(thm)],[766, 765])).
% 13.07/13.24 tff(768,plain,
% 13.07/13.24 (node3(c_bit0, s24, s25)),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[767, 59, 764])).
% 13.07/13.24 tff(769,plain,
% 13.07/13.24 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s25) | node1(c_bit0, s24) | (~node3(c_bit0, s24, s25)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s25) | node1(c_bit0, s24) | (~node3(c_bit0, s24, s25)))),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(770,plain,
% 13.07/13.24 ((node1(c_bit0, s24) | (~node3(c_bit0, s24, s25)) | m_counter_cell_v_value(c_bit0, s25)) <=> (m_counter_cell_v_value(c_bit0, s25) | node1(c_bit0, s24) | (~node3(c_bit0, s24, s25)))),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(771,plain,
% 13.07/13.24 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s24) | (~node3(c_bit0, s24, s25)) | m_counter_cell_v_value(c_bit0, s25))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s25) | node1(c_bit0, s24) | (~node3(c_bit0, s24, s25))))),
% 13.07/13.24 inference(monotonicity,[status(thm)],[770])).
% 13.07/13.24 tff(772,plain,
% 13.07/13.24 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s24) | (~node3(c_bit0, s24, s25)) | m_counter_cell_v_value(c_bit0, s25))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s25) | node1(c_bit0, s24) | (~node3(c_bit0, s24, s25)))),
% 13.07/13.24 inference(transitivity,[status(thm)],[771, 769])).
% 13.07/13.24 tff(773,plain,
% 13.07/13.24 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s24) | (~node3(c_bit0, s24, s25)) | m_counter_cell_v_value(c_bit0, s25))),
% 13.07/13.24 inference(quant_inst,[status(thm)],[])).
% 13.07/13.24 tff(774,plain,
% 13.07/13.24 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s25) | node1(c_bit0, s24) | (~node3(c_bit0, s24, s25))),
% 13.07/13.24 inference(modus_ponens,[status(thm)],[773, 772])).
% 13.07/13.24 tff(775,plain,
% 13.07/13.24 (m_counter_cell_v_value(c_bit0, s25) | node1(c_bit0, s24)),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[774, 73, 768])).
% 13.07/13.24 tff(776,plain,
% 13.07/13.24 (m_counter_cell_v_value(c_bit0, s25)),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[775, 757])).
% 13.07/13.24 tff(777,assumption,(~m_counter_cell_v_carry_in(c_bit0, s25)), introduced(assumption)).
% 13.07/13.24 tff(778,plain,
% 13.07/13.24 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s25)),
% 13.07/13.24 inference(quant_inst,[status(thm)],[])).
% 13.07/13.24 tff(779,plain,
% 13.07/13.24 ($false),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[778, 18, 777])).
% 13.07/13.24 tff(780,plain,(m_counter_cell_v_carry_in(c_bit0, s25)), inference(lemma,lemma(discharge,[]))).
% 13.07/13.24 tff(781,plain,
% 13.07/13.24 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s25)) | (~m_counter_cell_v_value(c_bit0, s25)) | (~node2(c_bit0, s25)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s25)) | (~m_counter_cell_v_value(c_bit0, s25)) | (~node2(c_bit0, s25)))),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(782,plain,
% 13.07/13.24 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s25)) | (~m_counter_cell_v_value(c_bit0, s25)) | (~node2(c_bit0, s25)))),
% 13.07/13.24 inference(quant_inst,[status(thm)],[])).
% 13.07/13.24 tff(783,plain,
% 13.07/13.24 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s25)) | (~m_counter_cell_v_value(c_bit0, s25)) | (~node2(c_bit0, s25))),
% 13.07/13.24 inference(modus_ponens,[status(thm)],[782, 781])).
% 13.07/13.24 tff(784,plain,
% 13.07/13.24 ((~m_counter_cell_v_value(c_bit0, s25)) | (~node2(c_bit0, s25))),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[783, 93, 780])).
% 13.07/13.24 tff(785,plain,
% 13.07/13.24 (~node2(c_bit0, s25)),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[784, 776])).
% 13.07/13.24 tff(786,plain,
% 13.07/13.24 (succ(s25, s26) <=> succ(s25, s26)),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(787,axiom,(succ(s25, s26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound26')).
% 13.07/13.24 tff(788,plain,
% 13.07/13.24 (succ(s25, s26)),
% 13.07/13.24 inference(modus_ponens,[status(thm)],[787, 786])).
% 13.07/13.24 tff(789,plain,
% 13.07/13.24 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s25, s26)) | trans(s25, s26))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s25, s26)) | trans(s25, s26))),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(790,plain,
% 13.07/13.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s25, s26)) | trans(s25, s26))),
% 13.07/13.24 inference(quant_inst,[status(thm)],[])).
% 13.07/13.24 tff(791,plain,
% 13.07/13.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s25, s26)) | trans(s25, s26)),
% 13.07/13.24 inference(modus_ponens,[status(thm)],[790, 789])).
% 13.07/13.24 tff(792,plain,
% 13.07/13.24 (trans(s25, s26)),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[791, 788, 45])).
% 13.07/13.24 tff(793,plain,
% 13.07/13.24 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s25, s26)) | node3(c_bit0, s25, s26))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s25, s26)) | node3(c_bit0, s25, s26))),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(794,plain,
% 13.07/13.24 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s25, s26)) | node3(c_bit0, s25, s26))),
% 13.07/13.24 inference(quant_inst,[status(thm)],[])).
% 13.07/13.24 tff(795,plain,
% 13.07/13.24 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s25, s26)) | node3(c_bit0, s25, s26)),
% 13.07/13.24 inference(modus_ponens,[status(thm)],[794, 793])).
% 13.07/13.24 tff(796,plain,
% 13.07/13.24 (node3(c_bit0, s25, s26)),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[795, 59, 792])).
% 13.07/13.24 tff(797,plain,
% 13.07/13.24 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s26)) | node2(c_bit0, s25) | (~node3(c_bit0, s25, s26)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s26)) | node2(c_bit0, s25) | (~node3(c_bit0, s25, s26)))),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(798,plain,
% 13.07/13.24 ((node2(c_bit0, s25) | (~node3(c_bit0, s25, s26)) | (~m_counter_cell_v_value(c_bit0, s26))) <=> ((~m_counter_cell_v_value(c_bit0, s26)) | node2(c_bit0, s25) | (~node3(c_bit0, s25, s26)))),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(799,plain,
% 13.07/13.24 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s25) | (~node3(c_bit0, s25, s26)) | (~m_counter_cell_v_value(c_bit0, s26)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s26)) | node2(c_bit0, s25) | (~node3(c_bit0, s25, s26))))),
% 13.07/13.24 inference(monotonicity,[status(thm)],[798])).
% 13.07/13.24 tff(800,plain,
% 13.07/13.24 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s25) | (~node3(c_bit0, s25, s26)) | (~m_counter_cell_v_value(c_bit0, s26)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s26)) | node2(c_bit0, s25) | (~node3(c_bit0, s25, s26)))),
% 13.07/13.24 inference(transitivity,[status(thm)],[799, 797])).
% 13.07/13.24 tff(801,plain,
% 13.07/13.24 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s25) | (~node3(c_bit0, s25, s26)) | (~m_counter_cell_v_value(c_bit0, s26)))),
% 13.07/13.24 inference(quant_inst,[status(thm)],[])).
% 13.07/13.24 tff(802,plain,
% 13.07/13.24 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s26)) | node2(c_bit0, s25) | (~node3(c_bit0, s25, s26))),
% 13.07/13.24 inference(modus_ponens,[status(thm)],[801, 800])).
% 13.07/13.24 tff(803,plain,
% 13.07/13.24 ((~m_counter_cell_v_value(c_bit0, s26)) | node2(c_bit0, s25)),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[802, 121, 796])).
% 13.07/13.24 tff(804,plain,
% 13.07/13.24 (~m_counter_cell_v_value(c_bit0, s26)),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[803, 785])).
% 13.07/13.24 tff(805,assumption,(~m_counter_cell_v_carry_in(c_bit0, s26)), introduced(assumption)).
% 13.07/13.24 tff(806,plain,
% 13.07/13.24 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s26)),
% 13.07/13.24 inference(quant_inst,[status(thm)],[])).
% 13.07/13.24 tff(807,plain,
% 13.07/13.24 ($false),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[806, 18, 805])).
% 13.07/13.24 tff(808,plain,(m_counter_cell_v_carry_in(c_bit0, s26)), inference(lemma,lemma(discharge,[]))).
% 13.07/13.24 tff(809,plain,
% 13.07/13.24 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s26)) | m_counter_cell_v_value(c_bit0, s26) | (~node1(c_bit0, s26)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s26)) | m_counter_cell_v_value(c_bit0, s26) | (~node1(c_bit0, s26)))),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(810,plain,
% 13.07/13.24 (((~node1(c_bit0, s26)) | (~m_counter_cell_v_carry_in(c_bit0, s26)) | m_counter_cell_v_value(c_bit0, s26)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s26)) | m_counter_cell_v_value(c_bit0, s26) | (~node1(c_bit0, s26)))),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(811,plain,
% 13.07/13.24 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s26)) | (~m_counter_cell_v_carry_in(c_bit0, s26)) | m_counter_cell_v_value(c_bit0, s26))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s26)) | m_counter_cell_v_value(c_bit0, s26) | (~node1(c_bit0, s26))))),
% 13.07/13.24 inference(monotonicity,[status(thm)],[810])).
% 13.07/13.24 tff(812,plain,
% 13.07/13.24 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s26)) | (~m_counter_cell_v_carry_in(c_bit0, s26)) | m_counter_cell_v_value(c_bit0, s26))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s26)) | m_counter_cell_v_value(c_bit0, s26) | (~node1(c_bit0, s26)))),
% 13.07/13.24 inference(transitivity,[status(thm)],[811, 809])).
% 13.07/13.24 tff(813,plain,
% 13.07/13.24 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s26)) | (~m_counter_cell_v_carry_in(c_bit0, s26)) | m_counter_cell_v_value(c_bit0, s26))),
% 13.07/13.24 inference(quant_inst,[status(thm)],[])).
% 13.07/13.24 tff(814,plain,
% 13.07/13.24 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s26)) | m_counter_cell_v_value(c_bit0, s26) | (~node1(c_bit0, s26))),
% 13.07/13.24 inference(modus_ponens,[status(thm)],[813, 812])).
% 13.07/13.24 tff(815,plain,
% 13.07/13.24 (m_counter_cell_v_value(c_bit0, s26) | (~node1(c_bit0, s26))),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[814, 30, 808])).
% 13.07/13.24 tff(816,plain,
% 13.07/13.24 (~node1(c_bit0, s26)),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[815, 804])).
% 13.07/13.24 tff(817,plain,
% 13.07/13.24 (succ(s26, s27) <=> succ(s26, s27)),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(818,axiom,(succ(s26, s27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound27')).
% 13.07/13.24 tff(819,plain,
% 13.07/13.24 (succ(s26, s27)),
% 13.07/13.24 inference(modus_ponens,[status(thm)],[818, 817])).
% 13.07/13.24 tff(820,plain,
% 13.07/13.24 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s26, s27)) | trans(s26, s27))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s26, s27)) | trans(s26, s27))),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(821,plain,
% 13.07/13.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s26, s27)) | trans(s26, s27))),
% 13.07/13.24 inference(quant_inst,[status(thm)],[])).
% 13.07/13.24 tff(822,plain,
% 13.07/13.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s26, s27)) | trans(s26, s27)),
% 13.07/13.24 inference(modus_ponens,[status(thm)],[821, 820])).
% 13.07/13.24 tff(823,plain,
% 13.07/13.24 (trans(s26, s27)),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[822, 819, 45])).
% 13.07/13.24 tff(824,plain,
% 13.07/13.24 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s26, s27)) | node3(c_bit0, s26, s27))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s26, s27)) | node3(c_bit0, s26, s27))),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(825,plain,
% 13.07/13.24 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s26, s27)) | node3(c_bit0, s26, s27))),
% 13.07/13.24 inference(quant_inst,[status(thm)],[])).
% 13.07/13.24 tff(826,plain,
% 13.07/13.24 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s26, s27)) | node3(c_bit0, s26, s27)),
% 13.07/13.24 inference(modus_ponens,[status(thm)],[825, 824])).
% 13.07/13.24 tff(827,plain,
% 13.07/13.24 (node3(c_bit0, s26, s27)),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[826, 59, 823])).
% 13.07/13.24 tff(828,plain,
% 13.07/13.24 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s27) | node1(c_bit0, s26) | (~node3(c_bit0, s26, s27)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s27) | node1(c_bit0, s26) | (~node3(c_bit0, s26, s27)))),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(829,plain,
% 13.07/13.24 ((node1(c_bit0, s26) | (~node3(c_bit0, s26, s27)) | m_counter_cell_v_value(c_bit0, s27)) <=> (m_counter_cell_v_value(c_bit0, s27) | node1(c_bit0, s26) | (~node3(c_bit0, s26, s27)))),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(830,plain,
% 13.07/13.24 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s26) | (~node3(c_bit0, s26, s27)) | m_counter_cell_v_value(c_bit0, s27))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s27) | node1(c_bit0, s26) | (~node3(c_bit0, s26, s27))))),
% 13.07/13.24 inference(monotonicity,[status(thm)],[829])).
% 13.07/13.24 tff(831,plain,
% 13.07/13.24 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s26) | (~node3(c_bit0, s26, s27)) | m_counter_cell_v_value(c_bit0, s27))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s27) | node1(c_bit0, s26) | (~node3(c_bit0, s26, s27)))),
% 13.07/13.24 inference(transitivity,[status(thm)],[830, 828])).
% 13.07/13.24 tff(832,plain,
% 13.07/13.24 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s26) | (~node3(c_bit0, s26, s27)) | m_counter_cell_v_value(c_bit0, s27))),
% 13.07/13.24 inference(quant_inst,[status(thm)],[])).
% 13.07/13.24 tff(833,plain,
% 13.07/13.24 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s27) | node1(c_bit0, s26) | (~node3(c_bit0, s26, s27))),
% 13.07/13.24 inference(modus_ponens,[status(thm)],[832, 831])).
% 13.07/13.24 tff(834,plain,
% 13.07/13.24 (m_counter_cell_v_value(c_bit0, s27) | node1(c_bit0, s26)),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[833, 73, 827])).
% 13.07/13.24 tff(835,plain,
% 13.07/13.24 (m_counter_cell_v_value(c_bit0, s27)),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[834, 816])).
% 13.07/13.24 tff(836,assumption,(~m_counter_cell_v_carry_in(c_bit0, s27)), introduced(assumption)).
% 13.07/13.24 tff(837,plain,
% 13.07/13.24 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s27)),
% 13.07/13.24 inference(quant_inst,[status(thm)],[])).
% 13.07/13.24 tff(838,plain,
% 13.07/13.24 ($false),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[837, 18, 836])).
% 13.07/13.24 tff(839,plain,(m_counter_cell_v_carry_in(c_bit0, s27)), inference(lemma,lemma(discharge,[]))).
% 13.07/13.24 tff(840,plain,
% 13.07/13.24 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s27)) | (~m_counter_cell_v_value(c_bit0, s27)) | (~node2(c_bit0, s27)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s27)) | (~m_counter_cell_v_value(c_bit0, s27)) | (~node2(c_bit0, s27)))),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(841,plain,
% 13.07/13.24 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s27)) | (~m_counter_cell_v_value(c_bit0, s27)) | (~node2(c_bit0, s27)))),
% 13.07/13.24 inference(quant_inst,[status(thm)],[])).
% 13.07/13.24 tff(842,plain,
% 13.07/13.24 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s27)) | (~m_counter_cell_v_value(c_bit0, s27)) | (~node2(c_bit0, s27))),
% 13.07/13.24 inference(modus_ponens,[status(thm)],[841, 840])).
% 13.07/13.24 tff(843,plain,
% 13.07/13.24 ((~m_counter_cell_v_value(c_bit0, s27)) | (~node2(c_bit0, s27))),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[842, 93, 839])).
% 13.07/13.24 tff(844,plain,
% 13.07/13.24 (~node2(c_bit0, s27)),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[843, 835])).
% 13.07/13.24 tff(845,plain,
% 13.07/13.24 (succ(s27, s28) <=> succ(s27, s28)),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(846,axiom,(succ(s27, s28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound28')).
% 13.07/13.24 tff(847,plain,
% 13.07/13.24 (succ(s27, s28)),
% 13.07/13.24 inference(modus_ponens,[status(thm)],[846, 845])).
% 13.07/13.24 tff(848,plain,
% 13.07/13.24 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s27, s28)) | trans(s27, s28))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s27, s28)) | trans(s27, s28))),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(849,plain,
% 13.07/13.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s27, s28)) | trans(s27, s28))),
% 13.07/13.24 inference(quant_inst,[status(thm)],[])).
% 13.07/13.24 tff(850,plain,
% 13.07/13.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s27, s28)) | trans(s27, s28)),
% 13.07/13.24 inference(modus_ponens,[status(thm)],[849, 848])).
% 13.07/13.24 tff(851,plain,
% 13.07/13.24 (trans(s27, s28)),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[850, 847, 45])).
% 13.07/13.24 tff(852,plain,
% 13.07/13.24 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s27, s28)) | node3(c_bit0, s27, s28))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s27, s28)) | node3(c_bit0, s27, s28))),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(853,plain,
% 13.07/13.24 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s27, s28)) | node3(c_bit0, s27, s28))),
% 13.07/13.24 inference(quant_inst,[status(thm)],[])).
% 13.07/13.24 tff(854,plain,
% 13.07/13.24 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s27, s28)) | node3(c_bit0, s27, s28)),
% 13.07/13.24 inference(modus_ponens,[status(thm)],[853, 852])).
% 13.07/13.24 tff(855,plain,
% 13.07/13.24 (node3(c_bit0, s27, s28)),
% 13.07/13.24 inference(unit_resolution,[status(thm)],[854, 59, 851])).
% 13.07/13.24 tff(856,plain,
% 13.07/13.24 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s28)) | node2(c_bit0, s27) | (~node3(c_bit0, s27, s28)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s28)) | node2(c_bit0, s27) | (~node3(c_bit0, s27, s28)))),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(857,plain,
% 13.07/13.24 ((node2(c_bit0, s27) | (~node3(c_bit0, s27, s28)) | (~m_counter_cell_v_value(c_bit0, s28))) <=> ((~m_counter_cell_v_value(c_bit0, s28)) | node2(c_bit0, s27) | (~node3(c_bit0, s27, s28)))),
% 13.07/13.24 inference(rewrite,[status(thm)],[])).
% 13.07/13.24 tff(858,plain,
% 13.07/13.24 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s27) | (~node3(c_bit0, s27, s28)) | (~m_counter_cell_v_value(c_bit0, s28)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s28)) | node2(c_bit0, s27) | (~node3(c_bit0, s27, s28))))),
% 13.07/13.24 inference(monotonicity,[status(thm)],[857])).
% 13.07/13.24 tff(859,plain,
% 13.07/13.24 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s27) | (~node3(c_bit0, s27, s28)) | (~m_counter_cell_v_value(c_bit0, s28)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s28)) | node2(c_bit0, s27) | (~node3(c_bit0, s27, s28)))),
% 13.07/13.24 inference(transitivity,[status(thm)],[858, 856])).
% 13.07/13.24 tff(860,plain,
% 13.07/13.24 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s27) | (~node3(c_bit0, s27, s28)) | (~m_counter_cell_v_value(c_bit0, s28)))),
% 13.07/13.24 inference(quant_inst,[status(thm)],[])).
% 13.07/13.24 tff(861,plain,
% 13.07/13.24 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s28)) | node2(c_bit0, s27) | (~node3(c_bit0, s27, s28))),
% 13.07/13.24 inference(modus_ponens,[status(thm)],[860, 859])).
% 13.07/13.24 tff(862,plain,
% 13.07/13.24 ((~m_counter_cell_v_value(c_bit0, s28)) | node2(c_bit0, s27)),
% 13.07/13.25 inference(unit_resolution,[status(thm)],[861, 121, 855])).
% 13.07/13.25 tff(863,plain,
% 13.07/13.25 (~m_counter_cell_v_value(c_bit0, s28)),
% 13.07/13.25 inference(unit_resolution,[status(thm)],[862, 844])).
% 13.07/13.25 tff(864,assumption,(~m_counter_cell_v_carry_in(c_bit0, s28)), introduced(assumption)).
% 13.07/13.25 tff(865,plain,
% 13.07/13.25 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s28)),
% 13.07/13.25 inference(quant_inst,[status(thm)],[])).
% 13.07/13.25 tff(866,plain,
% 13.07/13.25 ($false),
% 13.07/13.25 inference(unit_resolution,[status(thm)],[865, 18, 864])).
% 13.07/13.25 tff(867,plain,(m_counter_cell_v_carry_in(c_bit0, s28)), inference(lemma,lemma(discharge,[]))).
% 13.07/13.25 tff(868,plain,
% 13.07/13.25 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s28)) | m_counter_cell_v_value(c_bit0, s28) | (~node1(c_bit0, s28)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s28)) | m_counter_cell_v_value(c_bit0, s28) | (~node1(c_bit0, s28)))),
% 13.07/13.25 inference(rewrite,[status(thm)],[])).
% 13.07/13.25 tff(869,plain,
% 13.07/13.25 (((~node1(c_bit0, s28)) | (~m_counter_cell_v_carry_in(c_bit0, s28)) | m_counter_cell_v_value(c_bit0, s28)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s28)) | m_counter_cell_v_value(c_bit0, s28) | (~node1(c_bit0, s28)))),
% 13.07/13.25 inference(rewrite,[status(thm)],[])).
% 13.07/13.25 tff(870,plain,
% 13.07/13.25 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s28)) | (~m_counter_cell_v_carry_in(c_bit0, s28)) | m_counter_cell_v_value(c_bit0, s28))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s28)) | m_counter_cell_v_value(c_bit0, s28) | (~node1(c_bit0, s28))))),
% 13.07/13.25 inference(monotonicity,[status(thm)],[869])).
% 13.07/13.25 tff(871,plain,
% 13.07/13.25 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s28)) | (~m_counter_cell_v_carry_in(c_bit0, s28)) | m_counter_cell_v_value(c_bit0, s28))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s28)) | m_counter_cell_v_value(c_bit0, s28) | (~node1(c_bit0, s28)))),
% 13.07/13.25 inference(transitivity,[status(thm)],[870, 868])).
% 13.07/13.25 tff(872,plain,
% 13.07/13.25 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s28)) | (~m_counter_cell_v_carry_in(c_bit0, s28)) | m_counter_cell_v_value(c_bit0, s28))),
% 13.07/13.25 inference(quant_inst,[status(thm)],[])).
% 13.07/13.25 tff(873,plain,
% 13.07/13.25 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s28)) | m_counter_cell_v_value(c_bit0, s28) | (~node1(c_bit0, s28))),
% 13.07/13.25 inference(modus_ponens,[status(thm)],[872, 871])).
% 13.07/13.25 tff(874,plain,
% 13.07/13.25 (m_counter_cell_v_value(c_bit0, s28) | (~node1(c_bit0, s28))),
% 13.07/13.25 inference(unit_resolution,[status(thm)],[873, 30, 867])).
% 13.07/13.25 tff(875,plain,
% 13.07/13.25 (~node1(c_bit0, s28)),
% 13.07/13.25 inference(unit_resolution,[status(thm)],[874, 863])).
% 13.07/13.25 tff(876,plain,
% 13.07/13.25 (succ(s28, s29) <=> succ(s28, s29)),
% 13.07/13.25 inference(rewrite,[status(thm)],[])).
% 13.07/13.25 tff(877,axiom,(succ(s28, s29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound29')).
% 13.07/13.25 tff(878,plain,
% 13.07/13.25 (succ(s28, s29)),
% 13.07/13.25 inference(modus_ponens,[status(thm)],[877, 876])).
% 13.07/13.25 tff(879,plain,
% 13.07/13.25 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s28, s29)) | trans(s28, s29))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s28, s29)) | trans(s28, s29))),
% 13.07/13.25 inference(rewrite,[status(thm)],[])).
% 13.07/13.25 tff(880,plain,
% 13.07/13.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s28, s29)) | trans(s28, s29))),
% 13.07/13.25 inference(quant_inst,[status(thm)],[])).
% 13.07/13.25 tff(881,plain,
% 13.07/13.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s28, s29)) | trans(s28, s29)),
% 13.10/13.25 inference(modus_ponens,[status(thm)],[880, 879])).
% 13.10/13.25 tff(882,plain,
% 13.10/13.25 (trans(s28, s29)),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[881, 878, 45])).
% 13.10/13.25 tff(883,plain,
% 13.10/13.25 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s28, s29)) | node3(c_bit0, s28, s29))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s28, s29)) | node3(c_bit0, s28, s29))),
% 13.10/13.25 inference(rewrite,[status(thm)],[])).
% 13.10/13.25 tff(884,plain,
% 13.10/13.25 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s28, s29)) | node3(c_bit0, s28, s29))),
% 13.10/13.25 inference(quant_inst,[status(thm)],[])).
% 13.10/13.25 tff(885,plain,
% 13.10/13.25 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s28, s29)) | node3(c_bit0, s28, s29)),
% 13.10/13.25 inference(modus_ponens,[status(thm)],[884, 883])).
% 13.10/13.25 tff(886,plain,
% 13.10/13.25 (node3(c_bit0, s28, s29)),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[885, 59, 882])).
% 13.10/13.25 tff(887,plain,
% 13.10/13.25 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s29) | node1(c_bit0, s28) | (~node3(c_bit0, s28, s29)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s29) | node1(c_bit0, s28) | (~node3(c_bit0, s28, s29)))),
% 13.10/13.25 inference(rewrite,[status(thm)],[])).
% 13.10/13.25 tff(888,plain,
% 13.10/13.25 ((node1(c_bit0, s28) | (~node3(c_bit0, s28, s29)) | m_counter_cell_v_value(c_bit0, s29)) <=> (m_counter_cell_v_value(c_bit0, s29) | node1(c_bit0, s28) | (~node3(c_bit0, s28, s29)))),
% 13.10/13.25 inference(rewrite,[status(thm)],[])).
% 13.10/13.25 tff(889,plain,
% 13.10/13.25 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s28) | (~node3(c_bit0, s28, s29)) | m_counter_cell_v_value(c_bit0, s29))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s29) | node1(c_bit0, s28) | (~node3(c_bit0, s28, s29))))),
% 13.10/13.25 inference(monotonicity,[status(thm)],[888])).
% 13.10/13.25 tff(890,plain,
% 13.10/13.25 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s28) | (~node3(c_bit0, s28, s29)) | m_counter_cell_v_value(c_bit0, s29))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s29) | node1(c_bit0, s28) | (~node3(c_bit0, s28, s29)))),
% 13.10/13.25 inference(transitivity,[status(thm)],[889, 887])).
% 13.10/13.25 tff(891,plain,
% 13.10/13.25 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s28) | (~node3(c_bit0, s28, s29)) | m_counter_cell_v_value(c_bit0, s29))),
% 13.10/13.25 inference(quant_inst,[status(thm)],[])).
% 13.10/13.25 tff(892,plain,
% 13.10/13.25 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s29) | node1(c_bit0, s28) | (~node3(c_bit0, s28, s29))),
% 13.10/13.25 inference(modus_ponens,[status(thm)],[891, 890])).
% 13.10/13.25 tff(893,plain,
% 13.10/13.25 (m_counter_cell_v_value(c_bit0, s29) | node1(c_bit0, s28)),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[892, 73, 886])).
% 13.10/13.25 tff(894,plain,
% 13.10/13.25 (m_counter_cell_v_value(c_bit0, s29)),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[893, 875])).
% 13.10/13.25 tff(895,assumption,(~m_counter_cell_v_carry_in(c_bit0, s29)), introduced(assumption)).
% 13.10/13.25 tff(896,plain,
% 13.10/13.25 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s29)),
% 13.10/13.25 inference(quant_inst,[status(thm)],[])).
% 13.10/13.25 tff(897,plain,
% 13.10/13.25 ($false),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[896, 18, 895])).
% 13.10/13.25 tff(898,plain,(m_counter_cell_v_carry_in(c_bit0, s29)), inference(lemma,lemma(discharge,[]))).
% 13.10/13.25 tff(899,plain,
% 13.10/13.25 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s29)) | (~m_counter_cell_v_value(c_bit0, s29)) | (~node2(c_bit0, s29)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s29)) | (~m_counter_cell_v_value(c_bit0, s29)) | (~node2(c_bit0, s29)))),
% 13.10/13.25 inference(rewrite,[status(thm)],[])).
% 13.10/13.25 tff(900,plain,
% 13.10/13.25 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s29)) | (~m_counter_cell_v_value(c_bit0, s29)) | (~node2(c_bit0, s29)))),
% 13.10/13.25 inference(quant_inst,[status(thm)],[])).
% 13.10/13.25 tff(901,plain,
% 13.10/13.25 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s29)) | (~m_counter_cell_v_value(c_bit0, s29)) | (~node2(c_bit0, s29))),
% 13.10/13.25 inference(modus_ponens,[status(thm)],[900, 899])).
% 13.10/13.25 tff(902,plain,
% 13.10/13.25 ((~m_counter_cell_v_value(c_bit0, s29)) | (~node2(c_bit0, s29))),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[901, 93, 898])).
% 13.10/13.25 tff(903,plain,
% 13.10/13.25 (~node2(c_bit0, s29)),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[902, 894])).
% 13.10/13.25 tff(904,plain,
% 13.10/13.25 (succ(s29, s30) <=> succ(s29, s30)),
% 13.10/13.25 inference(rewrite,[status(thm)],[])).
% 13.10/13.25 tff(905,axiom,(succ(s29, s30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound30')).
% 13.10/13.25 tff(906,plain,
% 13.10/13.25 (succ(s29, s30)),
% 13.10/13.25 inference(modus_ponens,[status(thm)],[905, 904])).
% 13.10/13.25 tff(907,plain,
% 13.10/13.25 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s29, s30)) | trans(s29, s30))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s29, s30)) | trans(s29, s30))),
% 13.10/13.25 inference(rewrite,[status(thm)],[])).
% 13.10/13.25 tff(908,plain,
% 13.10/13.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s29, s30)) | trans(s29, s30))),
% 13.10/13.25 inference(quant_inst,[status(thm)],[])).
% 13.10/13.25 tff(909,plain,
% 13.10/13.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s29, s30)) | trans(s29, s30)),
% 13.10/13.25 inference(modus_ponens,[status(thm)],[908, 907])).
% 13.10/13.25 tff(910,plain,
% 13.10/13.25 (trans(s29, s30)),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[909, 906, 45])).
% 13.10/13.25 tff(911,plain,
% 13.10/13.25 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s29, s30)) | node3(c_bit0, s29, s30))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s29, s30)) | node3(c_bit0, s29, s30))),
% 13.10/13.25 inference(rewrite,[status(thm)],[])).
% 13.10/13.25 tff(912,plain,
% 13.10/13.25 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s29, s30)) | node3(c_bit0, s29, s30))),
% 13.10/13.25 inference(quant_inst,[status(thm)],[])).
% 13.10/13.25 tff(913,plain,
% 13.10/13.25 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s29, s30)) | node3(c_bit0, s29, s30)),
% 13.10/13.25 inference(modus_ponens,[status(thm)],[912, 911])).
% 13.10/13.25 tff(914,plain,
% 13.10/13.25 (node3(c_bit0, s29, s30)),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[913, 59, 910])).
% 13.10/13.25 tff(915,plain,
% 13.10/13.25 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s30)) | node2(c_bit0, s29) | (~node3(c_bit0, s29, s30)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s30)) | node2(c_bit0, s29) | (~node3(c_bit0, s29, s30)))),
% 13.10/13.25 inference(rewrite,[status(thm)],[])).
% 13.10/13.25 tff(916,plain,
% 13.10/13.25 ((node2(c_bit0, s29) | (~node3(c_bit0, s29, s30)) | (~m_counter_cell_v_value(c_bit0, s30))) <=> ((~m_counter_cell_v_value(c_bit0, s30)) | node2(c_bit0, s29) | (~node3(c_bit0, s29, s30)))),
% 13.10/13.25 inference(rewrite,[status(thm)],[])).
% 13.10/13.25 tff(917,plain,
% 13.10/13.25 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s29) | (~node3(c_bit0, s29, s30)) | (~m_counter_cell_v_value(c_bit0, s30)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s30)) | node2(c_bit0, s29) | (~node3(c_bit0, s29, s30))))),
% 13.10/13.25 inference(monotonicity,[status(thm)],[916])).
% 13.10/13.25 tff(918,plain,
% 13.10/13.25 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s29) | (~node3(c_bit0, s29, s30)) | (~m_counter_cell_v_value(c_bit0, s30)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s30)) | node2(c_bit0, s29) | (~node3(c_bit0, s29, s30)))),
% 13.10/13.25 inference(transitivity,[status(thm)],[917, 915])).
% 13.10/13.25 tff(919,plain,
% 13.10/13.25 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s29) | (~node3(c_bit0, s29, s30)) | (~m_counter_cell_v_value(c_bit0, s30)))),
% 13.10/13.25 inference(quant_inst,[status(thm)],[])).
% 13.10/13.25 tff(920,plain,
% 13.10/13.25 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s30)) | node2(c_bit0, s29) | (~node3(c_bit0, s29, s30))),
% 13.10/13.25 inference(modus_ponens,[status(thm)],[919, 918])).
% 13.10/13.25 tff(921,plain,
% 13.10/13.25 ((~m_counter_cell_v_value(c_bit0, s30)) | node2(c_bit0, s29)),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[920, 121, 914])).
% 13.10/13.25 tff(922,plain,
% 13.10/13.25 (~m_counter_cell_v_value(c_bit0, s30)),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[921, 903])).
% 13.10/13.25 tff(923,assumption,(~m_counter_cell_v_carry_in(c_bit0, s30)), introduced(assumption)).
% 13.10/13.25 tff(924,plain,
% 13.10/13.25 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s30)),
% 13.10/13.25 inference(quant_inst,[status(thm)],[])).
% 13.10/13.25 tff(925,plain,
% 13.10/13.25 ($false),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[924, 18, 923])).
% 13.10/13.25 tff(926,plain,(m_counter_cell_v_carry_in(c_bit0, s30)), inference(lemma,lemma(discharge,[]))).
% 13.10/13.25 tff(927,plain,
% 13.10/13.25 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s30)) | m_counter_cell_v_value(c_bit0, s30) | (~node1(c_bit0, s30)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s30)) | m_counter_cell_v_value(c_bit0, s30) | (~node1(c_bit0, s30)))),
% 13.10/13.25 inference(rewrite,[status(thm)],[])).
% 13.10/13.25 tff(928,plain,
% 13.10/13.25 (((~node1(c_bit0, s30)) | (~m_counter_cell_v_carry_in(c_bit0, s30)) | m_counter_cell_v_value(c_bit0, s30)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s30)) | m_counter_cell_v_value(c_bit0, s30) | (~node1(c_bit0, s30)))),
% 13.10/13.25 inference(rewrite,[status(thm)],[])).
% 13.10/13.25 tff(929,plain,
% 13.10/13.25 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s30)) | (~m_counter_cell_v_carry_in(c_bit0, s30)) | m_counter_cell_v_value(c_bit0, s30))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s30)) | m_counter_cell_v_value(c_bit0, s30) | (~node1(c_bit0, s30))))),
% 13.10/13.25 inference(monotonicity,[status(thm)],[928])).
% 13.10/13.25 tff(930,plain,
% 13.10/13.25 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s30)) | (~m_counter_cell_v_carry_in(c_bit0, s30)) | m_counter_cell_v_value(c_bit0, s30))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s30)) | m_counter_cell_v_value(c_bit0, s30) | (~node1(c_bit0, s30)))),
% 13.10/13.25 inference(transitivity,[status(thm)],[929, 927])).
% 13.10/13.25 tff(931,plain,
% 13.10/13.25 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s30)) | (~m_counter_cell_v_carry_in(c_bit0, s30)) | m_counter_cell_v_value(c_bit0, s30))),
% 13.10/13.25 inference(quant_inst,[status(thm)],[])).
% 13.10/13.25 tff(932,plain,
% 13.10/13.25 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s30)) | m_counter_cell_v_value(c_bit0, s30) | (~node1(c_bit0, s30))),
% 13.10/13.25 inference(modus_ponens,[status(thm)],[931, 930])).
% 13.10/13.25 tff(933,plain,
% 13.10/13.25 (m_counter_cell_v_value(c_bit0, s30) | (~node1(c_bit0, s30))),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[932, 30, 926])).
% 13.10/13.25 tff(934,plain,
% 13.10/13.25 (~node1(c_bit0, s30)),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[933, 922])).
% 13.10/13.25 tff(935,plain,
% 13.10/13.25 (succ(s30, s31) <=> succ(s30, s31)),
% 13.10/13.25 inference(rewrite,[status(thm)],[])).
% 13.10/13.25 tff(936,axiom,(succ(s30, s31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound31')).
% 13.10/13.25 tff(937,plain,
% 13.10/13.25 (succ(s30, s31)),
% 13.10/13.25 inference(modus_ponens,[status(thm)],[936, 935])).
% 13.10/13.25 tff(938,plain,
% 13.10/13.25 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s30, s31)) | trans(s30, s31))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s30, s31)) | trans(s30, s31))),
% 13.10/13.25 inference(rewrite,[status(thm)],[])).
% 13.10/13.25 tff(939,plain,
% 13.10/13.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s30, s31)) | trans(s30, s31))),
% 13.10/13.25 inference(quant_inst,[status(thm)],[])).
% 13.10/13.25 tff(940,plain,
% 13.10/13.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s30, s31)) | trans(s30, s31)),
% 13.10/13.25 inference(modus_ponens,[status(thm)],[939, 938])).
% 13.10/13.25 tff(941,plain,
% 13.10/13.25 (trans(s30, s31)),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[940, 937, 45])).
% 13.10/13.25 tff(942,plain,
% 13.10/13.25 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s30, s31)) | node3(c_bit0, s30, s31))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s30, s31)) | node3(c_bit0, s30, s31))),
% 13.10/13.25 inference(rewrite,[status(thm)],[])).
% 13.10/13.25 tff(943,plain,
% 13.10/13.25 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s30, s31)) | node3(c_bit0, s30, s31))),
% 13.10/13.25 inference(quant_inst,[status(thm)],[])).
% 13.10/13.25 tff(944,plain,
% 13.10/13.25 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s30, s31)) | node3(c_bit0, s30, s31)),
% 13.10/13.25 inference(modus_ponens,[status(thm)],[943, 942])).
% 13.10/13.25 tff(945,plain,
% 13.10/13.25 (node3(c_bit0, s30, s31)),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[944, 59, 941])).
% 13.10/13.25 tff(946,plain,
% 13.10/13.25 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s31) | node1(c_bit0, s30) | (~node3(c_bit0, s30, s31)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s31) | node1(c_bit0, s30) | (~node3(c_bit0, s30, s31)))),
% 13.10/13.25 inference(rewrite,[status(thm)],[])).
% 13.10/13.25 tff(947,plain,
% 13.10/13.25 ((node1(c_bit0, s30) | (~node3(c_bit0, s30, s31)) | m_counter_cell_v_value(c_bit0, s31)) <=> (m_counter_cell_v_value(c_bit0, s31) | node1(c_bit0, s30) | (~node3(c_bit0, s30, s31)))),
% 13.10/13.25 inference(rewrite,[status(thm)],[])).
% 13.10/13.25 tff(948,plain,
% 13.10/13.25 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s30) | (~node3(c_bit0, s30, s31)) | m_counter_cell_v_value(c_bit0, s31))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s31) | node1(c_bit0, s30) | (~node3(c_bit0, s30, s31))))),
% 13.10/13.25 inference(monotonicity,[status(thm)],[947])).
% 13.10/13.25 tff(949,plain,
% 13.10/13.25 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s30) | (~node3(c_bit0, s30, s31)) | m_counter_cell_v_value(c_bit0, s31))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s31) | node1(c_bit0, s30) | (~node3(c_bit0, s30, s31)))),
% 13.10/13.25 inference(transitivity,[status(thm)],[948, 946])).
% 13.10/13.25 tff(950,plain,
% 13.10/13.25 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s30) | (~node3(c_bit0, s30, s31)) | m_counter_cell_v_value(c_bit0, s31))),
% 13.10/13.25 inference(quant_inst,[status(thm)],[])).
% 13.10/13.25 tff(951,plain,
% 13.10/13.25 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s31) | node1(c_bit0, s30) | (~node3(c_bit0, s30, s31))),
% 13.10/13.25 inference(modus_ponens,[status(thm)],[950, 949])).
% 13.10/13.25 tff(952,plain,
% 13.10/13.25 (m_counter_cell_v_value(c_bit0, s31) | node1(c_bit0, s30)),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[951, 73, 945])).
% 13.10/13.25 tff(953,plain,
% 13.10/13.25 (m_counter_cell_v_value(c_bit0, s31)),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[952, 934])).
% 13.10/13.25 tff(954,assumption,(~m_counter_cell_v_carry_in(c_bit0, s31)), introduced(assumption)).
% 13.10/13.25 tff(955,plain,
% 13.10/13.25 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s31)),
% 13.10/13.25 inference(quant_inst,[status(thm)],[])).
% 13.10/13.25 tff(956,plain,
% 13.10/13.25 ($false),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[955, 18, 954])).
% 13.10/13.25 tff(957,plain,(m_counter_cell_v_carry_in(c_bit0, s31)), inference(lemma,lemma(discharge,[]))).
% 13.10/13.25 tff(958,plain,
% 13.10/13.25 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s31)) | (~m_counter_cell_v_value(c_bit0, s31)) | (~node2(c_bit0, s31)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s31)) | (~m_counter_cell_v_value(c_bit0, s31)) | (~node2(c_bit0, s31)))),
% 13.10/13.25 inference(rewrite,[status(thm)],[])).
% 13.10/13.25 tff(959,plain,
% 13.10/13.25 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s31)) | (~m_counter_cell_v_value(c_bit0, s31)) | (~node2(c_bit0, s31)))),
% 13.10/13.25 inference(quant_inst,[status(thm)],[])).
% 13.10/13.25 tff(960,plain,
% 13.10/13.25 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s31)) | (~m_counter_cell_v_value(c_bit0, s31)) | (~node2(c_bit0, s31))),
% 13.10/13.25 inference(modus_ponens,[status(thm)],[959, 958])).
% 13.10/13.25 tff(961,plain,
% 13.10/13.25 ((~m_counter_cell_v_value(c_bit0, s31)) | (~node2(c_bit0, s31))),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[960, 93, 957])).
% 13.10/13.25 tff(962,plain,
% 13.10/13.25 (~node2(c_bit0, s31)),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[961, 953])).
% 13.10/13.25 tff(963,plain,
% 13.10/13.25 (succ(s31, s32) <=> succ(s31, s32)),
% 13.10/13.25 inference(rewrite,[status(thm)],[])).
% 13.10/13.25 tff(964,axiom,(succ(s31, s32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound32')).
% 13.10/13.25 tff(965,plain,
% 13.10/13.25 (succ(s31, s32)),
% 13.10/13.25 inference(modus_ponens,[status(thm)],[964, 963])).
% 13.10/13.25 tff(966,plain,
% 13.10/13.25 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s31, s32)) | trans(s31, s32))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s31, s32)) | trans(s31, s32))),
% 13.10/13.25 inference(rewrite,[status(thm)],[])).
% 13.10/13.25 tff(967,plain,
% 13.10/13.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s31, s32)) | trans(s31, s32))),
% 13.10/13.25 inference(quant_inst,[status(thm)],[])).
% 13.10/13.25 tff(968,plain,
% 13.10/13.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s31, s32)) | trans(s31, s32)),
% 13.10/13.25 inference(modus_ponens,[status(thm)],[967, 966])).
% 13.10/13.25 tff(969,plain,
% 13.10/13.25 (trans(s31, s32)),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[968, 965, 45])).
% 13.10/13.25 tff(970,plain,
% 13.10/13.25 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s31, s32)) | node3(c_bit0, s31, s32))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s31, s32)) | node3(c_bit0, s31, s32))),
% 13.10/13.25 inference(rewrite,[status(thm)],[])).
% 13.10/13.25 tff(971,plain,
% 13.10/13.25 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s31, s32)) | node3(c_bit0, s31, s32))),
% 13.10/13.25 inference(quant_inst,[status(thm)],[])).
% 13.10/13.25 tff(972,plain,
% 13.10/13.25 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s31, s32)) | node3(c_bit0, s31, s32)),
% 13.10/13.25 inference(modus_ponens,[status(thm)],[971, 970])).
% 13.10/13.25 tff(973,plain,
% 13.10/13.25 (node3(c_bit0, s31, s32)),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[972, 59, 969])).
% 13.10/13.25 tff(974,plain,
% 13.10/13.25 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s32)) | node2(c_bit0, s31) | (~node3(c_bit0, s31, s32)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s32)) | node2(c_bit0, s31) | (~node3(c_bit0, s31, s32)))),
% 13.10/13.25 inference(rewrite,[status(thm)],[])).
% 13.10/13.25 tff(975,plain,
% 13.10/13.25 ((node2(c_bit0, s31) | (~node3(c_bit0, s31, s32)) | (~m_counter_cell_v_value(c_bit0, s32))) <=> ((~m_counter_cell_v_value(c_bit0, s32)) | node2(c_bit0, s31) | (~node3(c_bit0, s31, s32)))),
% 13.10/13.25 inference(rewrite,[status(thm)],[])).
% 13.10/13.25 tff(976,plain,
% 13.10/13.25 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s31) | (~node3(c_bit0, s31, s32)) | (~m_counter_cell_v_value(c_bit0, s32)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s32)) | node2(c_bit0, s31) | (~node3(c_bit0, s31, s32))))),
% 13.10/13.25 inference(monotonicity,[status(thm)],[975])).
% 13.10/13.25 tff(977,plain,
% 13.10/13.25 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s31) | (~node3(c_bit0, s31, s32)) | (~m_counter_cell_v_value(c_bit0, s32)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s32)) | node2(c_bit0, s31) | (~node3(c_bit0, s31, s32)))),
% 13.10/13.25 inference(transitivity,[status(thm)],[976, 974])).
% 13.10/13.25 tff(978,plain,
% 13.10/13.25 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s31) | (~node3(c_bit0, s31, s32)) | (~m_counter_cell_v_value(c_bit0, s32)))),
% 13.10/13.25 inference(quant_inst,[status(thm)],[])).
% 13.10/13.25 tff(979,plain,
% 13.10/13.25 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s32)) | node2(c_bit0, s31) | (~node3(c_bit0, s31, s32))),
% 13.10/13.25 inference(modus_ponens,[status(thm)],[978, 977])).
% 13.10/13.25 tff(980,plain,
% 13.10/13.25 ((~m_counter_cell_v_value(c_bit0, s32)) | node2(c_bit0, s31)),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[979, 121, 973])).
% 13.10/13.25 tff(981,plain,
% 13.10/13.25 (~m_counter_cell_v_value(c_bit0, s32)),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[980, 962])).
% 13.10/13.25 tff(982,assumption,(~m_counter_cell_v_carry_in(c_bit0, s32)), introduced(assumption)).
% 13.10/13.25 tff(983,plain,
% 13.10/13.25 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s32)),
% 13.10/13.25 inference(quant_inst,[status(thm)],[])).
% 13.10/13.25 tff(984,plain,
% 13.10/13.25 ($false),
% 13.10/13.25 inference(unit_resolution,[status(thm)],[983, 18, 982])).
% 13.10/13.25 tff(985,plain,(m_counter_cell_v_carry_in(c_bit0, s32)), inference(lemma,lemma(discharge,[]))).
% 13.10/13.25 tff(986,plain,
% 13.10/13.25 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s32)) | m_counter_cell_v_value(c_bit0, s32) | (~node1(c_bit0, s32)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s32)) | m_counter_cell_v_value(c_bit0, s32) | (~node1(c_bit0, s32)))),
% 13.10/13.25 inference(rewrite,[status(thm)],[])).
% 13.10/13.25 tff(987,plain,
% 13.10/13.25 (((~node1(c_bit0, s32)) | (~m_counter_cell_v_carry_in(c_bit0, s32)) | m_counter_cell_v_value(c_bit0, s32)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s32)) | m_counter_cell_v_value(c_bit0, s32) | (~node1(c_bit0, s32)))),
% 13.10/13.25 inference(rewrite,[status(thm)],[])).
% 13.10/13.25 tff(988,plain,
% 13.10/13.25 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s32)) | (~m_counter_cell_v_carry_in(c_bit0, s32)) | m_counter_cell_v_value(c_bit0, s32))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s32)) | m_counter_cell_v_value(c_bit0, s32) | (~node1(c_bit0, s32))))),
% 13.10/13.25 inference(monotonicity,[status(thm)],[987])).
% 13.10/13.25 tff(989,plain,
% 13.10/13.25 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s32)) | (~m_counter_cell_v_carry_in(c_bit0, s32)) | m_counter_cell_v_value(c_bit0, s32))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s32)) | m_counter_cell_v_value(c_bit0, s32) | (~node1(c_bit0, s32)))),
% 13.10/13.26 inference(transitivity,[status(thm)],[988, 986])).
% 13.10/13.26 tff(990,plain,
% 13.10/13.26 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s32)) | (~m_counter_cell_v_carry_in(c_bit0, s32)) | m_counter_cell_v_value(c_bit0, s32))),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(991,plain,
% 13.10/13.26 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s32)) | m_counter_cell_v_value(c_bit0, s32) | (~node1(c_bit0, s32))),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[990, 989])).
% 13.10/13.26 tff(992,plain,
% 13.10/13.26 (m_counter_cell_v_value(c_bit0, s32) | (~node1(c_bit0, s32))),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[991, 30, 985])).
% 13.10/13.26 tff(993,plain,
% 13.10/13.26 (~node1(c_bit0, s32)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[992, 981])).
% 13.10/13.26 tff(994,plain,
% 13.10/13.26 (succ(s32, s33) <=> succ(s32, s33)),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(995,axiom,(succ(s32, s33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound33')).
% 13.10/13.26 tff(996,plain,
% 13.10/13.26 (succ(s32, s33)),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[995, 994])).
% 13.10/13.26 tff(997,plain,
% 13.10/13.26 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s32, s33)) | trans(s32, s33))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s32, s33)) | trans(s32, s33))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(998,plain,
% 13.10/13.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s32, s33)) | trans(s32, s33))),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(999,plain,
% 13.10/13.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s32, s33)) | trans(s32, s33)),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[998, 997])).
% 13.10/13.26 tff(1000,plain,
% 13.10/13.26 (trans(s32, s33)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[999, 996, 45])).
% 13.10/13.26 tff(1001,plain,
% 13.10/13.26 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s32, s33)) | node3(c_bit0, s32, s33))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s32, s33)) | node3(c_bit0, s32, s33))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1002,plain,
% 13.10/13.26 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s32, s33)) | node3(c_bit0, s32, s33))),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(1003,plain,
% 13.10/13.26 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s32, s33)) | node3(c_bit0, s32, s33)),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[1002, 1001])).
% 13.10/13.26 tff(1004,plain,
% 13.10/13.26 (node3(c_bit0, s32, s33)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1003, 59, 1000])).
% 13.10/13.26 tff(1005,plain,
% 13.10/13.26 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s33) | node1(c_bit0, s32) | (~node3(c_bit0, s32, s33)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s33) | node1(c_bit0, s32) | (~node3(c_bit0, s32, s33)))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1006,plain,
% 13.10/13.26 ((node1(c_bit0, s32) | (~node3(c_bit0, s32, s33)) | m_counter_cell_v_value(c_bit0, s33)) <=> (m_counter_cell_v_value(c_bit0, s33) | node1(c_bit0, s32) | (~node3(c_bit0, s32, s33)))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1007,plain,
% 13.10/13.26 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s32) | (~node3(c_bit0, s32, s33)) | m_counter_cell_v_value(c_bit0, s33))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s33) | node1(c_bit0, s32) | (~node3(c_bit0, s32, s33))))),
% 13.10/13.26 inference(monotonicity,[status(thm)],[1006])).
% 13.10/13.26 tff(1008,plain,
% 13.10/13.26 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s32) | (~node3(c_bit0, s32, s33)) | m_counter_cell_v_value(c_bit0, s33))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s33) | node1(c_bit0, s32) | (~node3(c_bit0, s32, s33)))),
% 13.10/13.26 inference(transitivity,[status(thm)],[1007, 1005])).
% 13.10/13.26 tff(1009,plain,
% 13.10/13.26 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s32) | (~node3(c_bit0, s32, s33)) | m_counter_cell_v_value(c_bit0, s33))),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(1010,plain,
% 13.10/13.26 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s33) | node1(c_bit0, s32) | (~node3(c_bit0, s32, s33))),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[1009, 1008])).
% 13.10/13.26 tff(1011,plain,
% 13.10/13.26 (m_counter_cell_v_value(c_bit0, s33) | node1(c_bit0, s32)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1010, 73, 1004])).
% 13.10/13.26 tff(1012,plain,
% 13.10/13.26 (m_counter_cell_v_value(c_bit0, s33)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1011, 993])).
% 13.10/13.26 tff(1013,assumption,(~m_counter_cell_v_carry_in(c_bit0, s33)), introduced(assumption)).
% 13.10/13.26 tff(1014,plain,
% 13.10/13.26 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s33)),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(1015,plain,
% 13.10/13.26 ($false),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1014, 18, 1013])).
% 13.10/13.26 tff(1016,plain,(m_counter_cell_v_carry_in(c_bit0, s33)), inference(lemma,lemma(discharge,[]))).
% 13.10/13.26 tff(1017,plain,
% 13.10/13.26 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s33)) | (~m_counter_cell_v_value(c_bit0, s33)) | (~node2(c_bit0, s33)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s33)) | (~m_counter_cell_v_value(c_bit0, s33)) | (~node2(c_bit0, s33)))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1018,plain,
% 13.10/13.26 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s33)) | (~m_counter_cell_v_value(c_bit0, s33)) | (~node2(c_bit0, s33)))),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(1019,plain,
% 13.10/13.26 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s33)) | (~m_counter_cell_v_value(c_bit0, s33)) | (~node2(c_bit0, s33))),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[1018, 1017])).
% 13.10/13.26 tff(1020,plain,
% 13.10/13.26 ((~m_counter_cell_v_value(c_bit0, s33)) | (~node2(c_bit0, s33))),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1019, 93, 1016])).
% 13.10/13.26 tff(1021,plain,
% 13.10/13.26 (~node2(c_bit0, s33)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1020, 1012])).
% 13.10/13.26 tff(1022,plain,
% 13.10/13.26 (succ(s33, s34) <=> succ(s33, s34)),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1023,axiom,(succ(s33, s34)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound34')).
% 13.10/13.26 tff(1024,plain,
% 13.10/13.26 (succ(s33, s34)),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[1023, 1022])).
% 13.10/13.26 tff(1025,plain,
% 13.10/13.26 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s33, s34)) | trans(s33, s34))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s33, s34)) | trans(s33, s34))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1026,plain,
% 13.10/13.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s33, s34)) | trans(s33, s34))),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(1027,plain,
% 13.10/13.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s33, s34)) | trans(s33, s34)),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[1026, 1025])).
% 13.10/13.26 tff(1028,plain,
% 13.10/13.26 (trans(s33, s34)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1027, 1024, 45])).
% 13.10/13.26 tff(1029,plain,
% 13.10/13.26 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s33, s34)) | node3(c_bit0, s33, s34))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s33, s34)) | node3(c_bit0, s33, s34))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1030,plain,
% 13.10/13.26 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s33, s34)) | node3(c_bit0, s33, s34))),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(1031,plain,
% 13.10/13.26 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s33, s34)) | node3(c_bit0, s33, s34)),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[1030, 1029])).
% 13.10/13.26 tff(1032,plain,
% 13.10/13.26 (node3(c_bit0, s33, s34)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1031, 59, 1028])).
% 13.10/13.26 tff(1033,plain,
% 13.10/13.26 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s34)) | node2(c_bit0, s33) | (~node3(c_bit0, s33, s34)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s34)) | node2(c_bit0, s33) | (~node3(c_bit0, s33, s34)))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1034,plain,
% 13.10/13.26 ((node2(c_bit0, s33) | (~node3(c_bit0, s33, s34)) | (~m_counter_cell_v_value(c_bit0, s34))) <=> ((~m_counter_cell_v_value(c_bit0, s34)) | node2(c_bit0, s33) | (~node3(c_bit0, s33, s34)))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1035,plain,
% 13.10/13.26 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s33) | (~node3(c_bit0, s33, s34)) | (~m_counter_cell_v_value(c_bit0, s34)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s34)) | node2(c_bit0, s33) | (~node3(c_bit0, s33, s34))))),
% 13.10/13.26 inference(monotonicity,[status(thm)],[1034])).
% 13.10/13.26 tff(1036,plain,
% 13.10/13.26 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s33) | (~node3(c_bit0, s33, s34)) | (~m_counter_cell_v_value(c_bit0, s34)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s34)) | node2(c_bit0, s33) | (~node3(c_bit0, s33, s34)))),
% 13.10/13.26 inference(transitivity,[status(thm)],[1035, 1033])).
% 13.10/13.26 tff(1037,plain,
% 13.10/13.26 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s33) | (~node3(c_bit0, s33, s34)) | (~m_counter_cell_v_value(c_bit0, s34)))),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(1038,plain,
% 13.10/13.26 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s34)) | node2(c_bit0, s33) | (~node3(c_bit0, s33, s34))),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[1037, 1036])).
% 13.10/13.26 tff(1039,plain,
% 13.10/13.26 ((~m_counter_cell_v_value(c_bit0, s34)) | node2(c_bit0, s33)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1038, 121, 1032])).
% 13.10/13.26 tff(1040,plain,
% 13.10/13.26 (~m_counter_cell_v_value(c_bit0, s34)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1039, 1021])).
% 13.10/13.26 tff(1041,assumption,(~m_counter_cell_v_carry_in(c_bit0, s34)), introduced(assumption)).
% 13.10/13.26 tff(1042,plain,
% 13.10/13.26 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s34)),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(1043,plain,
% 13.10/13.26 ($false),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1042, 18, 1041])).
% 13.10/13.26 tff(1044,plain,(m_counter_cell_v_carry_in(c_bit0, s34)), inference(lemma,lemma(discharge,[]))).
% 13.10/13.26 tff(1045,plain,
% 13.10/13.26 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s34)) | m_counter_cell_v_value(c_bit0, s34) | (~node1(c_bit0, s34)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s34)) | m_counter_cell_v_value(c_bit0, s34) | (~node1(c_bit0, s34)))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1046,plain,
% 13.10/13.26 (((~node1(c_bit0, s34)) | (~m_counter_cell_v_carry_in(c_bit0, s34)) | m_counter_cell_v_value(c_bit0, s34)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s34)) | m_counter_cell_v_value(c_bit0, s34) | (~node1(c_bit0, s34)))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1047,plain,
% 13.10/13.26 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s34)) | (~m_counter_cell_v_carry_in(c_bit0, s34)) | m_counter_cell_v_value(c_bit0, s34))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s34)) | m_counter_cell_v_value(c_bit0, s34) | (~node1(c_bit0, s34))))),
% 13.10/13.26 inference(monotonicity,[status(thm)],[1046])).
% 13.10/13.26 tff(1048,plain,
% 13.10/13.26 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s34)) | (~m_counter_cell_v_carry_in(c_bit0, s34)) | m_counter_cell_v_value(c_bit0, s34))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s34)) | m_counter_cell_v_value(c_bit0, s34) | (~node1(c_bit0, s34)))),
% 13.10/13.26 inference(transitivity,[status(thm)],[1047, 1045])).
% 13.10/13.26 tff(1049,plain,
% 13.10/13.26 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s34)) | (~m_counter_cell_v_carry_in(c_bit0, s34)) | m_counter_cell_v_value(c_bit0, s34))),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(1050,plain,
% 13.10/13.26 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s34)) | m_counter_cell_v_value(c_bit0, s34) | (~node1(c_bit0, s34))),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[1049, 1048])).
% 13.10/13.26 tff(1051,plain,
% 13.10/13.26 (m_counter_cell_v_value(c_bit0, s34) | (~node1(c_bit0, s34))),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1050, 30, 1044])).
% 13.10/13.26 tff(1052,plain,
% 13.10/13.26 (~node1(c_bit0, s34)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1051, 1040])).
% 13.10/13.26 tff(1053,plain,
% 13.10/13.26 (succ(s34, s35) <=> succ(s34, s35)),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1054,axiom,(succ(s34, s35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound35')).
% 13.10/13.26 tff(1055,plain,
% 13.10/13.26 (succ(s34, s35)),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[1054, 1053])).
% 13.10/13.26 tff(1056,plain,
% 13.10/13.26 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s34, s35)) | trans(s34, s35))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s34, s35)) | trans(s34, s35))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1057,plain,
% 13.10/13.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s34, s35)) | trans(s34, s35))),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(1058,plain,
% 13.10/13.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s34, s35)) | trans(s34, s35)),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[1057, 1056])).
% 13.10/13.26 tff(1059,plain,
% 13.10/13.26 (trans(s34, s35)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1058, 1055, 45])).
% 13.10/13.26 tff(1060,plain,
% 13.10/13.26 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s34, s35)) | node3(c_bit0, s34, s35))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s34, s35)) | node3(c_bit0, s34, s35))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1061,plain,
% 13.10/13.26 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s34, s35)) | node3(c_bit0, s34, s35))),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(1062,plain,
% 13.10/13.26 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s34, s35)) | node3(c_bit0, s34, s35)),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[1061, 1060])).
% 13.10/13.26 tff(1063,plain,
% 13.10/13.26 (node3(c_bit0, s34, s35)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1062, 59, 1059])).
% 13.10/13.26 tff(1064,plain,
% 13.10/13.26 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s35) | node1(c_bit0, s34) | (~node3(c_bit0, s34, s35)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s35) | node1(c_bit0, s34) | (~node3(c_bit0, s34, s35)))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1065,plain,
% 13.10/13.26 ((node1(c_bit0, s34) | (~node3(c_bit0, s34, s35)) | m_counter_cell_v_value(c_bit0, s35)) <=> (m_counter_cell_v_value(c_bit0, s35) | node1(c_bit0, s34) | (~node3(c_bit0, s34, s35)))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1066,plain,
% 13.10/13.26 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s34) | (~node3(c_bit0, s34, s35)) | m_counter_cell_v_value(c_bit0, s35))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s35) | node1(c_bit0, s34) | (~node3(c_bit0, s34, s35))))),
% 13.10/13.26 inference(monotonicity,[status(thm)],[1065])).
% 13.10/13.26 tff(1067,plain,
% 13.10/13.26 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s34) | (~node3(c_bit0, s34, s35)) | m_counter_cell_v_value(c_bit0, s35))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s35) | node1(c_bit0, s34) | (~node3(c_bit0, s34, s35)))),
% 13.10/13.26 inference(transitivity,[status(thm)],[1066, 1064])).
% 13.10/13.26 tff(1068,plain,
% 13.10/13.26 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s34) | (~node3(c_bit0, s34, s35)) | m_counter_cell_v_value(c_bit0, s35))),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(1069,plain,
% 13.10/13.26 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s35) | node1(c_bit0, s34) | (~node3(c_bit0, s34, s35))),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[1068, 1067])).
% 13.10/13.26 tff(1070,plain,
% 13.10/13.26 (m_counter_cell_v_value(c_bit0, s35) | node1(c_bit0, s34)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1069, 73, 1063])).
% 13.10/13.26 tff(1071,plain,
% 13.10/13.26 (m_counter_cell_v_value(c_bit0, s35)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1070, 1052])).
% 13.10/13.26 tff(1072,assumption,(~m_counter_cell_v_carry_in(c_bit0, s35)), introduced(assumption)).
% 13.10/13.26 tff(1073,plain,
% 13.10/13.26 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s35)),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(1074,plain,
% 13.10/13.26 ($false),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1073, 18, 1072])).
% 13.10/13.26 tff(1075,plain,(m_counter_cell_v_carry_in(c_bit0, s35)), inference(lemma,lemma(discharge,[]))).
% 13.10/13.26 tff(1076,plain,
% 13.10/13.26 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s35)) | (~m_counter_cell_v_value(c_bit0, s35)) | (~node2(c_bit0, s35)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s35)) | (~m_counter_cell_v_value(c_bit0, s35)) | (~node2(c_bit0, s35)))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1077,plain,
% 13.10/13.26 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s35)) | (~m_counter_cell_v_value(c_bit0, s35)) | (~node2(c_bit0, s35)))),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(1078,plain,
% 13.10/13.26 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s35)) | (~m_counter_cell_v_value(c_bit0, s35)) | (~node2(c_bit0, s35))),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[1077, 1076])).
% 13.10/13.26 tff(1079,plain,
% 13.10/13.26 ((~m_counter_cell_v_value(c_bit0, s35)) | (~node2(c_bit0, s35))),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1078, 93, 1075])).
% 13.10/13.26 tff(1080,plain,
% 13.10/13.26 (~node2(c_bit0, s35)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1079, 1071])).
% 13.10/13.26 tff(1081,plain,
% 13.10/13.26 (succ(s35, s36) <=> succ(s35, s36)),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1082,axiom,(succ(s35, s36)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound36')).
% 13.10/13.26 tff(1083,plain,
% 13.10/13.26 (succ(s35, s36)),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[1082, 1081])).
% 13.10/13.26 tff(1084,plain,
% 13.10/13.26 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s35, s36)) | trans(s35, s36))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s35, s36)) | trans(s35, s36))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1085,plain,
% 13.10/13.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s35, s36)) | trans(s35, s36))),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(1086,plain,
% 13.10/13.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s35, s36)) | trans(s35, s36)),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[1085, 1084])).
% 13.10/13.26 tff(1087,plain,
% 13.10/13.26 (trans(s35, s36)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1086, 1083, 45])).
% 13.10/13.26 tff(1088,plain,
% 13.10/13.26 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s35, s36)) | node3(c_bit0, s35, s36))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s35, s36)) | node3(c_bit0, s35, s36))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1089,plain,
% 13.10/13.26 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s35, s36)) | node3(c_bit0, s35, s36))),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(1090,plain,
% 13.10/13.26 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s35, s36)) | node3(c_bit0, s35, s36)),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[1089, 1088])).
% 13.10/13.26 tff(1091,plain,
% 13.10/13.26 (node3(c_bit0, s35, s36)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1090, 59, 1087])).
% 13.10/13.26 tff(1092,plain,
% 13.10/13.26 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s36)) | node2(c_bit0, s35) | (~node3(c_bit0, s35, s36)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s36)) | node2(c_bit0, s35) | (~node3(c_bit0, s35, s36)))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1093,plain,
% 13.10/13.26 ((node2(c_bit0, s35) | (~node3(c_bit0, s35, s36)) | (~m_counter_cell_v_value(c_bit0, s36))) <=> ((~m_counter_cell_v_value(c_bit0, s36)) | node2(c_bit0, s35) | (~node3(c_bit0, s35, s36)))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1094,plain,
% 13.10/13.26 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s35) | (~node3(c_bit0, s35, s36)) | (~m_counter_cell_v_value(c_bit0, s36)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s36)) | node2(c_bit0, s35) | (~node3(c_bit0, s35, s36))))),
% 13.10/13.26 inference(monotonicity,[status(thm)],[1093])).
% 13.10/13.26 tff(1095,plain,
% 13.10/13.26 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s35) | (~node3(c_bit0, s35, s36)) | (~m_counter_cell_v_value(c_bit0, s36)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s36)) | node2(c_bit0, s35) | (~node3(c_bit0, s35, s36)))),
% 13.10/13.26 inference(transitivity,[status(thm)],[1094, 1092])).
% 13.10/13.26 tff(1096,plain,
% 13.10/13.26 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s35) | (~node3(c_bit0, s35, s36)) | (~m_counter_cell_v_value(c_bit0, s36)))),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(1097,plain,
% 13.10/13.26 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s36)) | node2(c_bit0, s35) | (~node3(c_bit0, s35, s36))),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[1096, 1095])).
% 13.10/13.26 tff(1098,plain,
% 13.10/13.26 ((~m_counter_cell_v_value(c_bit0, s36)) | node2(c_bit0, s35)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1097, 121, 1091])).
% 13.10/13.26 tff(1099,plain,
% 13.10/13.26 (~m_counter_cell_v_value(c_bit0, s36)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1098, 1080])).
% 13.10/13.26 tff(1100,assumption,(~m_counter_cell_v_carry_in(c_bit0, s36)), introduced(assumption)).
% 13.10/13.26 tff(1101,plain,
% 13.10/13.26 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s36)),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(1102,plain,
% 13.10/13.26 ($false),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1101, 18, 1100])).
% 13.10/13.26 tff(1103,plain,(m_counter_cell_v_carry_in(c_bit0, s36)), inference(lemma,lemma(discharge,[]))).
% 13.10/13.26 tff(1104,plain,
% 13.10/13.26 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s36)) | m_counter_cell_v_value(c_bit0, s36) | (~node1(c_bit0, s36)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s36)) | m_counter_cell_v_value(c_bit0, s36) | (~node1(c_bit0, s36)))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1105,plain,
% 13.10/13.26 (((~node1(c_bit0, s36)) | (~m_counter_cell_v_carry_in(c_bit0, s36)) | m_counter_cell_v_value(c_bit0, s36)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s36)) | m_counter_cell_v_value(c_bit0, s36) | (~node1(c_bit0, s36)))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1106,plain,
% 13.10/13.26 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s36)) | (~m_counter_cell_v_carry_in(c_bit0, s36)) | m_counter_cell_v_value(c_bit0, s36))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s36)) | m_counter_cell_v_value(c_bit0, s36) | (~node1(c_bit0, s36))))),
% 13.10/13.26 inference(monotonicity,[status(thm)],[1105])).
% 13.10/13.26 tff(1107,plain,
% 13.10/13.26 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s36)) | (~m_counter_cell_v_carry_in(c_bit0, s36)) | m_counter_cell_v_value(c_bit0, s36))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s36)) | m_counter_cell_v_value(c_bit0, s36) | (~node1(c_bit0, s36)))),
% 13.10/13.26 inference(transitivity,[status(thm)],[1106, 1104])).
% 13.10/13.26 tff(1108,plain,
% 13.10/13.26 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s36)) | (~m_counter_cell_v_carry_in(c_bit0, s36)) | m_counter_cell_v_value(c_bit0, s36))),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(1109,plain,
% 13.10/13.26 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s36)) | m_counter_cell_v_value(c_bit0, s36) | (~node1(c_bit0, s36))),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 13.10/13.26 tff(1110,plain,
% 13.10/13.26 (m_counter_cell_v_value(c_bit0, s36) | (~node1(c_bit0, s36))),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1109, 30, 1103])).
% 13.10/13.26 tff(1111,plain,
% 13.10/13.26 (~node1(c_bit0, s36)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1110, 1099])).
% 13.10/13.26 tff(1112,plain,
% 13.10/13.26 (succ(s36, s37) <=> succ(s36, s37)),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1113,axiom,(succ(s36, s37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound37')).
% 13.10/13.26 tff(1114,plain,
% 13.10/13.26 (succ(s36, s37)),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[1113, 1112])).
% 13.10/13.26 tff(1115,plain,
% 13.10/13.26 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s36, s37)) | trans(s36, s37))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s36, s37)) | trans(s36, s37))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1116,plain,
% 13.10/13.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s36, s37)) | trans(s36, s37))),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(1117,plain,
% 13.10/13.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s36, s37)) | trans(s36, s37)),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[1116, 1115])).
% 13.10/13.26 tff(1118,plain,
% 13.10/13.26 (trans(s36, s37)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1117, 1114, 45])).
% 13.10/13.26 tff(1119,plain,
% 13.10/13.26 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s36, s37)) | node3(c_bit0, s36, s37))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s36, s37)) | node3(c_bit0, s36, s37))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1120,plain,
% 13.10/13.26 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s36, s37)) | node3(c_bit0, s36, s37))),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(1121,plain,
% 13.10/13.26 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s36, s37)) | node3(c_bit0, s36, s37)),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[1120, 1119])).
% 13.10/13.26 tff(1122,plain,
% 13.10/13.26 (node3(c_bit0, s36, s37)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1121, 59, 1118])).
% 13.10/13.26 tff(1123,plain,
% 13.10/13.26 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s37) | node1(c_bit0, s36) | (~node3(c_bit0, s36, s37)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s37) | node1(c_bit0, s36) | (~node3(c_bit0, s36, s37)))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1124,plain,
% 13.10/13.26 ((node1(c_bit0, s36) | (~node3(c_bit0, s36, s37)) | m_counter_cell_v_value(c_bit0, s37)) <=> (m_counter_cell_v_value(c_bit0, s37) | node1(c_bit0, s36) | (~node3(c_bit0, s36, s37)))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1125,plain,
% 13.10/13.26 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s36) | (~node3(c_bit0, s36, s37)) | m_counter_cell_v_value(c_bit0, s37))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s37) | node1(c_bit0, s36) | (~node3(c_bit0, s36, s37))))),
% 13.10/13.26 inference(monotonicity,[status(thm)],[1124])).
% 13.10/13.26 tff(1126,plain,
% 13.10/13.26 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s36) | (~node3(c_bit0, s36, s37)) | m_counter_cell_v_value(c_bit0, s37))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s37) | node1(c_bit0, s36) | (~node3(c_bit0, s36, s37)))),
% 13.10/13.26 inference(transitivity,[status(thm)],[1125, 1123])).
% 13.10/13.26 tff(1127,plain,
% 13.10/13.26 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s36) | (~node3(c_bit0, s36, s37)) | m_counter_cell_v_value(c_bit0, s37))),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(1128,plain,
% 13.10/13.26 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s37) | node1(c_bit0, s36) | (~node3(c_bit0, s36, s37))),
% 13.10/13.26 inference(modus_ponens,[status(thm)],[1127, 1126])).
% 13.10/13.26 tff(1129,plain,
% 13.10/13.26 (m_counter_cell_v_value(c_bit0, s37) | node1(c_bit0, s36)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1128, 73, 1122])).
% 13.10/13.26 tff(1130,plain,
% 13.10/13.26 (m_counter_cell_v_value(c_bit0, s37)),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1129, 1111])).
% 13.10/13.26 tff(1131,assumption,(~m_counter_cell_v_carry_in(c_bit0, s37)), introduced(assumption)).
% 13.10/13.26 tff(1132,plain,
% 13.10/13.26 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s37)),
% 13.10/13.26 inference(quant_inst,[status(thm)],[])).
% 13.10/13.26 tff(1133,plain,
% 13.10/13.26 ($false),
% 13.10/13.26 inference(unit_resolution,[status(thm)],[1132, 18, 1131])).
% 13.10/13.26 tff(1134,plain,(m_counter_cell_v_carry_in(c_bit0, s37)), inference(lemma,lemma(discharge,[]))).
% 13.10/13.26 tff(1135,plain,
% 13.10/13.26 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s37)) | (~m_counter_cell_v_value(c_bit0, s37)) | (~node2(c_bit0, s37)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s37)) | (~m_counter_cell_v_value(c_bit0, s37)) | (~node2(c_bit0, s37)))),
% 13.10/13.26 inference(rewrite,[status(thm)],[])).
% 13.10/13.26 tff(1136,plain,
% 13.10/13.26 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s37)) | (~m_counter_cell_v_value(c_bit0, s37)) | (~node2(c_bit0, s37)))),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1137,plain,
% 13.10/13.27 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s37)) | (~m_counter_cell_v_value(c_bit0, s37)) | (~node2(c_bit0, s37))),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1136, 1135])).
% 13.10/13.27 tff(1138,plain,
% 13.10/13.27 ((~m_counter_cell_v_value(c_bit0, s37)) | (~node2(c_bit0, s37))),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1137, 93, 1134])).
% 13.10/13.27 tff(1139,plain,
% 13.10/13.27 (~node2(c_bit0, s37)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1138, 1130])).
% 13.10/13.27 tff(1140,plain,
% 13.10/13.27 (succ(s37, s38) <=> succ(s37, s38)),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1141,axiom,(succ(s37, s38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound38')).
% 13.10/13.27 tff(1142,plain,
% 13.10/13.27 (succ(s37, s38)),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1141, 1140])).
% 13.10/13.27 tff(1143,plain,
% 13.10/13.27 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s37, s38)) | trans(s37, s38))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s37, s38)) | trans(s37, s38))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1144,plain,
% 13.10/13.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s37, s38)) | trans(s37, s38))),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1145,plain,
% 13.10/13.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s37, s38)) | trans(s37, s38)),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1144, 1143])).
% 13.10/13.27 tff(1146,plain,
% 13.10/13.27 (trans(s37, s38)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1145, 1142, 45])).
% 13.10/13.27 tff(1147,plain,
% 13.10/13.27 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s37, s38)) | node3(c_bit0, s37, s38))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s37, s38)) | node3(c_bit0, s37, s38))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1148,plain,
% 13.10/13.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s37, s38)) | node3(c_bit0, s37, s38))),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1149,plain,
% 13.10/13.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s37, s38)) | node3(c_bit0, s37, s38)),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1148, 1147])).
% 13.10/13.27 tff(1150,plain,
% 13.10/13.27 (node3(c_bit0, s37, s38)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1149, 59, 1146])).
% 13.10/13.27 tff(1151,plain,
% 13.10/13.27 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s38)) | node2(c_bit0, s37) | (~node3(c_bit0, s37, s38)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s38)) | node2(c_bit0, s37) | (~node3(c_bit0, s37, s38)))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1152,plain,
% 13.10/13.27 ((node2(c_bit0, s37) | (~node3(c_bit0, s37, s38)) | (~m_counter_cell_v_value(c_bit0, s38))) <=> ((~m_counter_cell_v_value(c_bit0, s38)) | node2(c_bit0, s37) | (~node3(c_bit0, s37, s38)))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1153,plain,
% 13.10/13.27 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s37) | (~node3(c_bit0, s37, s38)) | (~m_counter_cell_v_value(c_bit0, s38)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s38)) | node2(c_bit0, s37) | (~node3(c_bit0, s37, s38))))),
% 13.10/13.27 inference(monotonicity,[status(thm)],[1152])).
% 13.10/13.27 tff(1154,plain,
% 13.10/13.27 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s37) | (~node3(c_bit0, s37, s38)) | (~m_counter_cell_v_value(c_bit0, s38)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s38)) | node2(c_bit0, s37) | (~node3(c_bit0, s37, s38)))),
% 13.10/13.27 inference(transitivity,[status(thm)],[1153, 1151])).
% 13.10/13.27 tff(1155,plain,
% 13.10/13.27 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s37) | (~node3(c_bit0, s37, s38)) | (~m_counter_cell_v_value(c_bit0, s38)))),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1156,plain,
% 13.10/13.27 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s38)) | node2(c_bit0, s37) | (~node3(c_bit0, s37, s38))),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1155, 1154])).
% 13.10/13.27 tff(1157,plain,
% 13.10/13.27 ((~m_counter_cell_v_value(c_bit0, s38)) | node2(c_bit0, s37)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1156, 121, 1150])).
% 13.10/13.27 tff(1158,plain,
% 13.10/13.27 (~m_counter_cell_v_value(c_bit0, s38)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1157, 1139])).
% 13.10/13.27 tff(1159,assumption,(~m_counter_cell_v_carry_in(c_bit0, s38)), introduced(assumption)).
% 13.10/13.27 tff(1160,plain,
% 13.10/13.27 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s38)),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1161,plain,
% 13.10/13.27 ($false),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1160, 18, 1159])).
% 13.10/13.27 tff(1162,plain,(m_counter_cell_v_carry_in(c_bit0, s38)), inference(lemma,lemma(discharge,[]))).
% 13.10/13.27 tff(1163,plain,
% 13.10/13.27 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s38)) | m_counter_cell_v_value(c_bit0, s38) | (~node1(c_bit0, s38)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s38)) | m_counter_cell_v_value(c_bit0, s38) | (~node1(c_bit0, s38)))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1164,plain,
% 13.10/13.27 (((~node1(c_bit0, s38)) | (~m_counter_cell_v_carry_in(c_bit0, s38)) | m_counter_cell_v_value(c_bit0, s38)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s38)) | m_counter_cell_v_value(c_bit0, s38) | (~node1(c_bit0, s38)))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1165,plain,
% 13.10/13.27 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s38)) | (~m_counter_cell_v_carry_in(c_bit0, s38)) | m_counter_cell_v_value(c_bit0, s38))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s38)) | m_counter_cell_v_value(c_bit0, s38) | (~node1(c_bit0, s38))))),
% 13.10/13.27 inference(monotonicity,[status(thm)],[1164])).
% 13.10/13.27 tff(1166,plain,
% 13.10/13.27 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s38)) | (~m_counter_cell_v_carry_in(c_bit0, s38)) | m_counter_cell_v_value(c_bit0, s38))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s38)) | m_counter_cell_v_value(c_bit0, s38) | (~node1(c_bit0, s38)))),
% 13.10/13.27 inference(transitivity,[status(thm)],[1165, 1163])).
% 13.10/13.27 tff(1167,plain,
% 13.10/13.27 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s38)) | (~m_counter_cell_v_carry_in(c_bit0, s38)) | m_counter_cell_v_value(c_bit0, s38))),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1168,plain,
% 13.10/13.27 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s38)) | m_counter_cell_v_value(c_bit0, s38) | (~node1(c_bit0, s38))),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1167, 1166])).
% 13.10/13.27 tff(1169,plain,
% 13.10/13.27 (m_counter_cell_v_value(c_bit0, s38) | (~node1(c_bit0, s38))),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1168, 30, 1162])).
% 13.10/13.27 tff(1170,plain,
% 13.10/13.27 (~node1(c_bit0, s38)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1169, 1158])).
% 13.10/13.27 tff(1171,plain,
% 13.10/13.27 (succ(s38, s39) <=> succ(s38, s39)),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1172,axiom,(succ(s38, s39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound39')).
% 13.10/13.27 tff(1173,plain,
% 13.10/13.27 (succ(s38, s39)),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1172, 1171])).
% 13.10/13.27 tff(1174,plain,
% 13.10/13.27 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s38, s39)) | trans(s38, s39))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s38, s39)) | trans(s38, s39))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1175,plain,
% 13.10/13.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s38, s39)) | trans(s38, s39))),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1176,plain,
% 13.10/13.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s38, s39)) | trans(s38, s39)),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1175, 1174])).
% 13.10/13.27 tff(1177,plain,
% 13.10/13.27 (trans(s38, s39)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1176, 1173, 45])).
% 13.10/13.27 tff(1178,plain,
% 13.10/13.27 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s38, s39)) | node3(c_bit0, s38, s39))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s38, s39)) | node3(c_bit0, s38, s39))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1179,plain,
% 13.10/13.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s38, s39)) | node3(c_bit0, s38, s39))),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1180,plain,
% 13.10/13.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s38, s39)) | node3(c_bit0, s38, s39)),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1179, 1178])).
% 13.10/13.27 tff(1181,plain,
% 13.10/13.27 (node3(c_bit0, s38, s39)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1180, 59, 1177])).
% 13.10/13.27 tff(1182,plain,
% 13.10/13.27 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s39) | node1(c_bit0, s38) | (~node3(c_bit0, s38, s39)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s39) | node1(c_bit0, s38) | (~node3(c_bit0, s38, s39)))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1183,plain,
% 13.10/13.27 ((node1(c_bit0, s38) | (~node3(c_bit0, s38, s39)) | m_counter_cell_v_value(c_bit0, s39)) <=> (m_counter_cell_v_value(c_bit0, s39) | node1(c_bit0, s38) | (~node3(c_bit0, s38, s39)))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1184,plain,
% 13.10/13.27 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s38) | (~node3(c_bit0, s38, s39)) | m_counter_cell_v_value(c_bit0, s39))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s39) | node1(c_bit0, s38) | (~node3(c_bit0, s38, s39))))),
% 13.10/13.27 inference(monotonicity,[status(thm)],[1183])).
% 13.10/13.27 tff(1185,plain,
% 13.10/13.27 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s38) | (~node3(c_bit0, s38, s39)) | m_counter_cell_v_value(c_bit0, s39))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s39) | node1(c_bit0, s38) | (~node3(c_bit0, s38, s39)))),
% 13.10/13.27 inference(transitivity,[status(thm)],[1184, 1182])).
% 13.10/13.27 tff(1186,plain,
% 13.10/13.27 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s38) | (~node3(c_bit0, s38, s39)) | m_counter_cell_v_value(c_bit0, s39))),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1187,plain,
% 13.10/13.27 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s39) | node1(c_bit0, s38) | (~node3(c_bit0, s38, s39))),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1186, 1185])).
% 13.10/13.27 tff(1188,plain,
% 13.10/13.27 (m_counter_cell_v_value(c_bit0, s39) | node1(c_bit0, s38)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1187, 73, 1181])).
% 13.10/13.27 tff(1189,plain,
% 13.10/13.27 (m_counter_cell_v_value(c_bit0, s39)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1188, 1170])).
% 13.10/13.27 tff(1190,assumption,(~m_counter_cell_v_carry_in(c_bit0, s39)), introduced(assumption)).
% 13.10/13.27 tff(1191,plain,
% 13.10/13.27 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s39)),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1192,plain,
% 13.10/13.27 ($false),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1191, 18, 1190])).
% 13.10/13.27 tff(1193,plain,(m_counter_cell_v_carry_in(c_bit0, s39)), inference(lemma,lemma(discharge,[]))).
% 13.10/13.27 tff(1194,plain,
% 13.10/13.27 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s39)) | (~m_counter_cell_v_value(c_bit0, s39)) | (~node2(c_bit0, s39)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s39)) | (~m_counter_cell_v_value(c_bit0, s39)) | (~node2(c_bit0, s39)))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1195,plain,
% 13.10/13.27 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s39)) | (~m_counter_cell_v_value(c_bit0, s39)) | (~node2(c_bit0, s39)))),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1196,plain,
% 13.10/13.27 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s39)) | (~m_counter_cell_v_value(c_bit0, s39)) | (~node2(c_bit0, s39))),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1195, 1194])).
% 13.10/13.27 tff(1197,plain,
% 13.10/13.27 ((~m_counter_cell_v_value(c_bit0, s39)) | (~node2(c_bit0, s39))),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1196, 93, 1193])).
% 13.10/13.27 tff(1198,plain,
% 13.10/13.27 (~node2(c_bit0, s39)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1197, 1189])).
% 13.10/13.27 tff(1199,plain,
% 13.10/13.27 (succ(s39, s40) <=> succ(s39, s40)),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1200,axiom,(succ(s39, s40)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound40')).
% 13.10/13.27 tff(1201,plain,
% 13.10/13.27 (succ(s39, s40)),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1200, 1199])).
% 13.10/13.27 tff(1202,plain,
% 13.10/13.27 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s39, s40)) | trans(s39, s40))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s39, s40)) | trans(s39, s40))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1203,plain,
% 13.10/13.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s39, s40)) | trans(s39, s40))),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1204,plain,
% 13.10/13.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s39, s40)) | trans(s39, s40)),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1203, 1202])).
% 13.10/13.27 tff(1205,plain,
% 13.10/13.27 (trans(s39, s40)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1204, 1201, 45])).
% 13.10/13.27 tff(1206,plain,
% 13.10/13.27 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s39, s40)) | node3(c_bit0, s39, s40))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s39, s40)) | node3(c_bit0, s39, s40))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1207,plain,
% 13.10/13.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s39, s40)) | node3(c_bit0, s39, s40))),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1208,plain,
% 13.10/13.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s39, s40)) | node3(c_bit0, s39, s40)),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1207, 1206])).
% 13.10/13.27 tff(1209,plain,
% 13.10/13.27 (node3(c_bit0, s39, s40)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1208, 59, 1205])).
% 13.10/13.27 tff(1210,plain,
% 13.10/13.27 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s40)) | node2(c_bit0, s39) | (~node3(c_bit0, s39, s40)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s40)) | node2(c_bit0, s39) | (~node3(c_bit0, s39, s40)))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1211,plain,
% 13.10/13.27 ((node2(c_bit0, s39) | (~node3(c_bit0, s39, s40)) | (~m_counter_cell_v_value(c_bit0, s40))) <=> ((~m_counter_cell_v_value(c_bit0, s40)) | node2(c_bit0, s39) | (~node3(c_bit0, s39, s40)))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1212,plain,
% 13.10/13.27 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s39) | (~node3(c_bit0, s39, s40)) | (~m_counter_cell_v_value(c_bit0, s40)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s40)) | node2(c_bit0, s39) | (~node3(c_bit0, s39, s40))))),
% 13.10/13.27 inference(monotonicity,[status(thm)],[1211])).
% 13.10/13.27 tff(1213,plain,
% 13.10/13.27 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s39) | (~node3(c_bit0, s39, s40)) | (~m_counter_cell_v_value(c_bit0, s40)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s40)) | node2(c_bit0, s39) | (~node3(c_bit0, s39, s40)))),
% 13.10/13.27 inference(transitivity,[status(thm)],[1212, 1210])).
% 13.10/13.27 tff(1214,plain,
% 13.10/13.27 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s39) | (~node3(c_bit0, s39, s40)) | (~m_counter_cell_v_value(c_bit0, s40)))),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1215,plain,
% 13.10/13.27 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s40)) | node2(c_bit0, s39) | (~node3(c_bit0, s39, s40))),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1214, 1213])).
% 13.10/13.27 tff(1216,plain,
% 13.10/13.27 ((~m_counter_cell_v_value(c_bit0, s40)) | node2(c_bit0, s39)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1215, 121, 1209])).
% 13.10/13.27 tff(1217,plain,
% 13.10/13.27 (~m_counter_cell_v_value(c_bit0, s40)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1216, 1198])).
% 13.10/13.27 tff(1218,assumption,(~m_counter_cell_v_carry_in(c_bit0, s40)), introduced(assumption)).
% 13.10/13.27 tff(1219,plain,
% 13.10/13.27 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s40)),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1220,plain,
% 13.10/13.27 ($false),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1219, 18, 1218])).
% 13.10/13.27 tff(1221,plain,(m_counter_cell_v_carry_in(c_bit0, s40)), inference(lemma,lemma(discharge,[]))).
% 13.10/13.27 tff(1222,plain,
% 13.10/13.27 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s40)) | m_counter_cell_v_value(c_bit0, s40) | (~node1(c_bit0, s40)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s40)) | m_counter_cell_v_value(c_bit0, s40) | (~node1(c_bit0, s40)))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1223,plain,
% 13.10/13.27 (((~node1(c_bit0, s40)) | (~m_counter_cell_v_carry_in(c_bit0, s40)) | m_counter_cell_v_value(c_bit0, s40)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s40)) | m_counter_cell_v_value(c_bit0, s40) | (~node1(c_bit0, s40)))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1224,plain,
% 13.10/13.27 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s40)) | (~m_counter_cell_v_carry_in(c_bit0, s40)) | m_counter_cell_v_value(c_bit0, s40))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s40)) | m_counter_cell_v_value(c_bit0, s40) | (~node1(c_bit0, s40))))),
% 13.10/13.27 inference(monotonicity,[status(thm)],[1223])).
% 13.10/13.27 tff(1225,plain,
% 13.10/13.27 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s40)) | (~m_counter_cell_v_carry_in(c_bit0, s40)) | m_counter_cell_v_value(c_bit0, s40))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s40)) | m_counter_cell_v_value(c_bit0, s40) | (~node1(c_bit0, s40)))),
% 13.10/13.27 inference(transitivity,[status(thm)],[1224, 1222])).
% 13.10/13.27 tff(1226,plain,
% 13.10/13.27 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s40)) | (~m_counter_cell_v_carry_in(c_bit0, s40)) | m_counter_cell_v_value(c_bit0, s40))),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1227,plain,
% 13.10/13.27 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s40)) | m_counter_cell_v_value(c_bit0, s40) | (~node1(c_bit0, s40))),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1226, 1225])).
% 13.10/13.27 tff(1228,plain,
% 13.10/13.27 (m_counter_cell_v_value(c_bit0, s40) | (~node1(c_bit0, s40))),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1227, 30, 1221])).
% 13.10/13.27 tff(1229,plain,
% 13.10/13.27 (~node1(c_bit0, s40)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1228, 1217])).
% 13.10/13.27 tff(1230,plain,
% 13.10/13.27 (succ(s40, s41) <=> succ(s40, s41)),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1231,axiom,(succ(s40, s41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound41')).
% 13.10/13.27 tff(1232,plain,
% 13.10/13.27 (succ(s40, s41)),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1231, 1230])).
% 13.10/13.27 tff(1233,plain,
% 13.10/13.27 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s40, s41)) | trans(s40, s41))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s40, s41)) | trans(s40, s41))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1234,plain,
% 13.10/13.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s40, s41)) | trans(s40, s41))),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1235,plain,
% 13.10/13.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s40, s41)) | trans(s40, s41)),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1234, 1233])).
% 13.10/13.27 tff(1236,plain,
% 13.10/13.27 (trans(s40, s41)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1235, 1232, 45])).
% 13.10/13.27 tff(1237,plain,
% 13.10/13.27 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s40, s41)) | node3(c_bit0, s40, s41))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s40, s41)) | node3(c_bit0, s40, s41))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1238,plain,
% 13.10/13.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s40, s41)) | node3(c_bit0, s40, s41))),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1239,plain,
% 13.10/13.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s40, s41)) | node3(c_bit0, s40, s41)),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1238, 1237])).
% 13.10/13.27 tff(1240,plain,
% 13.10/13.27 (node3(c_bit0, s40, s41)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1239, 59, 1236])).
% 13.10/13.27 tff(1241,plain,
% 13.10/13.27 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s41) | node1(c_bit0, s40) | (~node3(c_bit0, s40, s41)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s41) | node1(c_bit0, s40) | (~node3(c_bit0, s40, s41)))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1242,plain,
% 13.10/13.27 ((node1(c_bit0, s40) | (~node3(c_bit0, s40, s41)) | m_counter_cell_v_value(c_bit0, s41)) <=> (m_counter_cell_v_value(c_bit0, s41) | node1(c_bit0, s40) | (~node3(c_bit0, s40, s41)))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1243,plain,
% 13.10/13.27 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s40) | (~node3(c_bit0, s40, s41)) | m_counter_cell_v_value(c_bit0, s41))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s41) | node1(c_bit0, s40) | (~node3(c_bit0, s40, s41))))),
% 13.10/13.27 inference(monotonicity,[status(thm)],[1242])).
% 13.10/13.27 tff(1244,plain,
% 13.10/13.27 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s40) | (~node3(c_bit0, s40, s41)) | m_counter_cell_v_value(c_bit0, s41))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s41) | node1(c_bit0, s40) | (~node3(c_bit0, s40, s41)))),
% 13.10/13.27 inference(transitivity,[status(thm)],[1243, 1241])).
% 13.10/13.27 tff(1245,plain,
% 13.10/13.27 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s40) | (~node3(c_bit0, s40, s41)) | m_counter_cell_v_value(c_bit0, s41))),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1246,plain,
% 13.10/13.27 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s41) | node1(c_bit0, s40) | (~node3(c_bit0, s40, s41))),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 13.10/13.27 tff(1247,plain,
% 13.10/13.27 (m_counter_cell_v_value(c_bit0, s41) | node1(c_bit0, s40)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1246, 73, 1240])).
% 13.10/13.27 tff(1248,plain,
% 13.10/13.27 (m_counter_cell_v_value(c_bit0, s41)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1247, 1229])).
% 13.10/13.27 tff(1249,assumption,(~m_counter_cell_v_carry_in(c_bit0, s41)), introduced(assumption)).
% 13.10/13.27 tff(1250,plain,
% 13.10/13.27 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s41)),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1251,plain,
% 13.10/13.27 ($false),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1250, 18, 1249])).
% 13.10/13.27 tff(1252,plain,(m_counter_cell_v_carry_in(c_bit0, s41)), inference(lemma,lemma(discharge,[]))).
% 13.10/13.27 tff(1253,plain,
% 13.10/13.27 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s41)) | (~m_counter_cell_v_value(c_bit0, s41)) | (~node2(c_bit0, s41)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s41)) | (~m_counter_cell_v_value(c_bit0, s41)) | (~node2(c_bit0, s41)))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1254,plain,
% 13.10/13.27 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s41)) | (~m_counter_cell_v_value(c_bit0, s41)) | (~node2(c_bit0, s41)))),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1255,plain,
% 13.10/13.27 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s41)) | (~m_counter_cell_v_value(c_bit0, s41)) | (~node2(c_bit0, s41))),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1254, 1253])).
% 13.10/13.27 tff(1256,plain,
% 13.10/13.27 ((~m_counter_cell_v_value(c_bit0, s41)) | (~node2(c_bit0, s41))),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1255, 93, 1252])).
% 13.10/13.27 tff(1257,plain,
% 13.10/13.27 (~node2(c_bit0, s41)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1256, 1248])).
% 13.10/13.27 tff(1258,plain,
% 13.10/13.27 (succ(s41, s42) <=> succ(s41, s42)),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1259,axiom,(succ(s41, s42)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound42')).
% 13.10/13.27 tff(1260,plain,
% 13.10/13.27 (succ(s41, s42)),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1259, 1258])).
% 13.10/13.27 tff(1261,plain,
% 13.10/13.27 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s41, s42)) | trans(s41, s42))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s41, s42)) | trans(s41, s42))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1262,plain,
% 13.10/13.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s41, s42)) | trans(s41, s42))),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1263,plain,
% 13.10/13.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s41, s42)) | trans(s41, s42)),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1262, 1261])).
% 13.10/13.27 tff(1264,plain,
% 13.10/13.27 (trans(s41, s42)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1263, 1260, 45])).
% 13.10/13.27 tff(1265,plain,
% 13.10/13.27 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s41, s42)) | node3(c_bit0, s41, s42))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s41, s42)) | node3(c_bit0, s41, s42))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1266,plain,
% 13.10/13.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s41, s42)) | node3(c_bit0, s41, s42))),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1267,plain,
% 13.10/13.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s41, s42)) | node3(c_bit0, s41, s42)),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1266, 1265])).
% 13.10/13.27 tff(1268,plain,
% 13.10/13.27 (node3(c_bit0, s41, s42)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1267, 59, 1264])).
% 13.10/13.27 tff(1269,plain,
% 13.10/13.27 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s42)) | node2(c_bit0, s41) | (~node3(c_bit0, s41, s42)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s42)) | node2(c_bit0, s41) | (~node3(c_bit0, s41, s42)))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1270,plain,
% 13.10/13.27 ((node2(c_bit0, s41) | (~node3(c_bit0, s41, s42)) | (~m_counter_cell_v_value(c_bit0, s42))) <=> ((~m_counter_cell_v_value(c_bit0, s42)) | node2(c_bit0, s41) | (~node3(c_bit0, s41, s42)))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1271,plain,
% 13.10/13.27 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s41) | (~node3(c_bit0, s41, s42)) | (~m_counter_cell_v_value(c_bit0, s42)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s42)) | node2(c_bit0, s41) | (~node3(c_bit0, s41, s42))))),
% 13.10/13.27 inference(monotonicity,[status(thm)],[1270])).
% 13.10/13.27 tff(1272,plain,
% 13.10/13.27 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s41) | (~node3(c_bit0, s41, s42)) | (~m_counter_cell_v_value(c_bit0, s42)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s42)) | node2(c_bit0, s41) | (~node3(c_bit0, s41, s42)))),
% 13.10/13.27 inference(transitivity,[status(thm)],[1271, 1269])).
% 13.10/13.27 tff(1273,plain,
% 13.10/13.27 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s41) | (~node3(c_bit0, s41, s42)) | (~m_counter_cell_v_value(c_bit0, s42)))),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1274,plain,
% 13.10/13.27 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s42)) | node2(c_bit0, s41) | (~node3(c_bit0, s41, s42))),
% 13.10/13.27 inference(modus_ponens,[status(thm)],[1273, 1272])).
% 13.10/13.27 tff(1275,plain,
% 13.10/13.27 ((~m_counter_cell_v_value(c_bit0, s42)) | node2(c_bit0, s41)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1274, 121, 1268])).
% 13.10/13.27 tff(1276,plain,
% 13.10/13.27 (~m_counter_cell_v_value(c_bit0, s42)),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1275, 1257])).
% 13.10/13.27 tff(1277,assumption,(~m_counter_cell_v_carry_in(c_bit0, s42)), introduced(assumption)).
% 13.10/13.27 tff(1278,plain,
% 13.10/13.27 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s42)),
% 13.10/13.27 inference(quant_inst,[status(thm)],[])).
% 13.10/13.27 tff(1279,plain,
% 13.10/13.27 ($false),
% 13.10/13.27 inference(unit_resolution,[status(thm)],[1278, 18, 1277])).
% 13.10/13.27 tff(1280,plain,(m_counter_cell_v_carry_in(c_bit0, s42)), inference(lemma,lemma(discharge,[]))).
% 13.10/13.27 tff(1281,plain,
% 13.10/13.27 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s42)) | m_counter_cell_v_value(c_bit0, s42) | (~node1(c_bit0, s42)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s42)) | m_counter_cell_v_value(c_bit0, s42) | (~node1(c_bit0, s42)))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1282,plain,
% 13.10/13.27 (((~node1(c_bit0, s42)) | (~m_counter_cell_v_carry_in(c_bit0, s42)) | m_counter_cell_v_value(c_bit0, s42)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s42)) | m_counter_cell_v_value(c_bit0, s42) | (~node1(c_bit0, s42)))),
% 13.10/13.27 inference(rewrite,[status(thm)],[])).
% 13.10/13.27 tff(1283,plain,
% 13.10/13.27 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s42)) | (~m_counter_cell_v_carry_in(c_bit0, s42)) | m_counter_cell_v_value(c_bit0, s42))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s42)) | m_counter_cell_v_value(c_bit0, s42) | (~node1(c_bit0, s42))))),
% 13.10/13.28 inference(monotonicity,[status(thm)],[1282])).
% 13.10/13.28 tff(1284,plain,
% 13.10/13.28 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s42)) | (~m_counter_cell_v_carry_in(c_bit0, s42)) | m_counter_cell_v_value(c_bit0, s42))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s42)) | m_counter_cell_v_value(c_bit0, s42) | (~node1(c_bit0, s42)))),
% 13.10/13.28 inference(transitivity,[status(thm)],[1283, 1281])).
% 13.10/13.28 tff(1285,plain,
% 13.10/13.28 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s42)) | (~m_counter_cell_v_carry_in(c_bit0, s42)) | m_counter_cell_v_value(c_bit0, s42))),
% 13.10/13.28 inference(quant_inst,[status(thm)],[])).
% 13.10/13.28 tff(1286,plain,
% 13.10/13.28 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s42)) | m_counter_cell_v_value(c_bit0, s42) | (~node1(c_bit0, s42))),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1285, 1284])).
% 13.10/13.28 tff(1287,plain,
% 13.10/13.28 (m_counter_cell_v_value(c_bit0, s42) | (~node1(c_bit0, s42))),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1286, 30, 1280])).
% 13.10/13.28 tff(1288,plain,
% 13.10/13.28 (~node1(c_bit0, s42)),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1287, 1276])).
% 13.10/13.28 tff(1289,plain,
% 13.10/13.28 (succ(s42, s43) <=> succ(s42, s43)),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1290,axiom,(succ(s42, s43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound43')).
% 13.10/13.28 tff(1291,plain,
% 13.10/13.28 (succ(s42, s43)),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1290, 1289])).
% 13.10/13.28 tff(1292,plain,
% 13.10/13.28 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s42, s43)) | trans(s42, s43))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s42, s43)) | trans(s42, s43))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1293,plain,
% 13.10/13.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s42, s43)) | trans(s42, s43))),
% 13.10/13.28 inference(quant_inst,[status(thm)],[])).
% 13.10/13.28 tff(1294,plain,
% 13.10/13.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s42, s43)) | trans(s42, s43)),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1293, 1292])).
% 13.10/13.28 tff(1295,plain,
% 13.10/13.28 (trans(s42, s43)),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1294, 1291, 45])).
% 13.10/13.28 tff(1296,plain,
% 13.10/13.28 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s42, s43)) | node3(c_bit0, s42, s43))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s42, s43)) | node3(c_bit0, s42, s43))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1297,plain,
% 13.10/13.28 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s42, s43)) | node3(c_bit0, s42, s43))),
% 13.10/13.28 inference(quant_inst,[status(thm)],[])).
% 13.10/13.28 tff(1298,plain,
% 13.10/13.28 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s42, s43)) | node3(c_bit0, s42, s43)),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1297, 1296])).
% 13.10/13.28 tff(1299,plain,
% 13.10/13.28 (node3(c_bit0, s42, s43)),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1298, 59, 1295])).
% 13.10/13.28 tff(1300,plain,
% 13.10/13.28 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s43) | node1(c_bit0, s42) | (~node3(c_bit0, s42, s43)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s43) | node1(c_bit0, s42) | (~node3(c_bit0, s42, s43)))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1301,plain,
% 13.10/13.28 ((node1(c_bit0, s42) | (~node3(c_bit0, s42, s43)) | m_counter_cell_v_value(c_bit0, s43)) <=> (m_counter_cell_v_value(c_bit0, s43) | node1(c_bit0, s42) | (~node3(c_bit0, s42, s43)))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1302,plain,
% 13.10/13.28 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s42) | (~node3(c_bit0, s42, s43)) | m_counter_cell_v_value(c_bit0, s43))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s43) | node1(c_bit0, s42) | (~node3(c_bit0, s42, s43))))),
% 13.10/13.28 inference(monotonicity,[status(thm)],[1301])).
% 13.10/13.28 tff(1303,plain,
% 13.10/13.28 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s42) | (~node3(c_bit0, s42, s43)) | m_counter_cell_v_value(c_bit0, s43))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s43) | node1(c_bit0, s42) | (~node3(c_bit0, s42, s43)))),
% 13.10/13.28 inference(transitivity,[status(thm)],[1302, 1300])).
% 13.10/13.28 tff(1304,plain,
% 13.10/13.28 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s42) | (~node3(c_bit0, s42, s43)) | m_counter_cell_v_value(c_bit0, s43))),
% 13.10/13.28 inference(quant_inst,[status(thm)],[])).
% 13.10/13.28 tff(1305,plain,
% 13.10/13.28 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s43) | node1(c_bit0, s42) | (~node3(c_bit0, s42, s43))),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1304, 1303])).
% 13.10/13.28 tff(1306,plain,
% 13.10/13.28 (m_counter_cell_v_value(c_bit0, s43) | node1(c_bit0, s42)),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1305, 73, 1299])).
% 13.10/13.28 tff(1307,plain,
% 13.10/13.28 (m_counter_cell_v_value(c_bit0, s43)),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1306, 1288])).
% 13.10/13.28 tff(1308,assumption,(~m_counter_cell_v_carry_in(c_bit0, s43)), introduced(assumption)).
% 13.10/13.28 tff(1309,plain,
% 13.10/13.28 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s43)),
% 13.10/13.28 inference(quant_inst,[status(thm)],[])).
% 13.10/13.28 tff(1310,plain,
% 13.10/13.28 ($false),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1309, 18, 1308])).
% 13.10/13.28 tff(1311,plain,(m_counter_cell_v_carry_in(c_bit0, s43)), inference(lemma,lemma(discharge,[]))).
% 13.10/13.28 tff(1312,plain,
% 13.10/13.28 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s43)) | (~m_counter_cell_v_value(c_bit0, s43)) | (~node2(c_bit0, s43)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s43)) | (~m_counter_cell_v_value(c_bit0, s43)) | (~node2(c_bit0, s43)))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1313,plain,
% 13.10/13.28 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s43)) | (~m_counter_cell_v_value(c_bit0, s43)) | (~node2(c_bit0, s43)))),
% 13.10/13.28 inference(quant_inst,[status(thm)],[])).
% 13.10/13.28 tff(1314,plain,
% 13.10/13.28 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s43)) | (~m_counter_cell_v_value(c_bit0, s43)) | (~node2(c_bit0, s43))),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1313, 1312])).
% 13.10/13.28 tff(1315,plain,
% 13.10/13.28 ((~m_counter_cell_v_value(c_bit0, s43)) | (~node2(c_bit0, s43))),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1314, 93, 1311])).
% 13.10/13.28 tff(1316,plain,
% 13.10/13.28 (~node2(c_bit0, s43)),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1315, 1307])).
% 13.10/13.28 tff(1317,plain,
% 13.10/13.28 (succ(s43, s44) <=> succ(s43, s44)),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1318,axiom,(succ(s43, s44)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound44')).
% 13.10/13.28 tff(1319,plain,
% 13.10/13.28 (succ(s43, s44)),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1318, 1317])).
% 13.10/13.28 tff(1320,plain,
% 13.10/13.28 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s43, s44)) | trans(s43, s44))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s43, s44)) | trans(s43, s44))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1321,plain,
% 13.10/13.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s43, s44)) | trans(s43, s44))),
% 13.10/13.28 inference(quant_inst,[status(thm)],[])).
% 13.10/13.28 tff(1322,plain,
% 13.10/13.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s43, s44)) | trans(s43, s44)),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1321, 1320])).
% 13.10/13.28 tff(1323,plain,
% 13.10/13.28 (trans(s43, s44)),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1322, 1319, 45])).
% 13.10/13.28 tff(1324,plain,
% 13.10/13.28 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s43, s44)) | node3(c_bit0, s43, s44))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s43, s44)) | node3(c_bit0, s43, s44))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1325,plain,
% 13.10/13.28 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s43, s44)) | node3(c_bit0, s43, s44))),
% 13.10/13.28 inference(quant_inst,[status(thm)],[])).
% 13.10/13.28 tff(1326,plain,
% 13.10/13.28 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s43, s44)) | node3(c_bit0, s43, s44)),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1325, 1324])).
% 13.10/13.28 tff(1327,plain,
% 13.10/13.28 (node3(c_bit0, s43, s44)),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1326, 59, 1323])).
% 13.10/13.28 tff(1328,plain,
% 13.10/13.28 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s44)) | node2(c_bit0, s43) | (~node3(c_bit0, s43, s44)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s44)) | node2(c_bit0, s43) | (~node3(c_bit0, s43, s44)))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1329,plain,
% 13.10/13.28 ((node2(c_bit0, s43) | (~node3(c_bit0, s43, s44)) | (~m_counter_cell_v_value(c_bit0, s44))) <=> ((~m_counter_cell_v_value(c_bit0, s44)) | node2(c_bit0, s43) | (~node3(c_bit0, s43, s44)))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1330,plain,
% 13.10/13.28 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s43) | (~node3(c_bit0, s43, s44)) | (~m_counter_cell_v_value(c_bit0, s44)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s44)) | node2(c_bit0, s43) | (~node3(c_bit0, s43, s44))))),
% 13.10/13.28 inference(monotonicity,[status(thm)],[1329])).
% 13.10/13.28 tff(1331,plain,
% 13.10/13.28 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s43) | (~node3(c_bit0, s43, s44)) | (~m_counter_cell_v_value(c_bit0, s44)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s44)) | node2(c_bit0, s43) | (~node3(c_bit0, s43, s44)))),
% 13.10/13.28 inference(transitivity,[status(thm)],[1330, 1328])).
% 13.10/13.28 tff(1332,plain,
% 13.10/13.28 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s43) | (~node3(c_bit0, s43, s44)) | (~m_counter_cell_v_value(c_bit0, s44)))),
% 13.10/13.28 inference(quant_inst,[status(thm)],[])).
% 13.10/13.28 tff(1333,plain,
% 13.10/13.28 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s44)) | node2(c_bit0, s43) | (~node3(c_bit0, s43, s44))),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1332, 1331])).
% 13.10/13.28 tff(1334,plain,
% 13.10/13.28 ((~m_counter_cell_v_value(c_bit0, s44)) | node2(c_bit0, s43)),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1333, 121, 1327])).
% 13.10/13.28 tff(1335,plain,
% 13.10/13.28 (~m_counter_cell_v_value(c_bit0, s44)),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1334, 1316])).
% 13.10/13.28 tff(1336,assumption,(node4(c_bit0, s44)), introduced(assumption)).
% 13.10/13.28 tff(1337,assumption,(~m_counter_cell_v_value(c_bit0, s44)), introduced(assumption)).
% 13.10/13.28 tff(1338,plain,
% 13.10/13.28 (^[I0: $i, X: $i] : refl((m_counter_cell_v_value(I0, X) | (~node4(I0, X))) <=> (m_counter_cell_v_value(I0, X) | (~node4(I0, X))))),
% 13.10/13.28 inference(bind,[status(th)],[])).
% 13.10/13.28 tff(1339,plain,
% 13.10/13.28 (![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X))) <=> ![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))),
% 13.10/13.28 inference(quant_intro,[status(thm)],[1338])).
% 13.10/13.28 tff(1340,plain,
% 13.10/13.28 (![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X))) <=> ![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1341,axiom,(![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_counter_cell_9')).
% 13.10/13.28 tff(1342,plain,
% 13.10/13.28 (![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1341, 1340])).
% 13.10/13.28 tff(1343,plain,(
% 13.10/13.28 ![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))),
% 13.10/13.28 inference(skolemize,[status(sab)],[1342])).
% 13.10/13.28 tff(1344,plain,
% 13.10/13.28 (![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1343, 1339])).
% 13.10/13.28 tff(1345,plain,
% 13.10/13.28 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s44) | (~node4(c_bit0, s44)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s44) | (~node4(c_bit0, s44)))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1346,plain,
% 13.10/13.28 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s44) | (~node4(c_bit0, s44)))),
% 13.10/13.28 inference(quant_inst,[status(thm)],[])).
% 13.10/13.28 tff(1347,plain,
% 13.10/13.28 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s44) | (~node4(c_bit0, s44))),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1346, 1345])).
% 13.10/13.28 tff(1348,plain,
% 13.10/13.28 ($false),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1347, 1344, 1337, 1336])).
% 13.10/13.28 tff(1349,plain,(m_counter_cell_v_value(c_bit0, s44) | (~node4(c_bit0, s44))), inference(lemma,lemma(discharge,[]))).
% 13.10/13.28 tff(1350,plain,
% 13.10/13.28 (~node4(c_bit0, s44)),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1349, 1335])).
% 13.10/13.28 tff(1351,assumption,(~node4(c_bit0, s44)), introduced(assumption)).
% 13.10/13.28 tff(1352,assumption,(m_counter_cell_v_carry_out(c_bit0, s44)), introduced(assumption)).
% 13.10/13.28 tff(1353,plain,
% 13.10/13.28 (^[I0: $i, X: $i] : refl(((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X)) <=> ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X)))),
% 13.10/13.28 inference(bind,[status(th)],[])).
% 13.10/13.28 tff(1354,plain,
% 13.10/13.28 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X)) <=> ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))),
% 13.10/13.28 inference(quant_intro,[status(thm)],[1353])).
% 13.10/13.28 tff(1355,plain,
% 13.10/13.28 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X)) <=> ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1356,axiom,(![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_counter_cell_12')).
% 13.10/13.28 tff(1357,plain,
% 13.10/13.28 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1356, 1355])).
% 13.10/13.28 tff(1358,plain,(
% 13.10/13.28 ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))),
% 13.10/13.28 inference(skolemize,[status(sab)],[1357])).
% 13.10/13.28 tff(1359,plain,
% 13.10/13.28 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1358, 1354])).
% 13.10/13.28 tff(1360,plain,
% 13.10/13.28 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s44)) | node4(c_bit0, s44))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s44)) | node4(c_bit0, s44))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1361,plain,
% 13.10/13.28 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s44)) | node4(c_bit0, s44))),
% 13.10/13.28 inference(quant_inst,[status(thm)],[])).
% 13.10/13.28 tff(1362,plain,
% 13.10/13.28 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s44)) | node4(c_bit0, s44)),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1361, 1360])).
% 13.10/13.28 tff(1363,plain,
% 13.10/13.28 ($false),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1362, 1359, 1352, 1351])).
% 13.10/13.28 tff(1364,plain,((~m_counter_cell_v_carry_out(c_bit0, s44)) | node4(c_bit0, s44)), inference(lemma,lemma(discharge,[]))).
% 13.10/13.28 tff(1365,plain,
% 13.10/13.28 (~m_counter_cell_v_carry_out(c_bit0, s44)),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1364, 1350])).
% 13.10/13.28 tff(1366,assumption,(m_counter_cell_v_carry_in(c_bit1, s44)), introduced(assumption)).
% 13.10/13.28 tff(1367,assumption,(~m_counter_cell_v_carry_out(c_bit0, s44)), introduced(assumption)).
% 13.10/13.28 tff(1368,plain,
% 13.10/13.28 (^[X: $i] : refl(((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X)) <=> ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X)))),
% 13.10/13.28 inference(bind,[status(th)],[])).
% 13.10/13.28 tff(1369,plain,
% 13.10/13.28 (![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X)) <=> ![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))),
% 13.10/13.28 inference(quant_intro,[status(thm)],[1368])).
% 13.10/13.28 tff(1370,plain,
% 13.10/13.28 (![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X)) <=> ![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1371,axiom,(![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_3')).
% 13.10/13.28 tff(1372,plain,
% 13.10/13.28 (![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1371, 1370])).
% 13.10/13.28 tff(1373,plain,(
% 13.10/13.28 ![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))),
% 13.10/13.28 inference(skolemize,[status(sab)],[1372])).
% 13.10/13.28 tff(1374,plain,
% 13.10/13.28 (![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1373, 1369])).
% 13.10/13.28 tff(1375,plain,
% 13.10/13.28 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s44)) | m_counter_cell_v_carry_out(c_bit0, s44))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s44)) | m_counter_cell_v_carry_out(c_bit0, s44))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1376,plain,
% 13.10/13.28 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s44)) | m_counter_cell_v_carry_out(c_bit0, s44))),
% 13.10/13.28 inference(quant_inst,[status(thm)],[])).
% 13.10/13.28 tff(1377,plain,
% 13.10/13.28 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s44)) | m_counter_cell_v_carry_out(c_bit0, s44)),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1376, 1375])).
% 13.10/13.28 tff(1378,plain,
% 13.10/13.28 ($false),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1377, 1374, 1367, 1366])).
% 13.10/13.28 tff(1379,plain,((~m_counter_cell_v_carry_in(c_bit1, s44)) | m_counter_cell_v_carry_out(c_bit0, s44)), inference(lemma,lemma(discharge,[]))).
% 13.10/13.28 tff(1380,plain,
% 13.10/13.28 (~m_counter_cell_v_carry_in(c_bit1, s44)),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1379, 1365])).
% 13.10/13.28 tff(1381,plain,
% 13.10/13.28 (^[I0: $i, X: $i] : refl(((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X)) <=> ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X)))),
% 13.10/13.28 inference(bind,[status(th)],[])).
% 13.10/13.28 tff(1382,plain,
% 13.10/13.28 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X)) <=> ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))),
% 13.10/13.28 inference(quant_intro,[status(thm)],[1381])).
% 13.10/13.28 tff(1383,plain,
% 13.10/13.28 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X)) <=> ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1384,plain,
% 13.10/13.28 (^[I0: $i, X: $i] : trans(monotonicity(rewrite((m_counter_cell_v_carry_out(I0, X) | (~m_counter_cell_v_value(I0, X))) <=> ((~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))), (((m_counter_cell_v_carry_out(I0, X) | (~m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(I0, X))) <=> (((~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X)) | (~m_counter_cell_v_carry_in(I0, X))))), rewrite((((~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X)) | (~m_counter_cell_v_carry_in(I0, X))) <=> ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))), (((m_counter_cell_v_carry_out(I0, X) | (~m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(I0, X))) <=> ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))))),
% 13.10/13.28 inference(bind,[status(th)],[])).
% 13.10/13.28 tff(1385,plain,
% 13.10/13.28 (![I0: $i, X: $i] : ((m_counter_cell_v_carry_out(I0, X) | (~m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(I0, X))) <=> ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))),
% 13.10/13.28 inference(quant_intro,[status(thm)],[1384])).
% 13.10/13.28 tff(1386,axiom,(![I0: $i, X: $i] : ((m_counter_cell_v_carry_out(I0, X) | (~m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(I0, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_counter_cell_11')).
% 13.10/13.28 tff(1387,plain,
% 13.10/13.28 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1386, 1385])).
% 13.10/13.28 tff(1388,plain,
% 13.10/13.28 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1387, 1383])).
% 13.10/13.28 tff(1389,plain,(
% 13.10/13.28 ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))),
% 13.10/13.28 inference(skolemize,[status(sab)],[1388])).
% 13.10/13.28 tff(1390,plain,
% 13.10/13.28 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1389, 1382])).
% 13.10/13.28 tff(1391,plain,
% 13.10/13.28 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s31)) | (~m_counter_cell_v_value(c_bit0, s31)) | m_counter_cell_v_carry_out(c_bit0, s31))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s31)) | (~m_counter_cell_v_value(c_bit0, s31)) | m_counter_cell_v_carry_out(c_bit0, s31))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1392,plain,
% 13.10/13.28 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s31)) | (~m_counter_cell_v_value(c_bit0, s31)) | m_counter_cell_v_carry_out(c_bit0, s31))),
% 13.10/13.28 inference(quant_inst,[status(thm)],[])).
% 13.10/13.28 tff(1393,plain,
% 13.10/13.28 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s31)) | (~m_counter_cell_v_value(c_bit0, s31)) | m_counter_cell_v_carry_out(c_bit0, s31)),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1392, 1391])).
% 13.10/13.28 tff(1394,plain,
% 13.10/13.28 ((~m_counter_cell_v_value(c_bit0, s31)) | m_counter_cell_v_carry_out(c_bit0, s31)),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1393, 1390, 957])).
% 13.10/13.28 tff(1395,plain,
% 13.10/13.28 (m_counter_cell_v_carry_out(c_bit0, s31)),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1394, 953])).
% 13.10/13.28 tff(1396,plain,
% 13.10/13.28 (^[X: $i] : refl(((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X)) <=> ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X)))),
% 13.10/13.28 inference(bind,[status(th)],[])).
% 13.10/13.28 tff(1397,plain,
% 13.10/13.28 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X)) <=> ![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))),
% 13.10/13.28 inference(quant_intro,[status(thm)],[1396])).
% 13.10/13.28 tff(1398,plain,
% 13.10/13.28 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X)) <=> ![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1399,plain,
% 13.10/13.28 (^[X: $i] : rewrite((m_counter_cell_v_carry_in(c_bit1, X) | (~m_counter_cell_v_carry_out(c_bit0, X))) <=> ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X)))),
% 13.10/13.28 inference(bind,[status(th)],[])).
% 13.10/13.28 tff(1400,plain,
% 13.10/13.28 (![X: $i] : (m_counter_cell_v_carry_in(c_bit1, X) | (~m_counter_cell_v_carry_out(c_bit0, X))) <=> ![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))),
% 13.10/13.28 inference(quant_intro,[status(thm)],[1399])).
% 13.10/13.28 tff(1401,axiom,(![X: $i] : (m_counter_cell_v_carry_in(c_bit1, X) | (~m_counter_cell_v_carry_out(c_bit0, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_2')).
% 13.10/13.28 tff(1402,plain,
% 13.10/13.28 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1401, 1400])).
% 13.10/13.28 tff(1403,plain,
% 13.10/13.28 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1402, 1398])).
% 13.10/13.28 tff(1404,plain,(
% 13.10/13.28 ![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))),
% 13.10/13.28 inference(skolemize,[status(sab)],[1403])).
% 13.10/13.28 tff(1405,plain,
% 13.10/13.28 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1404, 1397])).
% 13.10/13.28 tff(1406,plain,
% 13.10/13.28 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s31)) | m_counter_cell_v_carry_in(c_bit1, s31))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s31)) | m_counter_cell_v_carry_in(c_bit1, s31))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1407,plain,
% 13.10/13.28 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s31)) | m_counter_cell_v_carry_in(c_bit1, s31))),
% 13.10/13.28 inference(quant_inst,[status(thm)],[])).
% 13.10/13.28 tff(1408,plain,
% 13.10/13.28 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s31)) | m_counter_cell_v_carry_in(c_bit1, s31)),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1407, 1406])).
% 13.10/13.28 tff(1409,plain,
% 13.10/13.28 (m_counter_cell_v_carry_in(c_bit1, s31)),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1408, 1405, 1395])).
% 13.10/13.28 tff(1410,plain,
% 13.10/13.28 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s30) | (~node4(c_bit0, s30)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s30) | (~node4(c_bit0, s30)))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1411,plain,
% 13.10/13.28 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s30) | (~node4(c_bit0, s30)))),
% 13.10/13.28 inference(quant_inst,[status(thm)],[])).
% 13.10/13.28 tff(1412,plain,
% 13.10/13.28 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s30) | (~node4(c_bit0, s30))),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1411, 1410])).
% 13.10/13.28 tff(1413,plain,
% 13.10/13.28 (~node4(c_bit0, s30)),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1412, 1344, 922])).
% 13.10/13.28 tff(1414,assumption,(m_counter_cell_v_carry_out(c_bit0, s30)), introduced(assumption)).
% 13.10/13.28 tff(1415,plain,
% 13.10/13.28 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s30)) | node4(c_bit0, s30))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s30)) | node4(c_bit0, s30))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1416,plain,
% 13.10/13.28 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s30)) | node4(c_bit0, s30))),
% 13.10/13.28 inference(quant_inst,[status(thm)],[])).
% 13.10/13.28 tff(1417,plain,
% 13.10/13.28 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s30)) | node4(c_bit0, s30)),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1416, 1415])).
% 13.10/13.28 tff(1418,plain,
% 13.10/13.28 ($false),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1417, 1359, 1414, 1413])).
% 13.10/13.28 tff(1419,plain,(~m_counter_cell_v_carry_out(c_bit0, s30)), inference(lemma,lemma(discharge,[]))).
% 13.10/13.28 tff(1420,plain,
% 13.10/13.28 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s30)) | m_counter_cell_v_carry_out(c_bit0, s30))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s30)) | m_counter_cell_v_carry_out(c_bit0, s30))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1421,plain,
% 13.10/13.28 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s30)) | m_counter_cell_v_carry_out(c_bit0, s30))),
% 13.10/13.28 inference(quant_inst,[status(thm)],[])).
% 13.10/13.28 tff(1422,plain,
% 13.10/13.28 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s30)) | m_counter_cell_v_carry_out(c_bit0, s30)),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1421, 1420])).
% 13.10/13.28 tff(1423,plain,
% 13.10/13.28 (~m_counter_cell_v_carry_in(c_bit1, s30)),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1422, 1374, 1419])).
% 13.10/13.28 tff(1424,assumption,(node1(c_bit1, s30)), introduced(assumption)).
% 13.10/13.28 tff(1425,plain,
% 13.10/13.28 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s27)) | (~m_counter_cell_v_value(c_bit0, s27)) | m_counter_cell_v_carry_out(c_bit0, s27))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s27)) | (~m_counter_cell_v_value(c_bit0, s27)) | m_counter_cell_v_carry_out(c_bit0, s27))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1426,plain,
% 13.10/13.28 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s27)) | (~m_counter_cell_v_value(c_bit0, s27)) | m_counter_cell_v_carry_out(c_bit0, s27))),
% 13.10/13.28 inference(quant_inst,[status(thm)],[])).
% 13.10/13.28 tff(1427,plain,
% 13.10/13.28 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s27)) | (~m_counter_cell_v_value(c_bit0, s27)) | m_counter_cell_v_carry_out(c_bit0, s27)),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1426, 1425])).
% 13.10/13.28 tff(1428,plain,
% 13.10/13.28 ((~m_counter_cell_v_value(c_bit0, s27)) | m_counter_cell_v_carry_out(c_bit0, s27)),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1427, 1390, 839])).
% 13.10/13.28 tff(1429,plain,
% 13.10/13.28 (m_counter_cell_v_carry_out(c_bit0, s27)),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1428, 835])).
% 13.10/13.28 tff(1430,plain,
% 13.10/13.28 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s27)) | m_counter_cell_v_carry_in(c_bit1, s27))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s27)) | m_counter_cell_v_carry_in(c_bit1, s27))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1431,plain,
% 13.10/13.28 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s27)) | m_counter_cell_v_carry_in(c_bit1, s27))),
% 13.10/13.28 inference(quant_inst,[status(thm)],[])).
% 13.10/13.28 tff(1432,plain,
% 13.10/13.28 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s27)) | m_counter_cell_v_carry_in(c_bit1, s27)),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1431, 1430])).
% 13.10/13.28 tff(1433,plain,
% 13.10/13.28 (m_counter_cell_v_carry_in(c_bit1, s27)),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1432, 1405, 1429])).
% 13.10/13.28 tff(1434,plain,
% 13.10/13.28 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s24) | (~node4(c_bit0, s24)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s24) | (~node4(c_bit0, s24)))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1435,plain,
% 13.10/13.28 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s24) | (~node4(c_bit0, s24)))),
% 13.10/13.28 inference(quant_inst,[status(thm)],[])).
% 13.10/13.28 tff(1436,plain,
% 13.10/13.28 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s24) | (~node4(c_bit0, s24))),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1435, 1434])).
% 13.10/13.28 tff(1437,plain,
% 13.10/13.28 (~node4(c_bit0, s24)),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1436, 1344, 745])).
% 13.10/13.28 tff(1438,assumption,(m_counter_cell_v_carry_out(c_bit0, s24)), introduced(assumption)).
% 13.10/13.28 tff(1439,plain,
% 13.10/13.28 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s24)) | node4(c_bit0, s24))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s24)) | node4(c_bit0, s24))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1440,plain,
% 13.10/13.28 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s24)) | node4(c_bit0, s24))),
% 13.10/13.28 inference(quant_inst,[status(thm)],[])).
% 13.10/13.28 tff(1441,plain,
% 13.10/13.28 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s24)) | node4(c_bit0, s24)),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1440, 1439])).
% 13.10/13.28 tff(1442,plain,
% 13.10/13.28 ($false),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1441, 1359, 1438, 1437])).
% 13.10/13.28 tff(1443,plain,(~m_counter_cell_v_carry_out(c_bit0, s24)), inference(lemma,lemma(discharge,[]))).
% 13.10/13.28 tff(1444,plain,
% 13.10/13.28 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s24)) | m_counter_cell_v_carry_out(c_bit0, s24))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s24)) | m_counter_cell_v_carry_out(c_bit0, s24))),
% 13.10/13.28 inference(rewrite,[status(thm)],[])).
% 13.10/13.28 tff(1445,plain,
% 13.10/13.28 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s24)) | m_counter_cell_v_carry_out(c_bit0, s24))),
% 13.10/13.28 inference(quant_inst,[status(thm)],[])).
% 13.10/13.28 tff(1446,plain,
% 13.10/13.28 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s24)) | m_counter_cell_v_carry_out(c_bit0, s24)),
% 13.10/13.28 inference(modus_ponens,[status(thm)],[1445, 1444])).
% 13.10/13.28 tff(1447,plain,
% 13.10/13.28 (~m_counter_cell_v_carry_in(c_bit1, s24)),
% 13.10/13.28 inference(unit_resolution,[status(thm)],[1446, 1374, 1443])).
% 13.10/13.28 tff(1448,assumption,(node2(c_bit1, s23)), introduced(assumption)).
% 13.10/13.28 tff(1449,plain,
% 13.10/13.28 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s20) | (~node4(c_bit0, s20)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s20) | (~node4(c_bit0, s20)))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1450,plain,
% 13.10/13.29 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s20) | (~node4(c_bit0, s20)))),
% 13.10/13.29 inference(quant_inst,[status(thm)],[])).
% 13.10/13.29 tff(1451,plain,
% 13.10/13.29 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s20) | (~node4(c_bit0, s20))),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1450, 1449])).
% 13.10/13.29 tff(1452,plain,
% 13.10/13.29 (~node4(c_bit0, s20)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1451, 1344, 627])).
% 13.10/13.29 tff(1453,assumption,(m_counter_cell_v_carry_out(c_bit0, s20)), introduced(assumption)).
% 13.10/13.29 tff(1454,plain,
% 13.10/13.29 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s20)) | node4(c_bit0, s20))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s20)) | node4(c_bit0, s20))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1455,plain,
% 13.10/13.29 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s20)) | node4(c_bit0, s20))),
% 13.10/13.29 inference(quant_inst,[status(thm)],[])).
% 13.10/13.29 tff(1456,plain,
% 13.10/13.29 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s20)) | node4(c_bit0, s20)),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1455, 1454])).
% 13.10/13.29 tff(1457,plain,
% 13.10/13.29 ($false),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1456, 1359, 1453, 1452])).
% 13.10/13.29 tff(1458,plain,(~m_counter_cell_v_carry_out(c_bit0, s20)), inference(lemma,lemma(discharge,[]))).
% 13.10/13.29 tff(1459,plain,
% 13.10/13.29 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s20)) | m_counter_cell_v_carry_out(c_bit0, s20))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s20)) | m_counter_cell_v_carry_out(c_bit0, s20))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1460,plain,
% 13.10/13.29 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s20)) | m_counter_cell_v_carry_out(c_bit0, s20))),
% 13.10/13.29 inference(quant_inst,[status(thm)],[])).
% 13.10/13.29 tff(1461,plain,
% 13.10/13.29 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s20)) | m_counter_cell_v_carry_out(c_bit0, s20)),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1460, 1459])).
% 13.10/13.29 tff(1462,plain,
% 13.10/13.29 (~m_counter_cell_v_carry_in(c_bit1, s20)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1461, 1374, 1458])).
% 13.10/13.29 tff(1463,assumption,(node1(c_bit1, s17)), introduced(assumption)).
% 13.10/13.29 tff(1464,plain,
% 13.10/13.29 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s17)) | (~m_counter_cell_v_value(c_bit0, s17)) | m_counter_cell_v_carry_out(c_bit0, s17))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s17)) | (~m_counter_cell_v_value(c_bit0, s17)) | m_counter_cell_v_carry_out(c_bit0, s17))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1465,plain,
% 13.10/13.29 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s17)) | (~m_counter_cell_v_value(c_bit0, s17)) | m_counter_cell_v_carry_out(c_bit0, s17))),
% 13.10/13.29 inference(quant_inst,[status(thm)],[])).
% 13.10/13.29 tff(1466,plain,
% 13.10/13.29 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s17)) | (~m_counter_cell_v_value(c_bit0, s17)) | m_counter_cell_v_carry_out(c_bit0, s17)),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1465, 1464])).
% 13.10/13.29 tff(1467,plain,
% 13.10/13.29 ((~m_counter_cell_v_value(c_bit0, s17)) | m_counter_cell_v_carry_out(c_bit0, s17)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1466, 1390, 544])).
% 13.10/13.29 tff(1468,plain,
% 13.10/13.29 (m_counter_cell_v_carry_out(c_bit0, s17)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1467, 540])).
% 13.10/13.29 tff(1469,plain,
% 13.10/13.29 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s17)) | m_counter_cell_v_carry_in(c_bit1, s17))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s17)) | m_counter_cell_v_carry_in(c_bit1, s17))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1470,plain,
% 13.10/13.29 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s17)) | m_counter_cell_v_carry_in(c_bit1, s17))),
% 13.10/13.29 inference(quant_inst,[status(thm)],[])).
% 13.10/13.29 tff(1471,plain,
% 13.10/13.29 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s17)) | m_counter_cell_v_carry_in(c_bit1, s17)),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1470, 1469])).
% 13.10/13.29 tff(1472,plain,
% 13.10/13.29 (m_counter_cell_v_carry_in(c_bit1, s17)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1471, 1405, 1468])).
% 13.10/13.29 tff(1473,assumption,(m_counter_cell_v_value(c_bit1, s0)), introduced(assumption)).
% 13.10/13.29 tff(1474,plain,
% 13.10/13.29 ((~![I0: $i] : (~m_counter_cell_v_value(I0, s0))) | (~m_counter_cell_v_value(c_bit1, s0))),
% 13.10/13.29 inference(quant_inst,[status(thm)],[])).
% 13.10/13.29 tff(1475,plain,
% 13.10/13.29 ($false),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1474, 8, 1473])).
% 13.10/13.29 tff(1476,plain,(~m_counter_cell_v_value(c_bit1, s0)), inference(lemma,lemma(discharge,[]))).
% 13.10/13.29 tff(1477,plain,
% 13.10/13.29 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s0) | (~node4(c_bit0, s0)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s0) | (~node4(c_bit0, s0)))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1478,plain,
% 13.10/13.29 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s0) | (~node4(c_bit0, s0)))),
% 13.10/13.29 inference(quant_inst,[status(thm)],[])).
% 13.10/13.29 tff(1479,plain,
% 13.10/13.29 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s0) | (~node4(c_bit0, s0))),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1478, 1477])).
% 13.10/13.29 tff(1480,plain,
% 13.10/13.29 (~node4(c_bit0, s0)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1479, 1344, 11])).
% 13.10/13.29 tff(1481,plain,
% 13.10/13.29 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s0)) | node4(c_bit0, s0))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s0)) | node4(c_bit0, s0))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1482,plain,
% 13.10/13.29 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s0)) | node4(c_bit0, s0))),
% 13.10/13.29 inference(quant_inst,[status(thm)],[])).
% 13.10/13.29 tff(1483,plain,
% 13.10/13.29 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s0)) | node4(c_bit0, s0)),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1482, 1481])).
% 13.10/13.29 tff(1484,plain,
% 13.10/13.29 (~m_counter_cell_v_carry_out(c_bit0, s0)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1483, 1359, 1480])).
% 13.10/13.29 tff(1485,plain,
% 13.10/13.29 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s0)) | m_counter_cell_v_carry_out(c_bit0, s0))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s0)) | m_counter_cell_v_carry_out(c_bit0, s0))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1486,plain,
% 13.10/13.29 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s0)) | m_counter_cell_v_carry_out(c_bit0, s0))),
% 13.10/13.29 inference(quant_inst,[status(thm)],[])).
% 13.10/13.29 tff(1487,plain,
% 13.10/13.29 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s0)) | m_counter_cell_v_carry_out(c_bit0, s0)),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1486, 1485])).
% 13.10/13.29 tff(1488,plain,
% 13.10/13.29 (~m_counter_cell_v_carry_in(c_bit1, s0)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1487, 1374, 1484])).
% 13.10/13.29 tff(1489,plain,
% 13.10/13.29 (^[I0: $i, X: $i] : refl((m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X))) <=> (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X))))),
% 13.10/13.29 inference(bind,[status(th)],[])).
% 13.10/13.29 tff(1490,plain,
% 13.10/13.29 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X))) <=> ![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))),
% 13.10/13.29 inference(quant_intro,[status(thm)],[1489])).
% 13.10/13.29 tff(1491,plain,
% 13.10/13.29 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X))) <=> ![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1492,plain,
% 13.10/13.29 (^[I0: $i, X: $i] : trans(monotonicity(rewrite((m_counter_cell_v_value(I0, X) | m_counter_cell_v_carry_in(I0, X)) <=> (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X))), (((m_counter_cell_v_value(I0, X) | m_counter_cell_v_carry_in(I0, X)) | (~node2(I0, X))) <=> ((m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X)) | (~node2(I0, X))))), rewrite(((m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X)) | (~node2(I0, X))) <=> (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))), (((m_counter_cell_v_value(I0, X) | m_counter_cell_v_carry_in(I0, X)) | (~node2(I0, X))) <=> (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))))),
% 13.10/13.29 inference(bind,[status(th)],[])).
% 13.10/13.29 tff(1493,plain,
% 13.10/13.29 (![I0: $i, X: $i] : ((m_counter_cell_v_value(I0, X) | m_counter_cell_v_carry_in(I0, X)) | (~node2(I0, X))) <=> ![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))),
% 13.10/13.29 inference(quant_intro,[status(thm)],[1492])).
% 13.10/13.29 tff(1494,axiom,(![I0: $i, X: $i] : ((m_counter_cell_v_value(I0, X) | m_counter_cell_v_carry_in(I0, X)) | (~node2(I0, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_counter_cell_4')).
% 13.10/13.29 tff(1495,plain,
% 13.10/13.29 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1494, 1493])).
% 13.10/13.29 tff(1496,plain,
% 13.10/13.29 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1495, 1491])).
% 13.10/13.29 tff(1497,plain,(
% 13.10/13.29 ![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))),
% 13.10/13.29 inference(skolemize,[status(sab)],[1496])).
% 13.10/13.29 tff(1498,plain,
% 13.10/13.29 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1497, 1490])).
% 13.10/13.29 tff(1499,plain,
% 13.10/13.29 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0)) | m_counter_cell_v_carry_in(c_bit1, s0))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0)) | m_counter_cell_v_carry_in(c_bit1, s0))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1500,plain,
% 13.10/13.29 ((m_counter_cell_v_carry_in(c_bit1, s0) | m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0))) <=> (m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0)) | m_counter_cell_v_carry_in(c_bit1, s0))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1501,plain,
% 13.10/13.29 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s0) | m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0)) | m_counter_cell_v_carry_in(c_bit1, s0)))),
% 13.10/13.29 inference(monotonicity,[status(thm)],[1500])).
% 13.10/13.29 tff(1502,plain,
% 13.10/13.29 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s0) | m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0)) | m_counter_cell_v_carry_in(c_bit1, s0))),
% 13.10/13.29 inference(transitivity,[status(thm)],[1501, 1499])).
% 13.10/13.29 tff(1503,plain,
% 13.10/13.29 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s0) | m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0)))),
% 13.10/13.29 inference(quant_inst,[status(thm)],[])).
% 13.10/13.29 tff(1504,plain,
% 13.10/13.29 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0)) | m_counter_cell_v_carry_in(c_bit1, s0)),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1503, 1502])).
% 13.10/13.29 tff(1505,plain,
% 13.10/13.29 (m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0))),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1504, 1498, 1488])).
% 13.10/13.29 tff(1506,plain,
% 13.10/13.29 (~node2(c_bit1, s0)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1505, 1476])).
% 13.10/13.29 tff(1507,plain,
% 13.10/13.29 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s0, s1)) | node3(c_bit1, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s0, s1)) | node3(c_bit1, s0, s1))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1508,plain,
% 13.10/13.29 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s0, s1)) | node3(c_bit1, s0, s1))),
% 13.10/13.29 inference(quant_inst,[status(thm)],[])).
% 13.10/13.29 tff(1509,plain,
% 13.10/13.29 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s0, s1)) | node3(c_bit1, s0, s1)),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1508, 1507])).
% 13.10/13.29 tff(1510,plain,
% 13.10/13.29 (node3(c_bit1, s0, s1)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1509, 59, 52])).
% 13.10/13.29 tff(1511,plain,
% 13.10/13.29 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s0) | (~m_counter_cell_v_value(c_bit1, s1)) | (~node3(c_bit1, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit1, s0) | (~m_counter_cell_v_value(c_bit1, s1)) | (~node3(c_bit1, s0, s1)))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1512,plain,
% 13.10/13.29 ((node2(c_bit1, s0) | (~node3(c_bit1, s0, s1)) | (~m_counter_cell_v_value(c_bit1, s1))) <=> (node2(c_bit1, s0) | (~m_counter_cell_v_value(c_bit1, s1)) | (~node3(c_bit1, s0, s1)))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1513,plain,
% 13.10/13.29 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s0) | (~node3(c_bit1, s0, s1)) | (~m_counter_cell_v_value(c_bit1, s1)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s0) | (~m_counter_cell_v_value(c_bit1, s1)) | (~node3(c_bit1, s0, s1))))),
% 13.10/13.29 inference(monotonicity,[status(thm)],[1512])).
% 13.10/13.29 tff(1514,plain,
% 13.10/13.29 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s0) | (~node3(c_bit1, s0, s1)) | (~m_counter_cell_v_value(c_bit1, s1)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit1, s0) | (~m_counter_cell_v_value(c_bit1, s1)) | (~node3(c_bit1, s0, s1)))),
% 13.10/13.29 inference(transitivity,[status(thm)],[1513, 1511])).
% 13.10/13.29 tff(1515,plain,
% 13.10/13.29 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s0) | (~node3(c_bit1, s0, s1)) | (~m_counter_cell_v_value(c_bit1, s1)))),
% 13.10/13.29 inference(quant_inst,[status(thm)],[])).
% 13.10/13.29 tff(1516,plain,
% 13.10/13.29 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit1, s0) | (~m_counter_cell_v_value(c_bit1, s1)) | (~node3(c_bit1, s0, s1))),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1515, 1514])).
% 13.10/13.29 tff(1517,plain,
% 13.10/13.29 (node2(c_bit1, s0) | (~m_counter_cell_v_value(c_bit1, s1))),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1516, 121, 1510])).
% 13.10/13.29 tff(1518,plain,
% 13.10/13.29 (~m_counter_cell_v_value(c_bit1, s1)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1517, 1506])).
% 13.10/13.29 tff(1519,plain,
% 13.10/13.29 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s1)) | (~m_counter_cell_v_value(c_bit0, s1)) | m_counter_cell_v_carry_out(c_bit0, s1))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s1)) | (~m_counter_cell_v_value(c_bit0, s1)) | m_counter_cell_v_carry_out(c_bit0, s1))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1520,plain,
% 13.10/13.29 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s1)) | (~m_counter_cell_v_value(c_bit0, s1)) | m_counter_cell_v_carry_out(c_bit0, s1))),
% 13.10/13.29 inference(quant_inst,[status(thm)],[])).
% 13.10/13.29 tff(1521,plain,
% 13.10/13.29 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s1)) | (~m_counter_cell_v_value(c_bit0, s1)) | m_counter_cell_v_carry_out(c_bit0, s1)),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1520, 1519])).
% 13.10/13.29 tff(1522,plain,
% 13.10/13.29 ((~m_counter_cell_v_value(c_bit0, s1)) | m_counter_cell_v_carry_out(c_bit0, s1)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1521, 1390, 83])).
% 13.10/13.29 tff(1523,plain,
% 13.10/13.29 (m_counter_cell_v_carry_out(c_bit0, s1)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1522, 81])).
% 13.10/13.29 tff(1524,plain,
% 13.10/13.29 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s1)) | m_counter_cell_v_carry_in(c_bit1, s1))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s1)) | m_counter_cell_v_carry_in(c_bit1, s1))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1525,plain,
% 13.10/13.29 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s1)) | m_counter_cell_v_carry_in(c_bit1, s1))),
% 13.10/13.29 inference(quant_inst,[status(thm)],[])).
% 13.10/13.29 tff(1526,plain,
% 13.10/13.29 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s1)) | m_counter_cell_v_carry_in(c_bit1, s1)),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1525, 1524])).
% 13.10/13.29 tff(1527,plain,
% 13.10/13.29 (m_counter_cell_v_carry_in(c_bit1, s1)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1526, 1405, 1523])).
% 13.10/13.29 tff(1528,plain,
% 13.10/13.29 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (m_counter_cell_v_value(c_bit1, s1) | (~node1(c_bit1, s1)) | (~m_counter_cell_v_carry_in(c_bit1, s1)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | m_counter_cell_v_value(c_bit1, s1) | (~node1(c_bit1, s1)) | (~m_counter_cell_v_carry_in(c_bit1, s1)))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1529,plain,
% 13.10/13.29 (((~node1(c_bit1, s1)) | (~m_counter_cell_v_carry_in(c_bit1, s1)) | m_counter_cell_v_value(c_bit1, s1)) <=> (m_counter_cell_v_value(c_bit1, s1) | (~node1(c_bit1, s1)) | (~m_counter_cell_v_carry_in(c_bit1, s1)))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1530,plain,
% 13.10/13.29 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s1)) | (~m_counter_cell_v_carry_in(c_bit1, s1)) | m_counter_cell_v_value(c_bit1, s1))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (m_counter_cell_v_value(c_bit1, s1) | (~node1(c_bit1, s1)) | (~m_counter_cell_v_carry_in(c_bit1, s1))))),
% 13.10/13.29 inference(monotonicity,[status(thm)],[1529])).
% 13.10/13.29 tff(1531,plain,
% 13.10/13.29 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s1)) | (~m_counter_cell_v_carry_in(c_bit1, s1)) | m_counter_cell_v_value(c_bit1, s1))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | m_counter_cell_v_value(c_bit1, s1) | (~node1(c_bit1, s1)) | (~m_counter_cell_v_carry_in(c_bit1, s1)))),
% 13.10/13.29 inference(transitivity,[status(thm)],[1530, 1528])).
% 13.10/13.29 tff(1532,plain,
% 13.10/13.29 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s1)) | (~m_counter_cell_v_carry_in(c_bit1, s1)) | m_counter_cell_v_value(c_bit1, s1))),
% 13.10/13.29 inference(quant_inst,[status(thm)],[])).
% 13.10/13.29 tff(1533,plain,
% 13.10/13.29 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | m_counter_cell_v_value(c_bit1, s1) | (~node1(c_bit1, s1)) | (~m_counter_cell_v_carry_in(c_bit1, s1))),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1532, 1531])).
% 13.10/13.29 tff(1534,plain,
% 13.10/13.29 (m_counter_cell_v_value(c_bit1, s1) | (~node1(c_bit1, s1))),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1533, 30, 1527])).
% 13.10/13.29 tff(1535,plain,
% 13.10/13.29 (~node1(c_bit1, s1)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1534, 1518])).
% 13.10/13.29 tff(1536,plain,
% 13.10/13.29 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s1, s2)) | node3(c_bit1, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s1, s2)) | node3(c_bit1, s1, s2))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1537,plain,
% 13.10/13.29 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s1, s2)) | node3(c_bit1, s1, s2))),
% 13.10/13.29 inference(quant_inst,[status(thm)],[])).
% 13.10/13.29 tff(1538,plain,
% 13.10/13.29 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s1, s2)) | node3(c_bit1, s1, s2)),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1537, 1536])).
% 13.10/13.29 tff(1539,plain,
% 13.10/13.29 (node3(c_bit1, s1, s2)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1538, 59, 106])).
% 13.10/13.29 tff(1540,plain,
% 13.10/13.29 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s2) | node1(c_bit1, s1) | (~node3(c_bit1, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s2) | node1(c_bit1, s1) | (~node3(c_bit1, s1, s2)))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1541,plain,
% 13.10/13.29 ((node1(c_bit1, s1) | (~node3(c_bit1, s1, s2)) | m_counter_cell_v_value(c_bit1, s2)) <=> (m_counter_cell_v_value(c_bit1, s2) | node1(c_bit1, s1) | (~node3(c_bit1, s1, s2)))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1542,plain,
% 13.10/13.29 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s1) | (~node3(c_bit1, s1, s2)) | m_counter_cell_v_value(c_bit1, s2))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s2) | node1(c_bit1, s1) | (~node3(c_bit1, s1, s2))))),
% 13.10/13.29 inference(monotonicity,[status(thm)],[1541])).
% 13.10/13.29 tff(1543,plain,
% 13.10/13.29 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s1) | (~node3(c_bit1, s1, s2)) | m_counter_cell_v_value(c_bit1, s2))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s2) | node1(c_bit1, s1) | (~node3(c_bit1, s1, s2)))),
% 13.10/13.29 inference(transitivity,[status(thm)],[1542, 1540])).
% 13.10/13.29 tff(1544,plain,
% 13.10/13.29 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s1) | (~node3(c_bit1, s1, s2)) | m_counter_cell_v_value(c_bit1, s2))),
% 13.10/13.29 inference(quant_inst,[status(thm)],[])).
% 13.10/13.29 tff(1545,plain,
% 13.10/13.29 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s2) | node1(c_bit1, s1) | (~node3(c_bit1, s1, s2))),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1544, 1543])).
% 13.10/13.29 tff(1546,plain,
% 13.10/13.29 (m_counter_cell_v_value(c_bit1, s2) | node1(c_bit1, s1)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1545, 73, 1539])).
% 13.10/13.29 tff(1547,plain,
% 13.10/13.29 (m_counter_cell_v_value(c_bit1, s2)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1546, 1535])).
% 13.10/13.29 tff(1548,plain,
% 13.10/13.29 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s2) | (~node4(c_bit0, s2)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s2) | (~node4(c_bit0, s2)))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1549,plain,
% 13.10/13.29 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s2) | (~node4(c_bit0, s2)))),
% 13.10/13.29 inference(quant_inst,[status(thm)],[])).
% 13.10/13.29 tff(1550,plain,
% 13.10/13.29 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s2) | (~node4(c_bit0, s2))),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1549, 1548])).
% 13.10/13.29 tff(1551,plain,
% 13.10/13.29 (~node4(c_bit0, s2)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1550, 1344, 129])).
% 13.10/13.29 tff(1552,plain,
% 13.10/13.29 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s2)) | node4(c_bit0, s2))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s2)) | node4(c_bit0, s2))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1553,plain,
% 13.10/13.29 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s2)) | node4(c_bit0, s2))),
% 13.10/13.29 inference(quant_inst,[status(thm)],[])).
% 13.10/13.29 tff(1554,plain,
% 13.10/13.29 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s2)) | node4(c_bit0, s2)),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1553, 1552])).
% 13.10/13.29 tff(1555,plain,
% 13.10/13.29 (~m_counter_cell_v_carry_out(c_bit0, s2)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1554, 1359, 1551])).
% 13.10/13.29 tff(1556,plain,
% 13.10/13.29 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s2)) | m_counter_cell_v_carry_out(c_bit0, s2))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s2)) | m_counter_cell_v_carry_out(c_bit0, s2))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1557,plain,
% 13.10/13.29 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s2)) | m_counter_cell_v_carry_out(c_bit0, s2))),
% 13.10/13.29 inference(quant_inst,[status(thm)],[])).
% 13.10/13.29 tff(1558,plain,
% 13.10/13.29 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s2)) | m_counter_cell_v_carry_out(c_bit0, s2)),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1557, 1556])).
% 13.10/13.29 tff(1559,plain,
% 13.10/13.29 (~m_counter_cell_v_carry_in(c_bit1, s2)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1558, 1374, 1555])).
% 13.10/13.29 tff(1560,plain,
% 13.10/13.29 (^[I0: $i, X: $i] : refl(((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X))) <=> ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X))))),
% 13.10/13.29 inference(bind,[status(th)],[])).
% 13.10/13.29 tff(1561,plain,
% 13.10/13.29 (![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X))) <=> ![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))),
% 13.10/13.29 inference(quant_intro,[status(thm)],[1560])).
% 13.10/13.29 tff(1562,plain,
% 13.10/13.29 (![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X))) <=> ![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1563,plain,
% 13.10/13.29 (^[I0: $i, X: $i] : rewrite((((~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_in(I0, X)) | (~node1(I0, X))) <=> ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X))))),
% 13.10/13.29 inference(bind,[status(th)],[])).
% 13.10/13.29 tff(1564,plain,
% 13.10/13.29 (![I0: $i, X: $i] : (((~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_in(I0, X)) | (~node1(I0, X))) <=> ![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))),
% 13.10/13.29 inference(quant_intro,[status(thm)],[1563])).
% 13.10/13.29 tff(1565,axiom,(![I0: $i, X: $i] : (((~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_in(I0, X)) | (~node1(I0, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_counter_cell_3')).
% 13.10/13.29 tff(1566,plain,
% 13.10/13.29 (![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1565, 1564])).
% 13.10/13.29 tff(1567,plain,
% 13.10/13.29 (![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1566, 1562])).
% 13.10/13.29 tff(1568,plain,(
% 13.10/13.29 ![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))),
% 13.10/13.29 inference(skolemize,[status(sab)],[1567])).
% 13.10/13.29 tff(1569,plain,
% 13.10/13.29 (![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1568, 1561])).
% 13.10/13.29 tff(1570,plain,
% 13.10/13.29 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s2) | (~node1(c_bit1, s2)) | (~m_counter_cell_v_value(c_bit1, s2)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s2) | (~node1(c_bit1, s2)) | (~m_counter_cell_v_value(c_bit1, s2)))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1571,plain,
% 13.10/13.29 (((~node1(c_bit1, s2)) | m_counter_cell_v_carry_in(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s2))) <=> (m_counter_cell_v_carry_in(c_bit1, s2) | (~node1(c_bit1, s2)) | (~m_counter_cell_v_value(c_bit1, s2)))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1572,plain,
% 13.10/13.29 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s2)) | m_counter_cell_v_carry_in(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s2)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s2) | (~node1(c_bit1, s2)) | (~m_counter_cell_v_value(c_bit1, s2))))),
% 13.10/13.29 inference(monotonicity,[status(thm)],[1571])).
% 13.10/13.29 tff(1573,plain,
% 13.10/13.29 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s2)) | m_counter_cell_v_carry_in(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s2)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s2) | (~node1(c_bit1, s2)) | (~m_counter_cell_v_value(c_bit1, s2)))),
% 13.10/13.29 inference(transitivity,[status(thm)],[1572, 1570])).
% 13.10/13.29 tff(1574,plain,
% 13.10/13.29 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s2)) | m_counter_cell_v_carry_in(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s2)))),
% 13.10/13.29 inference(quant_inst,[status(thm)],[])).
% 13.10/13.29 tff(1575,plain,
% 13.10/13.29 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s2) | (~node1(c_bit1, s2)) | (~m_counter_cell_v_value(c_bit1, s2))),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1574, 1573])).
% 13.10/13.29 tff(1576,plain,
% 13.10/13.29 ((~node1(c_bit1, s2)) | (~m_counter_cell_v_value(c_bit1, s2))),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1575, 1569, 1559])).
% 13.10/13.29 tff(1577,plain,
% 13.10/13.29 (~node1(c_bit1, s2)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1576, 1547])).
% 13.10/13.29 tff(1578,plain,
% 13.10/13.29 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s2, s3)) | node3(c_bit1, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s2, s3)) | node3(c_bit1, s2, s3))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1579,plain,
% 13.10/13.29 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s2, s3)) | node3(c_bit1, s2, s3))),
% 13.10/13.29 inference(quant_inst,[status(thm)],[])).
% 13.10/13.29 tff(1580,plain,
% 13.10/13.29 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s2, s3)) | node3(c_bit1, s2, s3)),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1579, 1578])).
% 13.10/13.29 tff(1581,plain,
% 13.10/13.29 (node3(c_bit1, s2, s3)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1580, 59, 143])).
% 13.10/13.29 tff(1582,plain,
% 13.10/13.29 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | ((~node3(c_bit1, s2, s3)) | node1(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s3))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (~node3(c_bit1, s2, s3)) | node1(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s3))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1583,plain,
% 13.10/13.29 ((node1(c_bit1, s2) | (~node3(c_bit1, s2, s3)) | m_counter_cell_v_value(c_bit1, s3)) <=> ((~node3(c_bit1, s2, s3)) | node1(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s3))),
% 13.10/13.29 inference(rewrite,[status(thm)],[])).
% 13.10/13.29 tff(1584,plain,
% 13.10/13.29 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s2) | (~node3(c_bit1, s2, s3)) | m_counter_cell_v_value(c_bit1, s3))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | ((~node3(c_bit1, s2, s3)) | node1(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s3)))),
% 13.10/13.29 inference(monotonicity,[status(thm)],[1583])).
% 13.10/13.29 tff(1585,plain,
% 13.10/13.29 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s2) | (~node3(c_bit1, s2, s3)) | m_counter_cell_v_value(c_bit1, s3))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (~node3(c_bit1, s2, s3)) | node1(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s3))),
% 13.10/13.29 inference(transitivity,[status(thm)],[1584, 1582])).
% 13.10/13.29 tff(1586,plain,
% 13.10/13.29 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s2) | (~node3(c_bit1, s2, s3)) | m_counter_cell_v_value(c_bit1, s3))),
% 13.10/13.29 inference(quant_inst,[status(thm)],[])).
% 13.10/13.29 tff(1587,plain,
% 13.10/13.29 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (~node3(c_bit1, s2, s3)) | node1(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s3)),
% 13.10/13.29 inference(modus_ponens,[status(thm)],[1586, 1585])).
% 13.10/13.29 tff(1588,plain,
% 13.10/13.29 (node1(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s3)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1587, 73, 1581])).
% 13.10/13.29 tff(1589,plain,
% 13.10/13.29 (m_counter_cell_v_value(c_bit1, s3)),
% 13.10/13.29 inference(unit_resolution,[status(thm)],[1588, 1577])).
% 13.10/13.29 tff(1590,plain,
% 13.10/13.29 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s3)) | (~m_counter_cell_v_value(c_bit0, s3)) | m_counter_cell_v_carry_out(c_bit0, s3))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s3)) | (~m_counter_cell_v_value(c_bit0, s3)) | m_counter_cell_v_carry_out(c_bit0, s3))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1591,plain,
% 13.10/13.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s3)) | (~m_counter_cell_v_value(c_bit0, s3)) | m_counter_cell_v_carry_out(c_bit0, s3))),
% 13.10/13.30 inference(quant_inst,[status(thm)],[])).
% 13.10/13.30 tff(1592,plain,
% 13.10/13.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s3)) | (~m_counter_cell_v_value(c_bit0, s3)) | m_counter_cell_v_carry_out(c_bit0, s3)),
% 13.10/13.30 inference(modus_ponens,[status(thm)],[1591, 1590])).
% 13.10/13.30 tff(1593,plain,
% 13.10/13.30 ((~m_counter_cell_v_value(c_bit0, s3)) | m_counter_cell_v_carry_out(c_bit0, s3)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1592, 1390, 157])).
% 13.10/13.30 tff(1594,plain,
% 13.10/13.30 (m_counter_cell_v_carry_out(c_bit0, s3)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1593, 155])).
% 13.10/13.30 tff(1595,plain,
% 13.10/13.30 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s3)) | m_counter_cell_v_carry_in(c_bit1, s3))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s3)) | m_counter_cell_v_carry_in(c_bit1, s3))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1596,plain,
% 13.10/13.30 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s3)) | m_counter_cell_v_carry_in(c_bit1, s3))),
% 13.10/13.30 inference(quant_inst,[status(thm)],[])).
% 13.10/13.30 tff(1597,plain,
% 13.10/13.30 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s3)) | m_counter_cell_v_carry_in(c_bit1, s3)),
% 13.10/13.30 inference(modus_ponens,[status(thm)],[1596, 1595])).
% 13.10/13.30 tff(1598,plain,
% 13.10/13.30 (m_counter_cell_v_carry_in(c_bit1, s3)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1597, 1405, 1594])).
% 13.10/13.30 tff(1599,plain,
% 13.10/13.30 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s3)) | (~m_counter_cell_v_value(c_bit1, s3)) | (~node2(c_bit1, s3)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s3)) | (~m_counter_cell_v_value(c_bit1, s3)) | (~node2(c_bit1, s3)))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1600,plain,
% 13.10/13.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s3)) | (~m_counter_cell_v_value(c_bit1, s3)) | (~node2(c_bit1, s3)))),
% 13.10/13.30 inference(quant_inst,[status(thm)],[])).
% 13.10/13.30 tff(1601,plain,
% 13.10/13.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s3)) | (~m_counter_cell_v_value(c_bit1, s3)) | (~node2(c_bit1, s3))),
% 13.10/13.30 inference(modus_ponens,[status(thm)],[1600, 1599])).
% 13.10/13.30 tff(1602,plain,
% 13.10/13.30 ((~m_counter_cell_v_value(c_bit1, s3)) | (~node2(c_bit1, s3))),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1601, 93, 1598])).
% 13.10/13.30 tff(1603,plain,
% 13.10/13.30 (~node2(c_bit1, s3)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1602, 1589])).
% 13.10/13.30 tff(1604,plain,
% 13.10/13.30 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s3, s4)) | node3(c_bit1, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s3, s4)) | node3(c_bit1, s3, s4))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1605,plain,
% 13.10/13.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s3, s4)) | node3(c_bit1, s3, s4))),
% 13.10/13.30 inference(quant_inst,[status(thm)],[])).
% 13.10/13.30 tff(1606,plain,
% 13.10/13.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s3, s4)) | node3(c_bit1, s3, s4)),
% 13.10/13.30 inference(modus_ponens,[status(thm)],[1605, 1604])).
% 13.10/13.30 tff(1607,plain,
% 13.10/13.30 (node3(c_bit1, s3, s4)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1606, 59, 169])).
% 13.10/13.30 tff(1608,plain,
% 13.10/13.30 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~node3(c_bit1, s3, s4)) | (~m_counter_cell_v_value(c_bit1, s4)) | node2(c_bit1, s3))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~node3(c_bit1, s3, s4)) | (~m_counter_cell_v_value(c_bit1, s4)) | node2(c_bit1, s3))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1609,plain,
% 13.10/13.30 ((node2(c_bit1, s3) | (~node3(c_bit1, s3, s4)) | (~m_counter_cell_v_value(c_bit1, s4))) <=> ((~node3(c_bit1, s3, s4)) | (~m_counter_cell_v_value(c_bit1, s4)) | node2(c_bit1, s3))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1610,plain,
% 13.10/13.30 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s3) | (~node3(c_bit1, s3, s4)) | (~m_counter_cell_v_value(c_bit1, s4)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~node3(c_bit1, s3, s4)) | (~m_counter_cell_v_value(c_bit1, s4)) | node2(c_bit1, s3)))),
% 13.10/13.30 inference(monotonicity,[status(thm)],[1609])).
% 13.10/13.30 tff(1611,plain,
% 13.10/13.30 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s3) | (~node3(c_bit1, s3, s4)) | (~m_counter_cell_v_value(c_bit1, s4)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~node3(c_bit1, s3, s4)) | (~m_counter_cell_v_value(c_bit1, s4)) | node2(c_bit1, s3))),
% 13.10/13.30 inference(transitivity,[status(thm)],[1610, 1608])).
% 13.10/13.30 tff(1612,plain,
% 13.10/13.30 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s3) | (~node3(c_bit1, s3, s4)) | (~m_counter_cell_v_value(c_bit1, s4)))),
% 13.10/13.30 inference(quant_inst,[status(thm)],[])).
% 13.10/13.30 tff(1613,plain,
% 13.10/13.30 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~node3(c_bit1, s3, s4)) | (~m_counter_cell_v_value(c_bit1, s4)) | node2(c_bit1, s3)),
% 13.10/13.30 inference(modus_ponens,[status(thm)],[1612, 1611])).
% 13.10/13.30 tff(1614,plain,
% 13.10/13.30 ((~m_counter_cell_v_value(c_bit1, s4)) | node2(c_bit1, s3)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1613, 121, 1607])).
% 13.10/13.30 tff(1615,plain,
% 13.10/13.30 (~m_counter_cell_v_value(c_bit1, s4)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1614, 1603])).
% 13.10/13.30 tff(1616,plain,
% 13.10/13.30 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s4) | (~node4(c_bit0, s4)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s4) | (~node4(c_bit0, s4)))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1617,plain,
% 13.10/13.30 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s4) | (~node4(c_bit0, s4)))),
% 13.10/13.30 inference(quant_inst,[status(thm)],[])).
% 13.10/13.30 tff(1618,plain,
% 13.10/13.30 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s4) | (~node4(c_bit0, s4))),
% 13.10/13.30 inference(modus_ponens,[status(thm)],[1617, 1616])).
% 13.10/13.30 tff(1619,plain,
% 13.10/13.30 (~node4(c_bit0, s4)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1618, 1344, 181])).
% 13.10/13.30 tff(1620,plain,
% 13.10/13.30 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s4)) | node4(c_bit0, s4))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s4)) | node4(c_bit0, s4))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1621,plain,
% 13.10/13.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s4)) | node4(c_bit0, s4))),
% 13.10/13.30 inference(quant_inst,[status(thm)],[])).
% 13.10/13.30 tff(1622,plain,
% 13.10/13.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s4)) | node4(c_bit0, s4)),
% 13.10/13.30 inference(modus_ponens,[status(thm)],[1621, 1620])).
% 13.10/13.30 tff(1623,plain,
% 13.10/13.30 (~m_counter_cell_v_carry_out(c_bit0, s4)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1622, 1359, 1619])).
% 13.10/13.30 tff(1624,plain,
% 13.10/13.30 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s4)) | m_counter_cell_v_carry_out(c_bit0, s4))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s4)) | m_counter_cell_v_carry_out(c_bit0, s4))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1625,plain,
% 13.10/13.30 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s4)) | m_counter_cell_v_carry_out(c_bit0, s4))),
% 13.10/13.30 inference(quant_inst,[status(thm)],[])).
% 13.10/13.30 tff(1626,plain,
% 13.10/13.30 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s4)) | m_counter_cell_v_carry_out(c_bit0, s4)),
% 13.10/13.30 inference(modus_ponens,[status(thm)],[1625, 1624])).
% 13.10/13.30 tff(1627,plain,
% 13.10/13.30 (~m_counter_cell_v_carry_in(c_bit1, s4)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1626, 1374, 1623])).
% 13.10/13.30 tff(1628,plain,
% 13.10/13.30 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s4) | m_counter_cell_v_value(c_bit1, s4) | (~node2(c_bit1, s4)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s4) | m_counter_cell_v_value(c_bit1, s4) | (~node2(c_bit1, s4)))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1629,plain,
% 13.10/13.30 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s4) | m_counter_cell_v_value(c_bit1, s4) | (~node2(c_bit1, s4)))),
% 13.10/13.30 inference(quant_inst,[status(thm)],[])).
% 13.10/13.30 tff(1630,plain,
% 13.10/13.30 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s4) | m_counter_cell_v_value(c_bit1, s4) | (~node2(c_bit1, s4))),
% 13.10/13.30 inference(modus_ponens,[status(thm)],[1629, 1628])).
% 13.10/13.30 tff(1631,plain,
% 13.10/13.30 (m_counter_cell_v_value(c_bit1, s4) | (~node2(c_bit1, s4))),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1630, 1498, 1627])).
% 13.10/13.30 tff(1632,plain,
% 13.10/13.30 (~node2(c_bit1, s4)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1631, 1615])).
% 13.10/13.30 tff(1633,plain,
% 13.10/13.30 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s4, s5)) | node3(c_bit1, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s4, s5)) | node3(c_bit1, s4, s5))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1634,plain,
% 13.10/13.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s4, s5)) | node3(c_bit1, s4, s5))),
% 13.10/13.30 inference(quant_inst,[status(thm)],[])).
% 13.10/13.30 tff(1635,plain,
% 13.10/13.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s4, s5)) | node3(c_bit1, s4, s5)),
% 13.10/13.30 inference(modus_ponens,[status(thm)],[1634, 1633])).
% 13.10/13.30 tff(1636,plain,
% 13.10/13.30 (node3(c_bit1, s4, s5)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1635, 59, 198])).
% 13.10/13.30 tff(1637,plain,
% 13.10/13.30 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s5)) | (~node3(c_bit1, s4, s5)) | node2(c_bit1, s4))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s5)) | (~node3(c_bit1, s4, s5)) | node2(c_bit1, s4))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1638,plain,
% 13.10/13.30 ((node2(c_bit1, s4) | (~node3(c_bit1, s4, s5)) | (~m_counter_cell_v_value(c_bit1, s5))) <=> ((~m_counter_cell_v_value(c_bit1, s5)) | (~node3(c_bit1, s4, s5)) | node2(c_bit1, s4))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1639,plain,
% 13.10/13.30 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s4) | (~node3(c_bit1, s4, s5)) | (~m_counter_cell_v_value(c_bit1, s5)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s5)) | (~node3(c_bit1, s4, s5)) | node2(c_bit1, s4)))),
% 13.10/13.30 inference(monotonicity,[status(thm)],[1638])).
% 13.10/13.30 tff(1640,plain,
% 13.10/13.30 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s4) | (~node3(c_bit1, s4, s5)) | (~m_counter_cell_v_value(c_bit1, s5)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s5)) | (~node3(c_bit1, s4, s5)) | node2(c_bit1, s4))),
% 13.10/13.30 inference(transitivity,[status(thm)],[1639, 1637])).
% 13.10/13.30 tff(1641,plain,
% 13.10/13.30 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s4) | (~node3(c_bit1, s4, s5)) | (~m_counter_cell_v_value(c_bit1, s5)))),
% 13.10/13.30 inference(quant_inst,[status(thm)],[])).
% 13.10/13.30 tff(1642,plain,
% 13.10/13.30 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s5)) | (~node3(c_bit1, s4, s5)) | node2(c_bit1, s4)),
% 13.10/13.30 inference(modus_ponens,[status(thm)],[1641, 1640])).
% 13.10/13.30 tff(1643,plain,
% 13.10/13.30 ((~m_counter_cell_v_value(c_bit1, s5)) | node2(c_bit1, s4)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1642, 121, 1636])).
% 13.10/13.30 tff(1644,plain,
% 13.10/13.30 (~m_counter_cell_v_value(c_bit1, s5)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1643, 1632])).
% 13.10/13.30 tff(1645,plain,
% 13.10/13.30 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s5)) | (~m_counter_cell_v_value(c_bit0, s5)) | m_counter_cell_v_carry_out(c_bit0, s5))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s5)) | (~m_counter_cell_v_value(c_bit0, s5)) | m_counter_cell_v_carry_out(c_bit0, s5))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1646,plain,
% 13.10/13.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s5)) | (~m_counter_cell_v_value(c_bit0, s5)) | m_counter_cell_v_carry_out(c_bit0, s5))),
% 13.10/13.30 inference(quant_inst,[status(thm)],[])).
% 13.10/13.30 tff(1647,plain,
% 13.10/13.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s5)) | (~m_counter_cell_v_value(c_bit0, s5)) | m_counter_cell_v_carry_out(c_bit0, s5)),
% 13.10/13.30 inference(modus_ponens,[status(thm)],[1646, 1645])).
% 13.10/13.30 tff(1648,plain,
% 13.10/13.30 ((~m_counter_cell_v_value(c_bit0, s5)) | m_counter_cell_v_carry_out(c_bit0, s5)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1647, 1390, 212])).
% 13.10/13.30 tff(1649,plain,
% 13.10/13.30 (m_counter_cell_v_carry_out(c_bit0, s5)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1648, 210])).
% 13.10/13.30 tff(1650,plain,
% 13.10/13.30 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s5)) | m_counter_cell_v_carry_in(c_bit1, s5))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s5)) | m_counter_cell_v_carry_in(c_bit1, s5))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1651,plain,
% 13.10/13.30 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s5)) | m_counter_cell_v_carry_in(c_bit1, s5))),
% 13.10/13.30 inference(quant_inst,[status(thm)],[])).
% 13.10/13.30 tff(1652,plain,
% 13.10/13.30 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s5)) | m_counter_cell_v_carry_in(c_bit1, s5)),
% 13.10/13.30 inference(modus_ponens,[status(thm)],[1651, 1650])).
% 13.10/13.30 tff(1653,plain,
% 13.10/13.30 (m_counter_cell_v_carry_in(c_bit1, s5)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1652, 1405, 1649])).
% 13.10/13.30 tff(1654,plain,
% 13.10/13.30 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s5)) | (~node1(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s5)) | (~node1(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1655,plain,
% 13.10/13.30 (((~node1(c_bit1, s5)) | (~m_counter_cell_v_carry_in(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s5)) | (~node1(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1656,plain,
% 13.10/13.30 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s5)) | (~m_counter_cell_v_carry_in(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s5)) | (~node1(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5)))),
% 13.10/13.30 inference(monotonicity,[status(thm)],[1655])).
% 13.10/13.30 tff(1657,plain,
% 13.10/13.30 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s5)) | (~m_counter_cell_v_carry_in(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s5)) | (~node1(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5))),
% 13.10/13.30 inference(transitivity,[status(thm)],[1656, 1654])).
% 13.10/13.30 tff(1658,plain,
% 13.10/13.30 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s5)) | (~m_counter_cell_v_carry_in(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5))),
% 13.10/13.30 inference(quant_inst,[status(thm)],[])).
% 13.10/13.30 tff(1659,plain,
% 13.10/13.30 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s5)) | (~node1(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5)),
% 13.10/13.30 inference(modus_ponens,[status(thm)],[1658, 1657])).
% 13.10/13.30 tff(1660,plain,
% 13.10/13.30 ((~node1(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1659, 30, 1653])).
% 13.10/13.30 tff(1661,plain,
% 13.10/13.30 (~node1(c_bit1, s5)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1660, 1644])).
% 13.10/13.30 tff(1662,plain,
% 13.10/13.30 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s5, s6)) | node3(c_bit1, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s5, s6)) | node3(c_bit1, s5, s6))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1663,plain,
% 13.10/13.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s5, s6)) | node3(c_bit1, s5, s6))),
% 13.10/13.30 inference(quant_inst,[status(thm)],[])).
% 13.10/13.30 tff(1664,plain,
% 13.10/13.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s5, s6)) | node3(c_bit1, s5, s6)),
% 13.10/13.30 inference(modus_ponens,[status(thm)],[1663, 1662])).
% 13.10/13.30 tff(1665,plain,
% 13.10/13.30 (node3(c_bit1, s5, s6)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1664, 59, 224])).
% 13.10/13.30 tff(1666,plain,
% 13.10/13.30 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s5) | m_counter_cell_v_value(c_bit1, s6) | (~node3(c_bit1, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit1, s5) | m_counter_cell_v_value(c_bit1, s6) | (~node3(c_bit1, s5, s6)))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1667,plain,
% 13.10/13.30 ((node1(c_bit1, s5) | (~node3(c_bit1, s5, s6)) | m_counter_cell_v_value(c_bit1, s6)) <=> (node1(c_bit1, s5) | m_counter_cell_v_value(c_bit1, s6) | (~node3(c_bit1, s5, s6)))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1668,plain,
% 13.10/13.30 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s5) | (~node3(c_bit1, s5, s6)) | m_counter_cell_v_value(c_bit1, s6))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s5) | m_counter_cell_v_value(c_bit1, s6) | (~node3(c_bit1, s5, s6))))),
% 13.10/13.30 inference(monotonicity,[status(thm)],[1667])).
% 13.10/13.30 tff(1669,plain,
% 13.10/13.30 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s5) | (~node3(c_bit1, s5, s6)) | m_counter_cell_v_value(c_bit1, s6))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit1, s5) | m_counter_cell_v_value(c_bit1, s6) | (~node3(c_bit1, s5, s6)))),
% 13.10/13.30 inference(transitivity,[status(thm)],[1668, 1666])).
% 13.10/13.30 tff(1670,plain,
% 13.10/13.30 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s5) | (~node3(c_bit1, s5, s6)) | m_counter_cell_v_value(c_bit1, s6))),
% 13.10/13.30 inference(quant_inst,[status(thm)],[])).
% 13.10/13.30 tff(1671,plain,
% 13.10/13.30 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit1, s5) | m_counter_cell_v_value(c_bit1, s6) | (~node3(c_bit1, s5, s6))),
% 13.10/13.30 inference(modus_ponens,[status(thm)],[1670, 1669])).
% 13.10/13.30 tff(1672,plain,
% 13.10/13.30 (node1(c_bit1, s5) | m_counter_cell_v_value(c_bit1, s6)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1671, 73, 1665])).
% 13.10/13.30 tff(1673,plain,
% 13.10/13.30 (m_counter_cell_v_value(c_bit1, s6)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1672, 1661])).
% 13.10/13.30 tff(1674,plain,
% 13.10/13.30 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s6) | (~node4(c_bit0, s6)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s6) | (~node4(c_bit0, s6)))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1675,plain,
% 13.10/13.30 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s6) | (~node4(c_bit0, s6)))),
% 13.10/13.30 inference(quant_inst,[status(thm)],[])).
% 13.10/13.30 tff(1676,plain,
% 13.10/13.30 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s6) | (~node4(c_bit0, s6))),
% 13.10/13.30 inference(modus_ponens,[status(thm)],[1675, 1674])).
% 13.10/13.30 tff(1677,plain,
% 13.10/13.30 (~node4(c_bit0, s6)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1676, 1344, 236])).
% 13.10/13.30 tff(1678,plain,
% 13.10/13.30 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s6)) | node4(c_bit0, s6))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s6)) | node4(c_bit0, s6))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1679,plain,
% 13.10/13.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s6)) | node4(c_bit0, s6))),
% 13.10/13.30 inference(quant_inst,[status(thm)],[])).
% 13.10/13.30 tff(1680,plain,
% 13.10/13.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s6)) | node4(c_bit0, s6)),
% 13.10/13.30 inference(modus_ponens,[status(thm)],[1679, 1678])).
% 13.10/13.30 tff(1681,plain,
% 13.10/13.30 (~m_counter_cell_v_carry_out(c_bit0, s6)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1680, 1359, 1677])).
% 13.10/13.30 tff(1682,plain,
% 13.10/13.30 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s6)) | m_counter_cell_v_carry_out(c_bit0, s6))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s6)) | m_counter_cell_v_carry_out(c_bit0, s6))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1683,plain,
% 13.10/13.30 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s6)) | m_counter_cell_v_carry_out(c_bit0, s6))),
% 13.10/13.30 inference(quant_inst,[status(thm)],[])).
% 13.10/13.30 tff(1684,plain,
% 13.10/13.30 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s6)) | m_counter_cell_v_carry_out(c_bit0, s6)),
% 13.10/13.30 inference(modus_ponens,[status(thm)],[1683, 1682])).
% 13.10/13.30 tff(1685,plain,
% 13.10/13.30 (~m_counter_cell_v_carry_in(c_bit1, s6)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1684, 1374, 1681])).
% 13.10/13.30 tff(1686,plain,
% 13.10/13.30 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s6) | (~node1(c_bit1, s6)) | (~m_counter_cell_v_value(c_bit1, s6)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s6) | (~node1(c_bit1, s6)) | (~m_counter_cell_v_value(c_bit1, s6)))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1687,plain,
% 13.10/13.30 (((~node1(c_bit1, s6)) | m_counter_cell_v_carry_in(c_bit1, s6) | (~m_counter_cell_v_value(c_bit1, s6))) <=> (m_counter_cell_v_carry_in(c_bit1, s6) | (~node1(c_bit1, s6)) | (~m_counter_cell_v_value(c_bit1, s6)))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1688,plain,
% 13.10/13.30 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s6)) | m_counter_cell_v_carry_in(c_bit1, s6) | (~m_counter_cell_v_value(c_bit1, s6)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s6) | (~node1(c_bit1, s6)) | (~m_counter_cell_v_value(c_bit1, s6))))),
% 13.10/13.30 inference(monotonicity,[status(thm)],[1687])).
% 13.10/13.30 tff(1689,plain,
% 13.10/13.30 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s6)) | m_counter_cell_v_carry_in(c_bit1, s6) | (~m_counter_cell_v_value(c_bit1, s6)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s6) | (~node1(c_bit1, s6)) | (~m_counter_cell_v_value(c_bit1, s6)))),
% 13.10/13.30 inference(transitivity,[status(thm)],[1688, 1686])).
% 13.10/13.30 tff(1690,plain,
% 13.10/13.30 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s6)) | m_counter_cell_v_carry_in(c_bit1, s6) | (~m_counter_cell_v_value(c_bit1, s6)))),
% 13.10/13.30 inference(quant_inst,[status(thm)],[])).
% 13.10/13.30 tff(1691,plain,
% 13.10/13.30 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s6) | (~node1(c_bit1, s6)) | (~m_counter_cell_v_value(c_bit1, s6))),
% 13.10/13.30 inference(modus_ponens,[status(thm)],[1690, 1689])).
% 13.10/13.30 tff(1692,plain,
% 13.10/13.30 ((~node1(c_bit1, s6)) | (~m_counter_cell_v_value(c_bit1, s6))),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1691, 1569, 1685])).
% 13.10/13.30 tff(1693,plain,
% 13.10/13.30 (~node1(c_bit1, s6)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1692, 1673])).
% 13.10/13.30 tff(1694,plain,
% 13.10/13.30 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s6, s7)) | node3(c_bit1, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s6, s7)) | node3(c_bit1, s6, s7))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1695,plain,
% 13.10/13.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s6, s7)) | node3(c_bit1, s6, s7))),
% 13.10/13.30 inference(quant_inst,[status(thm)],[])).
% 13.10/13.30 tff(1696,plain,
% 13.10/13.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s6, s7)) | node3(c_bit1, s6, s7)),
% 13.10/13.30 inference(modus_ponens,[status(thm)],[1695, 1694])).
% 13.10/13.30 tff(1697,plain,
% 13.10/13.30 (node3(c_bit1, s6, s7)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1696, 59, 253])).
% 13.10/13.30 tff(1698,plain,
% 13.10/13.30 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s6) | m_counter_cell_v_value(c_bit1, s7) | (~node3(c_bit1, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit1, s6) | m_counter_cell_v_value(c_bit1, s7) | (~node3(c_bit1, s6, s7)))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1699,plain,
% 13.10/13.30 ((node1(c_bit1, s6) | (~node3(c_bit1, s6, s7)) | m_counter_cell_v_value(c_bit1, s7)) <=> (node1(c_bit1, s6) | m_counter_cell_v_value(c_bit1, s7) | (~node3(c_bit1, s6, s7)))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1700,plain,
% 13.10/13.30 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s6) | (~node3(c_bit1, s6, s7)) | m_counter_cell_v_value(c_bit1, s7))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s6) | m_counter_cell_v_value(c_bit1, s7) | (~node3(c_bit1, s6, s7))))),
% 13.10/13.30 inference(monotonicity,[status(thm)],[1699])).
% 13.10/13.30 tff(1701,plain,
% 13.10/13.30 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s6) | (~node3(c_bit1, s6, s7)) | m_counter_cell_v_value(c_bit1, s7))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit1, s6) | m_counter_cell_v_value(c_bit1, s7) | (~node3(c_bit1, s6, s7)))),
% 13.10/13.30 inference(transitivity,[status(thm)],[1700, 1698])).
% 13.10/13.30 tff(1702,plain,
% 13.10/13.30 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s6) | (~node3(c_bit1, s6, s7)) | m_counter_cell_v_value(c_bit1, s7))),
% 13.10/13.30 inference(quant_inst,[status(thm)],[])).
% 13.10/13.30 tff(1703,plain,
% 13.10/13.30 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit1, s6) | m_counter_cell_v_value(c_bit1, s7) | (~node3(c_bit1, s6, s7))),
% 13.10/13.30 inference(modus_ponens,[status(thm)],[1702, 1701])).
% 13.10/13.30 tff(1704,plain,
% 13.10/13.30 (node1(c_bit1, s6) | m_counter_cell_v_value(c_bit1, s7)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1703, 73, 1697])).
% 13.10/13.30 tff(1705,plain,
% 13.10/13.30 (m_counter_cell_v_value(c_bit1, s7)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1704, 1693])).
% 13.10/13.30 tff(1706,plain,
% 13.10/13.30 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s7)) | (~m_counter_cell_v_value(c_bit0, s7)) | m_counter_cell_v_carry_out(c_bit0, s7))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s7)) | (~m_counter_cell_v_value(c_bit0, s7)) | m_counter_cell_v_carry_out(c_bit0, s7))),
% 13.10/13.30 inference(rewrite,[status(thm)],[])).
% 13.10/13.30 tff(1707,plain,
% 13.10/13.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s7)) | (~m_counter_cell_v_value(c_bit0, s7)) | m_counter_cell_v_carry_out(c_bit0, s7))),
% 13.10/13.30 inference(quant_inst,[status(thm)],[])).
% 13.10/13.30 tff(1708,plain,
% 13.10/13.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s7)) | (~m_counter_cell_v_value(c_bit0, s7)) | m_counter_cell_v_carry_out(c_bit0, s7)),
% 13.10/13.30 inference(modus_ponens,[status(thm)],[1707, 1706])).
% 13.10/13.30 tff(1709,plain,
% 13.10/13.30 ((~m_counter_cell_v_value(c_bit0, s7)) | m_counter_cell_v_carry_out(c_bit0, s7)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1708, 1390, 267])).
% 13.10/13.30 tff(1710,plain,
% 13.10/13.30 (m_counter_cell_v_carry_out(c_bit0, s7)),
% 13.10/13.30 inference(unit_resolution,[status(thm)],[1709, 265])).
% 13.10/13.30 tff(1711,plain,
% 13.10/13.30 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s7)) | m_counter_cell_v_carry_in(c_bit1, s7))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s7)) | m_counter_cell_v_carry_in(c_bit1, s7))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1712,plain,
% 13.10/13.31 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s7)) | m_counter_cell_v_carry_in(c_bit1, s7))),
% 13.10/13.31 inference(quant_inst,[status(thm)],[])).
% 13.10/13.31 tff(1713,plain,
% 13.10/13.31 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s7)) | m_counter_cell_v_carry_in(c_bit1, s7)),
% 13.10/13.31 inference(modus_ponens,[status(thm)],[1712, 1711])).
% 13.10/13.31 tff(1714,plain,
% 13.10/13.31 (m_counter_cell_v_carry_in(c_bit1, s7)),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1713, 1405, 1710])).
% 13.10/13.31 tff(1715,plain,
% 13.10/13.31 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s7)) | (~m_counter_cell_v_value(c_bit1, s7)) | (~node2(c_bit1, s7)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s7)) | (~m_counter_cell_v_value(c_bit1, s7)) | (~node2(c_bit1, s7)))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1716,plain,
% 13.10/13.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s7)) | (~m_counter_cell_v_value(c_bit1, s7)) | (~node2(c_bit1, s7)))),
% 13.10/13.31 inference(quant_inst,[status(thm)],[])).
% 13.10/13.31 tff(1717,plain,
% 13.10/13.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s7)) | (~m_counter_cell_v_value(c_bit1, s7)) | (~node2(c_bit1, s7))),
% 13.10/13.31 inference(modus_ponens,[status(thm)],[1716, 1715])).
% 13.10/13.31 tff(1718,plain,
% 13.10/13.31 ((~m_counter_cell_v_value(c_bit1, s7)) | (~node2(c_bit1, s7))),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1717, 93, 1714])).
% 13.10/13.31 tff(1719,plain,
% 13.10/13.31 (~node2(c_bit1, s7)),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1718, 1705])).
% 13.10/13.31 tff(1720,plain,
% 13.10/13.31 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s7, s8)) | node3(c_bit1, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s7, s8)) | node3(c_bit1, s7, s8))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1721,plain,
% 13.10/13.31 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s7, s8)) | node3(c_bit1, s7, s8))),
% 13.10/13.31 inference(quant_inst,[status(thm)],[])).
% 13.10/13.31 tff(1722,plain,
% 13.10/13.31 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s7, s8)) | node3(c_bit1, s7, s8)),
% 13.10/13.31 inference(modus_ponens,[status(thm)],[1721, 1720])).
% 13.10/13.31 tff(1723,plain,
% 13.10/13.31 (node3(c_bit1, s7, s8)),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1722, 59, 279])).
% 13.10/13.31 tff(1724,plain,
% 13.10/13.31 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s8)) | (~node3(c_bit1, s7, s8)) | node2(c_bit1, s7))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s8)) | (~node3(c_bit1, s7, s8)) | node2(c_bit1, s7))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1725,plain,
% 13.10/13.31 ((node2(c_bit1, s7) | (~node3(c_bit1, s7, s8)) | (~m_counter_cell_v_value(c_bit1, s8))) <=> ((~m_counter_cell_v_value(c_bit1, s8)) | (~node3(c_bit1, s7, s8)) | node2(c_bit1, s7))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1726,plain,
% 13.10/13.31 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s7) | (~node3(c_bit1, s7, s8)) | (~m_counter_cell_v_value(c_bit1, s8)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s8)) | (~node3(c_bit1, s7, s8)) | node2(c_bit1, s7)))),
% 13.10/13.31 inference(monotonicity,[status(thm)],[1725])).
% 13.10/13.31 tff(1727,plain,
% 13.10/13.31 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s7) | (~node3(c_bit1, s7, s8)) | (~m_counter_cell_v_value(c_bit1, s8)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s8)) | (~node3(c_bit1, s7, s8)) | node2(c_bit1, s7))),
% 13.10/13.31 inference(transitivity,[status(thm)],[1726, 1724])).
% 13.10/13.31 tff(1728,plain,
% 13.10/13.31 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s7) | (~node3(c_bit1, s7, s8)) | (~m_counter_cell_v_value(c_bit1, s8)))),
% 13.10/13.31 inference(quant_inst,[status(thm)],[])).
% 13.10/13.31 tff(1729,plain,
% 13.10/13.31 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s8)) | (~node3(c_bit1, s7, s8)) | node2(c_bit1, s7)),
% 13.10/13.31 inference(modus_ponens,[status(thm)],[1728, 1727])).
% 13.10/13.31 tff(1730,plain,
% 13.10/13.31 ((~m_counter_cell_v_value(c_bit1, s8)) | node2(c_bit1, s7)),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1729, 121, 1723])).
% 13.10/13.31 tff(1731,plain,
% 13.10/13.31 (~m_counter_cell_v_value(c_bit1, s8)),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1730, 1719])).
% 13.10/13.31 tff(1732,plain,
% 13.10/13.31 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s8) | (~node4(c_bit0, s8)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s8) | (~node4(c_bit0, s8)))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1733,plain,
% 13.10/13.31 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s8) | (~node4(c_bit0, s8)))),
% 13.10/13.31 inference(quant_inst,[status(thm)],[])).
% 13.10/13.31 tff(1734,plain,
% 13.10/13.31 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s8) | (~node4(c_bit0, s8))),
% 13.10/13.31 inference(modus_ponens,[status(thm)],[1733, 1732])).
% 13.10/13.31 tff(1735,plain,
% 13.10/13.31 (~node4(c_bit0, s8)),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1734, 1344, 291])).
% 13.10/13.31 tff(1736,plain,
% 13.10/13.31 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s8)) | node4(c_bit0, s8))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s8)) | node4(c_bit0, s8))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1737,plain,
% 13.10/13.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s8)) | node4(c_bit0, s8))),
% 13.10/13.31 inference(quant_inst,[status(thm)],[])).
% 13.10/13.31 tff(1738,plain,
% 13.10/13.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s8)) | node4(c_bit0, s8)),
% 13.10/13.31 inference(modus_ponens,[status(thm)],[1737, 1736])).
% 13.10/13.31 tff(1739,plain,
% 13.10/13.31 (~m_counter_cell_v_carry_out(c_bit0, s8)),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1738, 1359, 1735])).
% 13.10/13.31 tff(1740,plain,
% 13.10/13.31 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s8)) | m_counter_cell_v_carry_out(c_bit0, s8))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s8)) | m_counter_cell_v_carry_out(c_bit0, s8))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1741,plain,
% 13.10/13.31 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s8)) | m_counter_cell_v_carry_out(c_bit0, s8))),
% 13.10/13.31 inference(quant_inst,[status(thm)],[])).
% 13.10/13.31 tff(1742,plain,
% 13.10/13.31 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s8)) | m_counter_cell_v_carry_out(c_bit0, s8)),
% 13.10/13.31 inference(modus_ponens,[status(thm)],[1741, 1740])).
% 13.10/13.31 tff(1743,plain,
% 13.10/13.31 (~m_counter_cell_v_carry_in(c_bit1, s8)),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1742, 1374, 1739])).
% 13.10/13.31 tff(1744,plain,
% 13.10/13.31 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_value(c_bit1, s8) | (~node2(c_bit1, s8)) | m_counter_cell_v_carry_in(c_bit1, s8))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_value(c_bit1, s8) | (~node2(c_bit1, s8)) | m_counter_cell_v_carry_in(c_bit1, s8))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1745,plain,
% 13.10/13.31 ((m_counter_cell_v_carry_in(c_bit1, s8) | m_counter_cell_v_value(c_bit1, s8) | (~node2(c_bit1, s8))) <=> (m_counter_cell_v_value(c_bit1, s8) | (~node2(c_bit1, s8)) | m_counter_cell_v_carry_in(c_bit1, s8))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1746,plain,
% 13.10/13.31 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s8) | m_counter_cell_v_value(c_bit1, s8) | (~node2(c_bit1, s8)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_value(c_bit1, s8) | (~node2(c_bit1, s8)) | m_counter_cell_v_carry_in(c_bit1, s8)))),
% 13.10/13.31 inference(monotonicity,[status(thm)],[1745])).
% 13.10/13.31 tff(1747,plain,
% 13.10/13.31 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s8) | m_counter_cell_v_value(c_bit1, s8) | (~node2(c_bit1, s8)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_value(c_bit1, s8) | (~node2(c_bit1, s8)) | m_counter_cell_v_carry_in(c_bit1, s8))),
% 13.10/13.31 inference(transitivity,[status(thm)],[1746, 1744])).
% 13.10/13.31 tff(1748,plain,
% 13.10/13.31 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s8) | m_counter_cell_v_value(c_bit1, s8) | (~node2(c_bit1, s8)))),
% 13.10/13.31 inference(quant_inst,[status(thm)],[])).
% 13.10/13.31 tff(1749,plain,
% 13.10/13.31 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_value(c_bit1, s8) | (~node2(c_bit1, s8)) | m_counter_cell_v_carry_in(c_bit1, s8)),
% 13.10/13.31 inference(modus_ponens,[status(thm)],[1748, 1747])).
% 13.10/13.31 tff(1750,plain,
% 13.10/13.31 (m_counter_cell_v_value(c_bit1, s8) | (~node2(c_bit1, s8))),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1749, 1498, 1743])).
% 13.10/13.31 tff(1751,plain,
% 13.10/13.31 (~node2(c_bit1, s8)),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1750, 1731])).
% 13.10/13.31 tff(1752,plain,
% 13.10/13.31 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s8, s9)) | node3(c_bit1, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s8, s9)) | node3(c_bit1, s8, s9))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1753,plain,
% 13.10/13.31 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s8, s9)) | node3(c_bit1, s8, s9))),
% 13.10/13.31 inference(quant_inst,[status(thm)],[])).
% 13.10/13.31 tff(1754,plain,
% 13.10/13.31 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s8, s9)) | node3(c_bit1, s8, s9)),
% 13.10/13.31 inference(modus_ponens,[status(thm)],[1753, 1752])).
% 13.10/13.31 tff(1755,plain,
% 13.10/13.31 (node3(c_bit1, s8, s9)),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1754, 59, 308])).
% 13.10/13.31 tff(1756,plain,
% 13.10/13.31 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s9)) | node2(c_bit1, s8) | (~node3(c_bit1, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s9)) | node2(c_bit1, s8) | (~node3(c_bit1, s8, s9)))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1757,plain,
% 13.10/13.31 ((node2(c_bit1, s8) | (~node3(c_bit1, s8, s9)) | (~m_counter_cell_v_value(c_bit1, s9))) <=> ((~m_counter_cell_v_value(c_bit1, s9)) | node2(c_bit1, s8) | (~node3(c_bit1, s8, s9)))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1758,plain,
% 13.10/13.31 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s8) | (~node3(c_bit1, s8, s9)) | (~m_counter_cell_v_value(c_bit1, s9)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s9)) | node2(c_bit1, s8) | (~node3(c_bit1, s8, s9))))),
% 13.10/13.31 inference(monotonicity,[status(thm)],[1757])).
% 13.10/13.31 tff(1759,plain,
% 13.10/13.31 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s8) | (~node3(c_bit1, s8, s9)) | (~m_counter_cell_v_value(c_bit1, s9)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s9)) | node2(c_bit1, s8) | (~node3(c_bit1, s8, s9)))),
% 13.10/13.31 inference(transitivity,[status(thm)],[1758, 1756])).
% 13.10/13.31 tff(1760,plain,
% 13.10/13.31 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s8) | (~node3(c_bit1, s8, s9)) | (~m_counter_cell_v_value(c_bit1, s9)))),
% 13.10/13.31 inference(quant_inst,[status(thm)],[])).
% 13.10/13.31 tff(1761,plain,
% 13.10/13.31 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s9)) | node2(c_bit1, s8) | (~node3(c_bit1, s8, s9))),
% 13.10/13.31 inference(modus_ponens,[status(thm)],[1760, 1759])).
% 13.10/13.31 tff(1762,plain,
% 13.10/13.31 ((~m_counter_cell_v_value(c_bit1, s9)) | node2(c_bit1, s8)),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1761, 121, 1755])).
% 13.10/13.31 tff(1763,plain,
% 13.10/13.31 (~m_counter_cell_v_value(c_bit1, s9)),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1762, 1751])).
% 13.10/13.31 tff(1764,plain,
% 13.10/13.31 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s9)) | (~m_counter_cell_v_value(c_bit0, s9)) | m_counter_cell_v_carry_out(c_bit0, s9))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s9)) | (~m_counter_cell_v_value(c_bit0, s9)) | m_counter_cell_v_carry_out(c_bit0, s9))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1765,plain,
% 13.10/13.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s9)) | (~m_counter_cell_v_value(c_bit0, s9)) | m_counter_cell_v_carry_out(c_bit0, s9))),
% 13.10/13.31 inference(quant_inst,[status(thm)],[])).
% 13.10/13.31 tff(1766,plain,
% 13.10/13.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s9)) | (~m_counter_cell_v_value(c_bit0, s9)) | m_counter_cell_v_carry_out(c_bit0, s9)),
% 13.10/13.31 inference(modus_ponens,[status(thm)],[1765, 1764])).
% 13.10/13.31 tff(1767,plain,
% 13.10/13.31 ((~m_counter_cell_v_value(c_bit0, s9)) | m_counter_cell_v_carry_out(c_bit0, s9)),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1766, 1390, 322])).
% 13.10/13.31 tff(1768,plain,
% 13.10/13.31 (m_counter_cell_v_carry_out(c_bit0, s9)),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1767, 320])).
% 13.10/13.31 tff(1769,plain,
% 13.10/13.31 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s9)) | m_counter_cell_v_carry_in(c_bit1, s9))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s9)) | m_counter_cell_v_carry_in(c_bit1, s9))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1770,plain,
% 13.10/13.31 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s9)) | m_counter_cell_v_carry_in(c_bit1, s9))),
% 13.10/13.31 inference(quant_inst,[status(thm)],[])).
% 13.10/13.31 tff(1771,plain,
% 13.10/13.31 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s9)) | m_counter_cell_v_carry_in(c_bit1, s9)),
% 13.10/13.31 inference(modus_ponens,[status(thm)],[1770, 1769])).
% 13.10/13.31 tff(1772,plain,
% 13.10/13.31 (m_counter_cell_v_carry_in(c_bit1, s9)),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1771, 1405, 1768])).
% 13.10/13.31 tff(1773,plain,
% 13.10/13.31 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s9)) | m_counter_cell_v_value(c_bit1, s9) | (~node1(c_bit1, s9)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s9)) | m_counter_cell_v_value(c_bit1, s9) | (~node1(c_bit1, s9)))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1774,plain,
% 13.10/13.31 (((~node1(c_bit1, s9)) | (~m_counter_cell_v_carry_in(c_bit1, s9)) | m_counter_cell_v_value(c_bit1, s9)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s9)) | m_counter_cell_v_value(c_bit1, s9) | (~node1(c_bit1, s9)))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1775,plain,
% 13.10/13.31 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s9)) | (~m_counter_cell_v_carry_in(c_bit1, s9)) | m_counter_cell_v_value(c_bit1, s9))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s9)) | m_counter_cell_v_value(c_bit1, s9) | (~node1(c_bit1, s9))))),
% 13.10/13.31 inference(monotonicity,[status(thm)],[1774])).
% 13.10/13.31 tff(1776,plain,
% 13.10/13.31 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s9)) | (~m_counter_cell_v_carry_in(c_bit1, s9)) | m_counter_cell_v_value(c_bit1, s9))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s9)) | m_counter_cell_v_value(c_bit1, s9) | (~node1(c_bit1, s9)))),
% 13.10/13.31 inference(transitivity,[status(thm)],[1775, 1773])).
% 13.10/13.31 tff(1777,plain,
% 13.10/13.31 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s9)) | (~m_counter_cell_v_carry_in(c_bit1, s9)) | m_counter_cell_v_value(c_bit1, s9))),
% 13.10/13.31 inference(quant_inst,[status(thm)],[])).
% 13.10/13.31 tff(1778,plain,
% 13.10/13.31 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s9)) | m_counter_cell_v_value(c_bit1, s9) | (~node1(c_bit1, s9))),
% 13.10/13.31 inference(modus_ponens,[status(thm)],[1777, 1776])).
% 13.10/13.31 tff(1779,plain,
% 13.10/13.31 (m_counter_cell_v_value(c_bit1, s9) | (~node1(c_bit1, s9))),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1778, 30, 1772])).
% 13.10/13.31 tff(1780,plain,
% 13.10/13.31 (~node1(c_bit1, s9)),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1779, 1763])).
% 13.10/13.31 tff(1781,plain,
% 13.10/13.31 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s9, s10)) | node3(c_bit1, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s9, s10)) | node3(c_bit1, s9, s10))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1782,plain,
% 13.10/13.31 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s9, s10)) | node3(c_bit1, s9, s10))),
% 13.10/13.31 inference(quant_inst,[status(thm)],[])).
% 13.10/13.31 tff(1783,plain,
% 13.10/13.31 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s9, s10)) | node3(c_bit1, s9, s10)),
% 13.10/13.31 inference(modus_ponens,[status(thm)],[1782, 1781])).
% 13.10/13.31 tff(1784,plain,
% 13.10/13.31 (node3(c_bit1, s9, s10)),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1783, 59, 334])).
% 13.10/13.31 tff(1785,plain,
% 13.10/13.31 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s10) | node1(c_bit1, s9) | (~node3(c_bit1, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s10) | node1(c_bit1, s9) | (~node3(c_bit1, s9, s10)))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1786,plain,
% 13.10/13.31 ((node1(c_bit1, s9) | (~node3(c_bit1, s9, s10)) | m_counter_cell_v_value(c_bit1, s10)) <=> (m_counter_cell_v_value(c_bit1, s10) | node1(c_bit1, s9) | (~node3(c_bit1, s9, s10)))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1787,plain,
% 13.10/13.31 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s9) | (~node3(c_bit1, s9, s10)) | m_counter_cell_v_value(c_bit1, s10))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s10) | node1(c_bit1, s9) | (~node3(c_bit1, s9, s10))))),
% 13.10/13.31 inference(monotonicity,[status(thm)],[1786])).
% 13.10/13.31 tff(1788,plain,
% 13.10/13.31 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s9) | (~node3(c_bit1, s9, s10)) | m_counter_cell_v_value(c_bit1, s10))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s10) | node1(c_bit1, s9) | (~node3(c_bit1, s9, s10)))),
% 13.10/13.31 inference(transitivity,[status(thm)],[1787, 1785])).
% 13.10/13.31 tff(1789,plain,
% 13.10/13.31 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s9) | (~node3(c_bit1, s9, s10)) | m_counter_cell_v_value(c_bit1, s10))),
% 13.10/13.31 inference(quant_inst,[status(thm)],[])).
% 13.10/13.31 tff(1790,plain,
% 13.10/13.31 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s10) | node1(c_bit1, s9) | (~node3(c_bit1, s9, s10))),
% 13.10/13.31 inference(modus_ponens,[status(thm)],[1789, 1788])).
% 13.10/13.31 tff(1791,plain,
% 13.10/13.31 (m_counter_cell_v_value(c_bit1, s10) | node1(c_bit1, s9)),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1790, 73, 1784])).
% 13.10/13.31 tff(1792,plain,
% 13.10/13.31 (m_counter_cell_v_value(c_bit1, s10)),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1791, 1780])).
% 13.10/13.31 tff(1793,plain,
% 13.10/13.31 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s10) | (~node4(c_bit0, s10)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s10) | (~node4(c_bit0, s10)))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1794,plain,
% 13.10/13.31 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s10) | (~node4(c_bit0, s10)))),
% 13.10/13.31 inference(quant_inst,[status(thm)],[])).
% 13.10/13.31 tff(1795,plain,
% 13.10/13.31 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s10) | (~node4(c_bit0, s10))),
% 13.10/13.31 inference(modus_ponens,[status(thm)],[1794, 1793])).
% 13.10/13.31 tff(1796,plain,
% 13.10/13.31 (~node4(c_bit0, s10)),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1795, 1344, 346])).
% 13.10/13.31 tff(1797,plain,
% 13.10/13.31 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s10)) | node4(c_bit0, s10))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s10)) | node4(c_bit0, s10))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1798,plain,
% 13.10/13.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s10)) | node4(c_bit0, s10))),
% 13.10/13.31 inference(quant_inst,[status(thm)],[])).
% 13.10/13.31 tff(1799,plain,
% 13.10/13.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s10)) | node4(c_bit0, s10)),
% 13.10/13.31 inference(modus_ponens,[status(thm)],[1798, 1797])).
% 13.10/13.31 tff(1800,plain,
% 13.10/13.31 (~m_counter_cell_v_carry_out(c_bit0, s10)),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1799, 1359, 1796])).
% 13.10/13.31 tff(1801,plain,
% 13.10/13.31 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s10)) | m_counter_cell_v_carry_out(c_bit0, s10))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s10)) | m_counter_cell_v_carry_out(c_bit0, s10))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1802,plain,
% 13.10/13.31 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s10)) | m_counter_cell_v_carry_out(c_bit0, s10))),
% 13.10/13.31 inference(quant_inst,[status(thm)],[])).
% 13.10/13.31 tff(1803,plain,
% 13.10/13.31 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s10)) | m_counter_cell_v_carry_out(c_bit0, s10)),
% 13.10/13.31 inference(modus_ponens,[status(thm)],[1802, 1801])).
% 13.10/13.31 tff(1804,plain,
% 13.10/13.31 (~m_counter_cell_v_carry_in(c_bit1, s10)),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1803, 1374, 1800])).
% 13.10/13.31 tff(1805,plain,
% 13.10/13.31 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s10) | (~m_counter_cell_v_value(c_bit1, s10)) | (~node1(c_bit1, s10)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s10) | (~m_counter_cell_v_value(c_bit1, s10)) | (~node1(c_bit1, s10)))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1806,plain,
% 13.10/13.31 (((~node1(c_bit1, s10)) | m_counter_cell_v_carry_in(c_bit1, s10) | (~m_counter_cell_v_value(c_bit1, s10))) <=> (m_counter_cell_v_carry_in(c_bit1, s10) | (~m_counter_cell_v_value(c_bit1, s10)) | (~node1(c_bit1, s10)))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1807,plain,
% 13.10/13.31 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s10)) | m_counter_cell_v_carry_in(c_bit1, s10) | (~m_counter_cell_v_value(c_bit1, s10)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s10) | (~m_counter_cell_v_value(c_bit1, s10)) | (~node1(c_bit1, s10))))),
% 13.10/13.31 inference(monotonicity,[status(thm)],[1806])).
% 13.10/13.31 tff(1808,plain,
% 13.10/13.31 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s10)) | m_counter_cell_v_carry_in(c_bit1, s10) | (~m_counter_cell_v_value(c_bit1, s10)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s10) | (~m_counter_cell_v_value(c_bit1, s10)) | (~node1(c_bit1, s10)))),
% 13.10/13.31 inference(transitivity,[status(thm)],[1807, 1805])).
% 13.10/13.31 tff(1809,plain,
% 13.10/13.31 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s10)) | m_counter_cell_v_carry_in(c_bit1, s10) | (~m_counter_cell_v_value(c_bit1, s10)))),
% 13.10/13.31 inference(quant_inst,[status(thm)],[])).
% 13.10/13.31 tff(1810,plain,
% 13.10/13.31 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s10) | (~m_counter_cell_v_value(c_bit1, s10)) | (~node1(c_bit1, s10))),
% 13.10/13.31 inference(modus_ponens,[status(thm)],[1809, 1808])).
% 13.10/13.31 tff(1811,plain,
% 13.10/13.31 ((~m_counter_cell_v_value(c_bit1, s10)) | (~node1(c_bit1, s10))),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1810, 1569, 1804])).
% 13.10/13.31 tff(1812,plain,
% 13.10/13.31 (~node1(c_bit1, s10)),
% 13.10/13.31 inference(unit_resolution,[status(thm)],[1811, 1792])).
% 13.10/13.31 tff(1813,plain,
% 13.10/13.31 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s10, s11)) | node3(c_bit1, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s10, s11)) | node3(c_bit1, s10, s11))),
% 13.10/13.31 inference(rewrite,[status(thm)],[])).
% 13.10/13.31 tff(1814,plain,
% 13.10/13.31 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s10, s11)) | node3(c_bit1, s10, s11))),
% 13.10/13.31 inference(quant_inst,[status(thm)],[])).
% 13.10/13.31 tff(1815,plain,
% 13.10/13.31 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s10, s11)) | node3(c_bit1, s10, s11)),
% 13.10/13.31 inference(modus_ponens,[status(thm)],[1814, 1813])).
% 13.10/13.32 tff(1816,plain,
% 13.10/13.32 (node3(c_bit1, s10, s11)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1815, 59, 363])).
% 13.10/13.32 tff(1817,plain,
% 13.10/13.32 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s11) | node1(c_bit1, s10) | (~node3(c_bit1, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s11) | node1(c_bit1, s10) | (~node3(c_bit1, s10, s11)))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1818,plain,
% 13.10/13.32 ((node1(c_bit1, s10) | (~node3(c_bit1, s10, s11)) | m_counter_cell_v_value(c_bit1, s11)) <=> (m_counter_cell_v_value(c_bit1, s11) | node1(c_bit1, s10) | (~node3(c_bit1, s10, s11)))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1819,plain,
% 13.10/13.32 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s10) | (~node3(c_bit1, s10, s11)) | m_counter_cell_v_value(c_bit1, s11))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s11) | node1(c_bit1, s10) | (~node3(c_bit1, s10, s11))))),
% 13.10/13.32 inference(monotonicity,[status(thm)],[1818])).
% 13.10/13.32 tff(1820,plain,
% 13.10/13.32 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s10) | (~node3(c_bit1, s10, s11)) | m_counter_cell_v_value(c_bit1, s11))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s11) | node1(c_bit1, s10) | (~node3(c_bit1, s10, s11)))),
% 13.10/13.32 inference(transitivity,[status(thm)],[1819, 1817])).
% 13.10/13.32 tff(1821,plain,
% 13.10/13.32 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s10) | (~node3(c_bit1, s10, s11)) | m_counter_cell_v_value(c_bit1, s11))),
% 13.10/13.32 inference(quant_inst,[status(thm)],[])).
% 13.10/13.32 tff(1822,plain,
% 13.10/13.32 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s11) | node1(c_bit1, s10) | (~node3(c_bit1, s10, s11))),
% 13.10/13.32 inference(modus_ponens,[status(thm)],[1821, 1820])).
% 13.10/13.32 tff(1823,plain,
% 13.10/13.32 (m_counter_cell_v_value(c_bit1, s11) | node1(c_bit1, s10)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1822, 73, 1816])).
% 13.10/13.32 tff(1824,plain,
% 13.10/13.32 (m_counter_cell_v_value(c_bit1, s11)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1823, 1812])).
% 13.10/13.32 tff(1825,plain,
% 13.10/13.32 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s11)) | (~m_counter_cell_v_value(c_bit0, s11)) | m_counter_cell_v_carry_out(c_bit0, s11))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s11)) | (~m_counter_cell_v_value(c_bit0, s11)) | m_counter_cell_v_carry_out(c_bit0, s11))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1826,plain,
% 13.10/13.32 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s11)) | (~m_counter_cell_v_value(c_bit0, s11)) | m_counter_cell_v_carry_out(c_bit0, s11))),
% 13.10/13.32 inference(quant_inst,[status(thm)],[])).
% 13.10/13.32 tff(1827,plain,
% 13.10/13.32 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s11)) | (~m_counter_cell_v_value(c_bit0, s11)) | m_counter_cell_v_carry_out(c_bit0, s11)),
% 13.10/13.32 inference(modus_ponens,[status(thm)],[1826, 1825])).
% 13.10/13.32 tff(1828,plain,
% 13.10/13.32 ((~m_counter_cell_v_value(c_bit0, s11)) | m_counter_cell_v_carry_out(c_bit0, s11)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1827, 1390, 377])).
% 13.10/13.32 tff(1829,plain,
% 13.10/13.32 (m_counter_cell_v_carry_out(c_bit0, s11)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1828, 375])).
% 13.10/13.32 tff(1830,plain,
% 13.10/13.32 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s11)) | m_counter_cell_v_carry_in(c_bit1, s11))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s11)) | m_counter_cell_v_carry_in(c_bit1, s11))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1831,plain,
% 13.10/13.32 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s11)) | m_counter_cell_v_carry_in(c_bit1, s11))),
% 13.10/13.32 inference(quant_inst,[status(thm)],[])).
% 13.10/13.32 tff(1832,plain,
% 13.10/13.32 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s11)) | m_counter_cell_v_carry_in(c_bit1, s11)),
% 13.10/13.32 inference(modus_ponens,[status(thm)],[1831, 1830])).
% 13.10/13.32 tff(1833,plain,
% 13.10/13.32 (m_counter_cell_v_carry_in(c_bit1, s11)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1832, 1405, 1829])).
% 13.10/13.32 tff(1834,plain,
% 13.10/13.32 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s11)) | (~m_counter_cell_v_value(c_bit1, s11)) | (~node2(c_bit1, s11)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s11)) | (~m_counter_cell_v_value(c_bit1, s11)) | (~node2(c_bit1, s11)))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1835,plain,
% 13.10/13.32 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s11)) | (~m_counter_cell_v_value(c_bit1, s11)) | (~node2(c_bit1, s11)))),
% 13.10/13.32 inference(quant_inst,[status(thm)],[])).
% 13.10/13.32 tff(1836,plain,
% 13.10/13.32 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s11)) | (~m_counter_cell_v_value(c_bit1, s11)) | (~node2(c_bit1, s11))),
% 13.10/13.32 inference(modus_ponens,[status(thm)],[1835, 1834])).
% 13.10/13.32 tff(1837,plain,
% 13.10/13.32 ((~m_counter_cell_v_value(c_bit1, s11)) | (~node2(c_bit1, s11))),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1836, 93, 1833])).
% 13.10/13.32 tff(1838,plain,
% 13.10/13.32 (~node2(c_bit1, s11)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1837, 1824])).
% 13.10/13.32 tff(1839,plain,
% 13.10/13.32 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s11, s12)) | node3(c_bit1, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s11, s12)) | node3(c_bit1, s11, s12))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1840,plain,
% 13.10/13.32 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s11, s12)) | node3(c_bit1, s11, s12))),
% 13.10/13.32 inference(quant_inst,[status(thm)],[])).
% 13.10/13.32 tff(1841,plain,
% 13.10/13.32 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s11, s12)) | node3(c_bit1, s11, s12)),
% 13.10/13.32 inference(modus_ponens,[status(thm)],[1840, 1839])).
% 13.10/13.32 tff(1842,plain,
% 13.10/13.32 (node3(c_bit1, s11, s12)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1841, 59, 389])).
% 13.10/13.32 tff(1843,plain,
% 13.10/13.32 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s12)) | node2(c_bit1, s11) | (~node3(c_bit1, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s12)) | node2(c_bit1, s11) | (~node3(c_bit1, s11, s12)))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1844,plain,
% 13.10/13.32 ((node2(c_bit1, s11) | (~node3(c_bit1, s11, s12)) | (~m_counter_cell_v_value(c_bit1, s12))) <=> ((~m_counter_cell_v_value(c_bit1, s12)) | node2(c_bit1, s11) | (~node3(c_bit1, s11, s12)))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1845,plain,
% 13.10/13.32 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s11) | (~node3(c_bit1, s11, s12)) | (~m_counter_cell_v_value(c_bit1, s12)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s12)) | node2(c_bit1, s11) | (~node3(c_bit1, s11, s12))))),
% 13.10/13.32 inference(monotonicity,[status(thm)],[1844])).
% 13.10/13.32 tff(1846,plain,
% 13.10/13.32 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s11) | (~node3(c_bit1, s11, s12)) | (~m_counter_cell_v_value(c_bit1, s12)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s12)) | node2(c_bit1, s11) | (~node3(c_bit1, s11, s12)))),
% 13.10/13.32 inference(transitivity,[status(thm)],[1845, 1843])).
% 13.10/13.32 tff(1847,plain,
% 13.10/13.32 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s11) | (~node3(c_bit1, s11, s12)) | (~m_counter_cell_v_value(c_bit1, s12)))),
% 13.10/13.32 inference(quant_inst,[status(thm)],[])).
% 13.10/13.32 tff(1848,plain,
% 13.10/13.32 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s12)) | node2(c_bit1, s11) | (~node3(c_bit1, s11, s12))),
% 13.10/13.32 inference(modus_ponens,[status(thm)],[1847, 1846])).
% 13.10/13.32 tff(1849,plain,
% 13.10/13.32 ((~m_counter_cell_v_value(c_bit1, s12)) | node2(c_bit1, s11)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1848, 121, 1842])).
% 13.10/13.32 tff(1850,plain,
% 13.10/13.32 (~m_counter_cell_v_value(c_bit1, s12)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1849, 1838])).
% 13.10/13.32 tff(1851,plain,
% 13.10/13.32 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s12) | (~node4(c_bit0, s12)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s12) | (~node4(c_bit0, s12)))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1852,plain,
% 13.10/13.32 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s12) | (~node4(c_bit0, s12)))),
% 13.10/13.32 inference(quant_inst,[status(thm)],[])).
% 13.10/13.32 tff(1853,plain,
% 13.10/13.32 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s12) | (~node4(c_bit0, s12))),
% 13.10/13.32 inference(modus_ponens,[status(thm)],[1852, 1851])).
% 13.10/13.32 tff(1854,plain,
% 13.10/13.32 (~node4(c_bit0, s12)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1853, 1344, 401])).
% 13.10/13.32 tff(1855,plain,
% 13.10/13.32 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s12)) | node4(c_bit0, s12))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s12)) | node4(c_bit0, s12))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1856,plain,
% 13.10/13.32 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s12)) | node4(c_bit0, s12))),
% 13.10/13.32 inference(quant_inst,[status(thm)],[])).
% 13.10/13.32 tff(1857,plain,
% 13.10/13.32 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s12)) | node4(c_bit0, s12)),
% 13.10/13.32 inference(modus_ponens,[status(thm)],[1856, 1855])).
% 13.10/13.32 tff(1858,plain,
% 13.10/13.32 (~m_counter_cell_v_carry_out(c_bit0, s12)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1857, 1359, 1854])).
% 13.10/13.32 tff(1859,plain,
% 13.10/13.32 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s12)) | m_counter_cell_v_carry_out(c_bit0, s12))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s12)) | m_counter_cell_v_carry_out(c_bit0, s12))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1860,plain,
% 13.10/13.32 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s12)) | m_counter_cell_v_carry_out(c_bit0, s12))),
% 13.10/13.32 inference(quant_inst,[status(thm)],[])).
% 13.10/13.32 tff(1861,plain,
% 13.10/13.32 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s12)) | m_counter_cell_v_carry_out(c_bit0, s12)),
% 13.10/13.32 inference(modus_ponens,[status(thm)],[1860, 1859])).
% 13.10/13.32 tff(1862,plain,
% 13.10/13.32 (~m_counter_cell_v_carry_in(c_bit1, s12)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1861, 1374, 1858])).
% 13.10/13.32 tff(1863,plain,
% 13.10/13.32 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s12) | m_counter_cell_v_value(c_bit1, s12) | (~node2(c_bit1, s12)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s12) | m_counter_cell_v_value(c_bit1, s12) | (~node2(c_bit1, s12)))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1864,plain,
% 13.10/13.32 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s12) | m_counter_cell_v_value(c_bit1, s12) | (~node2(c_bit1, s12)))),
% 13.10/13.32 inference(quant_inst,[status(thm)],[])).
% 13.10/13.32 tff(1865,plain,
% 13.10/13.32 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s12) | m_counter_cell_v_value(c_bit1, s12) | (~node2(c_bit1, s12))),
% 13.10/13.32 inference(modus_ponens,[status(thm)],[1864, 1863])).
% 13.10/13.32 tff(1866,plain,
% 13.10/13.32 (m_counter_cell_v_value(c_bit1, s12) | (~node2(c_bit1, s12))),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1865, 1498, 1862])).
% 13.10/13.32 tff(1867,plain,
% 13.10/13.32 (~node2(c_bit1, s12)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1866, 1850])).
% 13.10/13.32 tff(1868,plain,
% 13.10/13.32 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s12, s13)) | node3(c_bit1, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s12, s13)) | node3(c_bit1, s12, s13))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1869,plain,
% 13.10/13.32 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s12, s13)) | node3(c_bit1, s12, s13))),
% 13.10/13.32 inference(quant_inst,[status(thm)],[])).
% 13.10/13.32 tff(1870,plain,
% 13.10/13.32 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s12, s13)) | node3(c_bit1, s12, s13)),
% 13.10/13.32 inference(modus_ponens,[status(thm)],[1869, 1868])).
% 13.10/13.32 tff(1871,plain,
% 13.10/13.32 (node3(c_bit1, s12, s13)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1870, 59, 418])).
% 13.10/13.32 tff(1872,plain,
% 13.10/13.32 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s13)) | node2(c_bit1, s12) | (~node3(c_bit1, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s13)) | node2(c_bit1, s12) | (~node3(c_bit1, s12, s13)))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1873,plain,
% 13.10/13.32 ((node2(c_bit1, s12) | (~node3(c_bit1, s12, s13)) | (~m_counter_cell_v_value(c_bit1, s13))) <=> ((~m_counter_cell_v_value(c_bit1, s13)) | node2(c_bit1, s12) | (~node3(c_bit1, s12, s13)))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1874,plain,
% 13.10/13.32 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s12) | (~node3(c_bit1, s12, s13)) | (~m_counter_cell_v_value(c_bit1, s13)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s13)) | node2(c_bit1, s12) | (~node3(c_bit1, s12, s13))))),
% 13.10/13.32 inference(monotonicity,[status(thm)],[1873])).
% 13.10/13.32 tff(1875,plain,
% 13.10/13.32 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s12) | (~node3(c_bit1, s12, s13)) | (~m_counter_cell_v_value(c_bit1, s13)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s13)) | node2(c_bit1, s12) | (~node3(c_bit1, s12, s13)))),
% 13.10/13.32 inference(transitivity,[status(thm)],[1874, 1872])).
% 13.10/13.32 tff(1876,plain,
% 13.10/13.32 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s12) | (~node3(c_bit1, s12, s13)) | (~m_counter_cell_v_value(c_bit1, s13)))),
% 13.10/13.32 inference(quant_inst,[status(thm)],[])).
% 13.10/13.32 tff(1877,plain,
% 13.10/13.32 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s13)) | node2(c_bit1, s12) | (~node3(c_bit1, s12, s13))),
% 13.10/13.32 inference(modus_ponens,[status(thm)],[1876, 1875])).
% 13.10/13.32 tff(1878,plain,
% 13.10/13.32 ((~m_counter_cell_v_value(c_bit1, s13)) | node2(c_bit1, s12)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1877, 121, 1871])).
% 13.10/13.32 tff(1879,plain,
% 13.10/13.32 (~m_counter_cell_v_value(c_bit1, s13)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1878, 1867])).
% 13.10/13.32 tff(1880,plain,
% 13.10/13.32 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s13)) | (~m_counter_cell_v_value(c_bit0, s13)) | m_counter_cell_v_carry_out(c_bit0, s13))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s13)) | (~m_counter_cell_v_value(c_bit0, s13)) | m_counter_cell_v_carry_out(c_bit0, s13))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1881,plain,
% 13.10/13.32 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s13)) | (~m_counter_cell_v_value(c_bit0, s13)) | m_counter_cell_v_carry_out(c_bit0, s13))),
% 13.10/13.32 inference(quant_inst,[status(thm)],[])).
% 13.10/13.32 tff(1882,plain,
% 13.10/13.32 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s13)) | (~m_counter_cell_v_value(c_bit0, s13)) | m_counter_cell_v_carry_out(c_bit0, s13)),
% 13.10/13.32 inference(modus_ponens,[status(thm)],[1881, 1880])).
% 13.10/13.32 tff(1883,plain,
% 13.10/13.32 ((~m_counter_cell_v_value(c_bit0, s13)) | m_counter_cell_v_carry_out(c_bit0, s13)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1882, 1390, 432])).
% 13.10/13.32 tff(1884,plain,
% 13.10/13.32 (m_counter_cell_v_carry_out(c_bit0, s13)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1883, 430])).
% 13.10/13.32 tff(1885,plain,
% 13.10/13.32 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s13)) | m_counter_cell_v_carry_in(c_bit1, s13))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s13)) | m_counter_cell_v_carry_in(c_bit1, s13))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1886,plain,
% 13.10/13.32 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s13)) | m_counter_cell_v_carry_in(c_bit1, s13))),
% 13.10/13.32 inference(quant_inst,[status(thm)],[])).
% 13.10/13.32 tff(1887,plain,
% 13.10/13.32 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s13)) | m_counter_cell_v_carry_in(c_bit1, s13)),
% 13.10/13.32 inference(modus_ponens,[status(thm)],[1886, 1885])).
% 13.10/13.32 tff(1888,plain,
% 13.10/13.32 (m_counter_cell_v_carry_in(c_bit1, s13)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1887, 1405, 1884])).
% 13.10/13.32 tff(1889,plain,
% 13.10/13.32 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s13)) | m_counter_cell_v_value(c_bit1, s13) | (~node1(c_bit1, s13)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s13)) | m_counter_cell_v_value(c_bit1, s13) | (~node1(c_bit1, s13)))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1890,plain,
% 13.10/13.32 (((~node1(c_bit1, s13)) | (~m_counter_cell_v_carry_in(c_bit1, s13)) | m_counter_cell_v_value(c_bit1, s13)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s13)) | m_counter_cell_v_value(c_bit1, s13) | (~node1(c_bit1, s13)))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1891,plain,
% 13.10/13.32 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s13)) | (~m_counter_cell_v_carry_in(c_bit1, s13)) | m_counter_cell_v_value(c_bit1, s13))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s13)) | m_counter_cell_v_value(c_bit1, s13) | (~node1(c_bit1, s13))))),
% 13.10/13.32 inference(monotonicity,[status(thm)],[1890])).
% 13.10/13.32 tff(1892,plain,
% 13.10/13.32 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s13)) | (~m_counter_cell_v_carry_in(c_bit1, s13)) | m_counter_cell_v_value(c_bit1, s13))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s13)) | m_counter_cell_v_value(c_bit1, s13) | (~node1(c_bit1, s13)))),
% 13.10/13.32 inference(transitivity,[status(thm)],[1891, 1889])).
% 13.10/13.32 tff(1893,plain,
% 13.10/13.32 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s13)) | (~m_counter_cell_v_carry_in(c_bit1, s13)) | m_counter_cell_v_value(c_bit1, s13))),
% 13.10/13.32 inference(quant_inst,[status(thm)],[])).
% 13.10/13.32 tff(1894,plain,
% 13.10/13.32 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s13)) | m_counter_cell_v_value(c_bit1, s13) | (~node1(c_bit1, s13))),
% 13.10/13.32 inference(modus_ponens,[status(thm)],[1893, 1892])).
% 13.10/13.32 tff(1895,plain,
% 13.10/13.32 (m_counter_cell_v_value(c_bit1, s13) | (~node1(c_bit1, s13))),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1894, 30, 1888])).
% 13.10/13.32 tff(1896,plain,
% 13.10/13.32 (~node1(c_bit1, s13)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1895, 1879])).
% 13.10/13.32 tff(1897,plain,
% 13.10/13.32 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s13, s14)) | node3(c_bit1, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s13, s14)) | node3(c_bit1, s13, s14))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1898,plain,
% 13.10/13.32 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s13, s14)) | node3(c_bit1, s13, s14))),
% 13.10/13.32 inference(quant_inst,[status(thm)],[])).
% 13.10/13.32 tff(1899,plain,
% 13.10/13.32 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s13, s14)) | node3(c_bit1, s13, s14)),
% 13.10/13.32 inference(modus_ponens,[status(thm)],[1898, 1897])).
% 13.10/13.32 tff(1900,plain,
% 13.10/13.32 (node3(c_bit1, s13, s14)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1899, 59, 444])).
% 13.10/13.32 tff(1901,plain,
% 13.10/13.32 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s14) | node1(c_bit1, s13) | (~node3(c_bit1, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s14) | node1(c_bit1, s13) | (~node3(c_bit1, s13, s14)))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1902,plain,
% 13.10/13.32 ((node1(c_bit1, s13) | (~node3(c_bit1, s13, s14)) | m_counter_cell_v_value(c_bit1, s14)) <=> (m_counter_cell_v_value(c_bit1, s14) | node1(c_bit1, s13) | (~node3(c_bit1, s13, s14)))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1903,plain,
% 13.10/13.32 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s13) | (~node3(c_bit1, s13, s14)) | m_counter_cell_v_value(c_bit1, s14))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s14) | node1(c_bit1, s13) | (~node3(c_bit1, s13, s14))))),
% 13.10/13.32 inference(monotonicity,[status(thm)],[1902])).
% 13.10/13.32 tff(1904,plain,
% 13.10/13.32 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s13) | (~node3(c_bit1, s13, s14)) | m_counter_cell_v_value(c_bit1, s14))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s14) | node1(c_bit1, s13) | (~node3(c_bit1, s13, s14)))),
% 13.10/13.32 inference(transitivity,[status(thm)],[1903, 1901])).
% 13.10/13.32 tff(1905,plain,
% 13.10/13.32 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s13) | (~node3(c_bit1, s13, s14)) | m_counter_cell_v_value(c_bit1, s14))),
% 13.10/13.32 inference(quant_inst,[status(thm)],[])).
% 13.10/13.32 tff(1906,plain,
% 13.10/13.32 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s14) | node1(c_bit1, s13) | (~node3(c_bit1, s13, s14))),
% 13.10/13.32 inference(modus_ponens,[status(thm)],[1905, 1904])).
% 13.10/13.32 tff(1907,plain,
% 13.10/13.32 (m_counter_cell_v_value(c_bit1, s14) | node1(c_bit1, s13)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1906, 73, 1900])).
% 13.10/13.32 tff(1908,plain,
% 13.10/13.32 (m_counter_cell_v_value(c_bit1, s14)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1907, 1896])).
% 13.10/13.32 tff(1909,plain,
% 13.10/13.32 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s14) | (~node4(c_bit0, s14)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s14) | (~node4(c_bit0, s14)))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1910,plain,
% 13.10/13.32 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s14) | (~node4(c_bit0, s14)))),
% 13.10/13.32 inference(quant_inst,[status(thm)],[])).
% 13.10/13.32 tff(1911,plain,
% 13.10/13.32 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s14) | (~node4(c_bit0, s14))),
% 13.10/13.32 inference(modus_ponens,[status(thm)],[1910, 1909])).
% 13.10/13.32 tff(1912,plain,
% 13.10/13.32 (~node4(c_bit0, s14)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1911, 1344, 456])).
% 13.10/13.32 tff(1913,plain,
% 13.10/13.32 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s14)) | node4(c_bit0, s14))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s14)) | node4(c_bit0, s14))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1914,plain,
% 13.10/13.32 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s14)) | node4(c_bit0, s14))),
% 13.10/13.32 inference(quant_inst,[status(thm)],[])).
% 13.10/13.32 tff(1915,plain,
% 13.10/13.32 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s14)) | node4(c_bit0, s14)),
% 13.10/13.32 inference(modus_ponens,[status(thm)],[1914, 1913])).
% 13.10/13.32 tff(1916,plain,
% 13.10/13.32 (~m_counter_cell_v_carry_out(c_bit0, s14)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1915, 1359, 1912])).
% 13.10/13.32 tff(1917,plain,
% 13.10/13.32 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s14)) | m_counter_cell_v_carry_out(c_bit0, s14))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s14)) | m_counter_cell_v_carry_out(c_bit0, s14))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1918,plain,
% 13.10/13.32 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s14)) | m_counter_cell_v_carry_out(c_bit0, s14))),
% 13.10/13.32 inference(quant_inst,[status(thm)],[])).
% 13.10/13.32 tff(1919,plain,
% 13.10/13.32 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s14)) | m_counter_cell_v_carry_out(c_bit0, s14)),
% 13.10/13.32 inference(modus_ponens,[status(thm)],[1918, 1917])).
% 13.10/13.32 tff(1920,plain,
% 13.10/13.32 (~m_counter_cell_v_carry_in(c_bit1, s14)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1919, 1374, 1916])).
% 13.10/13.32 tff(1921,plain,
% 13.10/13.32 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s14) | (~m_counter_cell_v_value(c_bit1, s14)) | (~node1(c_bit1, s14)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s14) | (~m_counter_cell_v_value(c_bit1, s14)) | (~node1(c_bit1, s14)))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1922,plain,
% 13.10/13.32 (((~node1(c_bit1, s14)) | m_counter_cell_v_carry_in(c_bit1, s14) | (~m_counter_cell_v_value(c_bit1, s14))) <=> (m_counter_cell_v_carry_in(c_bit1, s14) | (~m_counter_cell_v_value(c_bit1, s14)) | (~node1(c_bit1, s14)))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1923,plain,
% 13.10/13.32 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s14)) | m_counter_cell_v_carry_in(c_bit1, s14) | (~m_counter_cell_v_value(c_bit1, s14)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s14) | (~m_counter_cell_v_value(c_bit1, s14)) | (~node1(c_bit1, s14))))),
% 13.10/13.32 inference(monotonicity,[status(thm)],[1922])).
% 13.10/13.32 tff(1924,plain,
% 13.10/13.32 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s14)) | m_counter_cell_v_carry_in(c_bit1, s14) | (~m_counter_cell_v_value(c_bit1, s14)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s14) | (~m_counter_cell_v_value(c_bit1, s14)) | (~node1(c_bit1, s14)))),
% 13.10/13.32 inference(transitivity,[status(thm)],[1923, 1921])).
% 13.10/13.32 tff(1925,plain,
% 13.10/13.32 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s14)) | m_counter_cell_v_carry_in(c_bit1, s14) | (~m_counter_cell_v_value(c_bit1, s14)))),
% 13.10/13.32 inference(quant_inst,[status(thm)],[])).
% 13.10/13.32 tff(1926,plain,
% 13.10/13.32 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s14) | (~m_counter_cell_v_value(c_bit1, s14)) | (~node1(c_bit1, s14))),
% 13.10/13.32 inference(modus_ponens,[status(thm)],[1925, 1924])).
% 13.10/13.32 tff(1927,plain,
% 13.10/13.32 ((~m_counter_cell_v_value(c_bit1, s14)) | (~node1(c_bit1, s14))),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1926, 1569, 1920])).
% 13.10/13.32 tff(1928,plain,
% 13.10/13.32 (~node1(c_bit1, s14)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1927, 1908])).
% 13.10/13.32 tff(1929,plain,
% 13.10/13.32 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s14, s15)) | node3(c_bit1, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s14, s15)) | node3(c_bit1, s14, s15))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1930,plain,
% 13.10/13.32 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s14, s15)) | node3(c_bit1, s14, s15))),
% 13.10/13.32 inference(quant_inst,[status(thm)],[])).
% 13.10/13.32 tff(1931,plain,
% 13.10/13.32 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s14, s15)) | node3(c_bit1, s14, s15)),
% 13.10/13.32 inference(modus_ponens,[status(thm)],[1930, 1929])).
% 13.10/13.32 tff(1932,plain,
% 13.10/13.32 (node3(c_bit1, s14, s15)),
% 13.10/13.32 inference(unit_resolution,[status(thm)],[1931, 59, 473])).
% 13.10/13.32 tff(1933,plain,
% 13.10/13.32 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s15) | node1(c_bit1, s14) | (~node3(c_bit1, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s15) | node1(c_bit1, s14) | (~node3(c_bit1, s14, s15)))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1934,plain,
% 13.10/13.32 ((node1(c_bit1, s14) | (~node3(c_bit1, s14, s15)) | m_counter_cell_v_value(c_bit1, s15)) <=> (m_counter_cell_v_value(c_bit1, s15) | node1(c_bit1, s14) | (~node3(c_bit1, s14, s15)))),
% 13.10/13.32 inference(rewrite,[status(thm)],[])).
% 13.10/13.32 tff(1935,plain,
% 13.10/13.32 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s14) | (~node3(c_bit1, s14, s15)) | m_counter_cell_v_value(c_bit1, s15))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s15) | node1(c_bit1, s14) | (~node3(c_bit1, s14, s15))))),
% 13.18/13.33 inference(monotonicity,[status(thm)],[1934])).
% 13.18/13.33 tff(1936,plain,
% 13.18/13.33 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s14) | (~node3(c_bit1, s14, s15)) | m_counter_cell_v_value(c_bit1, s15))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s15) | node1(c_bit1, s14) | (~node3(c_bit1, s14, s15)))),
% 13.18/13.33 inference(transitivity,[status(thm)],[1935, 1933])).
% 13.18/13.33 tff(1937,plain,
% 13.18/13.33 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s14) | (~node3(c_bit1, s14, s15)) | m_counter_cell_v_value(c_bit1, s15))),
% 13.18/13.33 inference(quant_inst,[status(thm)],[])).
% 13.18/13.33 tff(1938,plain,
% 13.18/13.33 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s15) | node1(c_bit1, s14) | (~node3(c_bit1, s14, s15))),
% 13.18/13.33 inference(modus_ponens,[status(thm)],[1937, 1936])).
% 13.18/13.33 tff(1939,plain,
% 13.18/13.33 (m_counter_cell_v_value(c_bit1, s15) | node1(c_bit1, s14)),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[1938, 73, 1932])).
% 13.18/13.33 tff(1940,plain,
% 13.18/13.33 (m_counter_cell_v_value(c_bit1, s15)),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[1939, 1928])).
% 13.18/13.33 tff(1941,plain,
% 13.18/13.33 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s15)) | (~m_counter_cell_v_value(c_bit0, s15)) | m_counter_cell_v_carry_out(c_bit0, s15))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s15)) | (~m_counter_cell_v_value(c_bit0, s15)) | m_counter_cell_v_carry_out(c_bit0, s15))),
% 13.18/13.33 inference(rewrite,[status(thm)],[])).
% 13.18/13.33 tff(1942,plain,
% 13.18/13.33 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s15)) | (~m_counter_cell_v_value(c_bit0, s15)) | m_counter_cell_v_carry_out(c_bit0, s15))),
% 13.18/13.33 inference(quant_inst,[status(thm)],[])).
% 13.18/13.33 tff(1943,plain,
% 13.18/13.33 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s15)) | (~m_counter_cell_v_value(c_bit0, s15)) | m_counter_cell_v_carry_out(c_bit0, s15)),
% 13.18/13.33 inference(modus_ponens,[status(thm)],[1942, 1941])).
% 13.18/13.33 tff(1944,plain,
% 13.18/13.33 ((~m_counter_cell_v_value(c_bit0, s15)) | m_counter_cell_v_carry_out(c_bit0, s15)),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[1943, 1390, 487])).
% 13.18/13.33 tff(1945,plain,
% 13.18/13.33 (m_counter_cell_v_carry_out(c_bit0, s15)),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[1944, 485])).
% 13.18/13.33 tff(1946,plain,
% 13.18/13.33 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s15)) | m_counter_cell_v_carry_in(c_bit1, s15))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s15)) | m_counter_cell_v_carry_in(c_bit1, s15))),
% 13.18/13.33 inference(rewrite,[status(thm)],[])).
% 13.18/13.33 tff(1947,plain,
% 13.18/13.33 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s15)) | m_counter_cell_v_carry_in(c_bit1, s15))),
% 13.18/13.33 inference(quant_inst,[status(thm)],[])).
% 13.18/13.33 tff(1948,plain,
% 13.18/13.33 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s15)) | m_counter_cell_v_carry_in(c_bit1, s15)),
% 13.18/13.33 inference(modus_ponens,[status(thm)],[1947, 1946])).
% 13.18/13.33 tff(1949,plain,
% 13.18/13.33 (m_counter_cell_v_carry_in(c_bit1, s15)),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[1948, 1405, 1945])).
% 13.18/13.33 tff(1950,plain,
% 13.18/13.33 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s15)) | (~m_counter_cell_v_value(c_bit1, s15)) | (~node2(c_bit1, s15)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s15)) | (~m_counter_cell_v_value(c_bit1, s15)) | (~node2(c_bit1, s15)))),
% 13.18/13.33 inference(rewrite,[status(thm)],[])).
% 13.18/13.33 tff(1951,plain,
% 13.18/13.33 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s15)) | (~m_counter_cell_v_value(c_bit1, s15)) | (~node2(c_bit1, s15)))),
% 13.18/13.33 inference(quant_inst,[status(thm)],[])).
% 13.18/13.33 tff(1952,plain,
% 13.18/13.33 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s15)) | (~m_counter_cell_v_value(c_bit1, s15)) | (~node2(c_bit1, s15))),
% 13.18/13.33 inference(modus_ponens,[status(thm)],[1951, 1950])).
% 13.18/13.33 tff(1953,plain,
% 13.18/13.33 ((~m_counter_cell_v_value(c_bit1, s15)) | (~node2(c_bit1, s15))),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[1952, 93, 1949])).
% 13.18/13.33 tff(1954,plain,
% 13.18/13.33 (~node2(c_bit1, s15)),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[1953, 1940])).
% 13.18/13.33 tff(1955,plain,
% 13.18/13.33 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s15, s16)) | node3(c_bit1, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s15, s16)) | node3(c_bit1, s15, s16))),
% 13.18/13.33 inference(rewrite,[status(thm)],[])).
% 13.18/13.33 tff(1956,plain,
% 13.18/13.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s15, s16)) | node3(c_bit1, s15, s16))),
% 13.18/13.33 inference(quant_inst,[status(thm)],[])).
% 13.18/13.33 tff(1957,plain,
% 13.18/13.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s15, s16)) | node3(c_bit1, s15, s16)),
% 13.18/13.33 inference(modus_ponens,[status(thm)],[1956, 1955])).
% 13.18/13.33 tff(1958,plain,
% 13.18/13.33 (node3(c_bit1, s15, s16)),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[1957, 59, 499])).
% 13.18/13.33 tff(1959,plain,
% 13.18/13.33 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s16)) | node2(c_bit1, s15) | (~node3(c_bit1, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s16)) | node2(c_bit1, s15) | (~node3(c_bit1, s15, s16)))),
% 13.18/13.33 inference(rewrite,[status(thm)],[])).
% 13.18/13.33 tff(1960,plain,
% 13.18/13.33 ((node2(c_bit1, s15) | (~node3(c_bit1, s15, s16)) | (~m_counter_cell_v_value(c_bit1, s16))) <=> ((~m_counter_cell_v_value(c_bit1, s16)) | node2(c_bit1, s15) | (~node3(c_bit1, s15, s16)))),
% 13.18/13.33 inference(rewrite,[status(thm)],[])).
% 13.18/13.33 tff(1961,plain,
% 13.18/13.33 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s15) | (~node3(c_bit1, s15, s16)) | (~m_counter_cell_v_value(c_bit1, s16)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s16)) | node2(c_bit1, s15) | (~node3(c_bit1, s15, s16))))),
% 13.18/13.33 inference(monotonicity,[status(thm)],[1960])).
% 13.18/13.33 tff(1962,plain,
% 13.18/13.33 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s15) | (~node3(c_bit1, s15, s16)) | (~m_counter_cell_v_value(c_bit1, s16)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s16)) | node2(c_bit1, s15) | (~node3(c_bit1, s15, s16)))),
% 13.18/13.33 inference(transitivity,[status(thm)],[1961, 1959])).
% 13.18/13.33 tff(1963,plain,
% 13.18/13.33 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s15) | (~node3(c_bit1, s15, s16)) | (~m_counter_cell_v_value(c_bit1, s16)))),
% 13.18/13.33 inference(quant_inst,[status(thm)],[])).
% 13.18/13.33 tff(1964,plain,
% 13.18/13.33 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s16)) | node2(c_bit1, s15) | (~node3(c_bit1, s15, s16))),
% 13.18/13.33 inference(modus_ponens,[status(thm)],[1963, 1962])).
% 13.18/13.33 tff(1965,plain,
% 13.18/13.33 ((~m_counter_cell_v_value(c_bit1, s16)) | node2(c_bit1, s15)),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[1964, 121, 1958])).
% 13.18/13.33 tff(1966,plain,
% 13.18/13.33 (~m_counter_cell_v_value(c_bit1, s16)),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[1965, 1954])).
% 13.18/13.33 tff(1967,plain,
% 13.18/13.33 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s16) | (~node4(c_bit0, s16)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s16) | (~node4(c_bit0, s16)))),
% 13.18/13.33 inference(rewrite,[status(thm)],[])).
% 13.18/13.33 tff(1968,plain,
% 13.18/13.33 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s16) | (~node4(c_bit0, s16)))),
% 13.18/13.33 inference(quant_inst,[status(thm)],[])).
% 13.18/13.33 tff(1969,plain,
% 13.18/13.33 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s16) | (~node4(c_bit0, s16))),
% 13.18/13.33 inference(modus_ponens,[status(thm)],[1968, 1967])).
% 13.18/13.33 tff(1970,plain,
% 13.18/13.33 (~node4(c_bit0, s16)),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[1969, 1344, 511])).
% 13.18/13.33 tff(1971,plain,
% 13.18/13.33 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s16)) | node4(c_bit0, s16))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s16)) | node4(c_bit0, s16))),
% 13.18/13.33 inference(rewrite,[status(thm)],[])).
% 13.18/13.33 tff(1972,plain,
% 13.18/13.33 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s16)) | node4(c_bit0, s16))),
% 13.18/13.33 inference(quant_inst,[status(thm)],[])).
% 13.18/13.33 tff(1973,plain,
% 13.18/13.33 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s16)) | node4(c_bit0, s16)),
% 13.18/13.33 inference(modus_ponens,[status(thm)],[1972, 1971])).
% 13.18/13.33 tff(1974,plain,
% 13.18/13.33 (~m_counter_cell_v_carry_out(c_bit0, s16)),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[1973, 1359, 1970])).
% 13.18/13.33 tff(1975,plain,
% 13.18/13.33 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s16)) | m_counter_cell_v_carry_out(c_bit0, s16))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s16)) | m_counter_cell_v_carry_out(c_bit0, s16))),
% 13.18/13.33 inference(rewrite,[status(thm)],[])).
% 13.18/13.33 tff(1976,plain,
% 13.18/13.33 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s16)) | m_counter_cell_v_carry_out(c_bit0, s16))),
% 13.18/13.33 inference(quant_inst,[status(thm)],[])).
% 13.18/13.33 tff(1977,plain,
% 13.18/13.33 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s16)) | m_counter_cell_v_carry_out(c_bit0, s16)),
% 13.18/13.33 inference(modus_ponens,[status(thm)],[1976, 1975])).
% 13.18/13.33 tff(1978,plain,
% 13.18/13.33 (~m_counter_cell_v_carry_in(c_bit1, s16)),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[1977, 1374, 1974])).
% 13.18/13.33 tff(1979,plain,
% 13.18/13.33 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s16) | m_counter_cell_v_value(c_bit1, s16) | (~node2(c_bit1, s16)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s16) | m_counter_cell_v_value(c_bit1, s16) | (~node2(c_bit1, s16)))),
% 13.18/13.33 inference(rewrite,[status(thm)],[])).
% 13.18/13.33 tff(1980,plain,
% 13.18/13.33 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s16) | m_counter_cell_v_value(c_bit1, s16) | (~node2(c_bit1, s16)))),
% 13.18/13.33 inference(quant_inst,[status(thm)],[])).
% 13.18/13.33 tff(1981,plain,
% 13.18/13.33 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s16) | m_counter_cell_v_value(c_bit1, s16) | (~node2(c_bit1, s16))),
% 13.18/13.33 inference(modus_ponens,[status(thm)],[1980, 1979])).
% 13.18/13.33 tff(1982,plain,
% 13.18/13.33 (m_counter_cell_v_value(c_bit1, s16) | (~node2(c_bit1, s16))),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[1981, 1498, 1978])).
% 13.18/13.33 tff(1983,plain,
% 13.18/13.33 (~node2(c_bit1, s16)),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[1982, 1966])).
% 13.18/13.33 tff(1984,plain,
% 13.18/13.33 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s16, s17)) | node3(c_bit1, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s16, s17)) | node3(c_bit1, s16, s17))),
% 13.18/13.33 inference(rewrite,[status(thm)],[])).
% 13.18/13.33 tff(1985,plain,
% 13.18/13.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s16, s17)) | node3(c_bit1, s16, s17))),
% 13.18/13.33 inference(quant_inst,[status(thm)],[])).
% 13.18/13.33 tff(1986,plain,
% 13.18/13.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s16, s17)) | node3(c_bit1, s16, s17)),
% 13.18/13.33 inference(modus_ponens,[status(thm)],[1985, 1984])).
% 13.18/13.33 tff(1987,plain,
% 13.18/13.33 (node3(c_bit1, s16, s17)),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[1986, 59, 528])).
% 13.18/13.33 tff(1988,plain,
% 13.18/13.33 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s17)) | node2(c_bit1, s16) | (~node3(c_bit1, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s17)) | node2(c_bit1, s16) | (~node3(c_bit1, s16, s17)))),
% 13.18/13.33 inference(rewrite,[status(thm)],[])).
% 13.18/13.33 tff(1989,plain,
% 13.18/13.33 ((node2(c_bit1, s16) | (~node3(c_bit1, s16, s17)) | (~m_counter_cell_v_value(c_bit1, s17))) <=> ((~m_counter_cell_v_value(c_bit1, s17)) | node2(c_bit1, s16) | (~node3(c_bit1, s16, s17)))),
% 13.18/13.33 inference(rewrite,[status(thm)],[])).
% 13.18/13.33 tff(1990,plain,
% 13.18/13.33 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s16) | (~node3(c_bit1, s16, s17)) | (~m_counter_cell_v_value(c_bit1, s17)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s17)) | node2(c_bit1, s16) | (~node3(c_bit1, s16, s17))))),
% 13.18/13.33 inference(monotonicity,[status(thm)],[1989])).
% 13.18/13.33 tff(1991,plain,
% 13.18/13.33 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s16) | (~node3(c_bit1, s16, s17)) | (~m_counter_cell_v_value(c_bit1, s17)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s17)) | node2(c_bit1, s16) | (~node3(c_bit1, s16, s17)))),
% 13.18/13.33 inference(transitivity,[status(thm)],[1990, 1988])).
% 13.18/13.33 tff(1992,plain,
% 13.18/13.33 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s16) | (~node3(c_bit1, s16, s17)) | (~m_counter_cell_v_value(c_bit1, s17)))),
% 13.18/13.33 inference(quant_inst,[status(thm)],[])).
% 13.18/13.33 tff(1993,plain,
% 13.18/13.33 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s17)) | node2(c_bit1, s16) | (~node3(c_bit1, s16, s17))),
% 13.18/13.33 inference(modus_ponens,[status(thm)],[1992, 1991])).
% 13.18/13.33 tff(1994,plain,
% 13.18/13.33 ((~m_counter_cell_v_value(c_bit1, s17)) | node2(c_bit1, s16)),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[1993, 121, 1987])).
% 13.18/13.33 tff(1995,plain,
% 13.18/13.33 (~m_counter_cell_v_value(c_bit1, s17)),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[1994, 1983])).
% 13.18/13.33 tff(1996,plain,
% 13.18/13.33 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s17)) | m_counter_cell_v_value(c_bit1, s17) | (~node1(c_bit1, s17)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s17)) | m_counter_cell_v_value(c_bit1, s17) | (~node1(c_bit1, s17)))),
% 13.18/13.33 inference(rewrite,[status(thm)],[])).
% 13.18/13.33 tff(1997,plain,
% 13.18/13.33 (((~node1(c_bit1, s17)) | (~m_counter_cell_v_carry_in(c_bit1, s17)) | m_counter_cell_v_value(c_bit1, s17)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s17)) | m_counter_cell_v_value(c_bit1, s17) | (~node1(c_bit1, s17)))),
% 13.18/13.33 inference(rewrite,[status(thm)],[])).
% 13.18/13.33 tff(1998,plain,
% 13.18/13.33 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s17)) | (~m_counter_cell_v_carry_in(c_bit1, s17)) | m_counter_cell_v_value(c_bit1, s17))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s17)) | m_counter_cell_v_value(c_bit1, s17) | (~node1(c_bit1, s17))))),
% 13.18/13.33 inference(monotonicity,[status(thm)],[1997])).
% 13.18/13.33 tff(1999,plain,
% 13.18/13.33 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s17)) | (~m_counter_cell_v_carry_in(c_bit1, s17)) | m_counter_cell_v_value(c_bit1, s17))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s17)) | m_counter_cell_v_value(c_bit1, s17) | (~node1(c_bit1, s17)))),
% 13.18/13.33 inference(transitivity,[status(thm)],[1998, 1996])).
% 13.18/13.33 tff(2000,plain,
% 13.18/13.33 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s17)) | (~m_counter_cell_v_carry_in(c_bit1, s17)) | m_counter_cell_v_value(c_bit1, s17))),
% 13.18/13.33 inference(quant_inst,[status(thm)],[])).
% 13.18/13.33 tff(2001,plain,
% 13.18/13.33 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s17)) | m_counter_cell_v_value(c_bit1, s17) | (~node1(c_bit1, s17))),
% 13.18/13.33 inference(modus_ponens,[status(thm)],[2000, 1999])).
% 13.18/13.33 tff(2002,plain,
% 13.18/13.33 ($false),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[2001, 30, 1995, 1472, 1463])).
% 13.18/13.33 tff(2003,plain,(~node1(c_bit1, s17)), inference(lemma,lemma(discharge,[]))).
% 13.18/13.33 tff(2004,plain,
% 13.18/13.33 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s17, s18)) | node3(c_bit1, s17, s18))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s17, s18)) | node3(c_bit1, s17, s18))),
% 13.18/13.33 inference(rewrite,[status(thm)],[])).
% 13.18/13.33 tff(2005,plain,
% 13.18/13.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s17, s18)) | node3(c_bit1, s17, s18))),
% 13.18/13.33 inference(quant_inst,[status(thm)],[])).
% 13.18/13.33 tff(2006,plain,
% 13.18/13.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s17, s18)) | node3(c_bit1, s17, s18)),
% 13.18/13.33 inference(modus_ponens,[status(thm)],[2005, 2004])).
% 13.18/13.33 tff(2007,plain,
% 13.18/13.33 (node3(c_bit1, s17, s18)),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[2006, 59, 556])).
% 13.18/13.33 tff(2008,plain,
% 13.18/13.33 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s18) | node1(c_bit1, s17) | (~node3(c_bit1, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s18) | node1(c_bit1, s17) | (~node3(c_bit1, s17, s18)))),
% 13.18/13.33 inference(rewrite,[status(thm)],[])).
% 13.18/13.33 tff(2009,plain,
% 13.18/13.33 ((node1(c_bit1, s17) | (~node3(c_bit1, s17, s18)) | m_counter_cell_v_value(c_bit1, s18)) <=> (m_counter_cell_v_value(c_bit1, s18) | node1(c_bit1, s17) | (~node3(c_bit1, s17, s18)))),
% 13.18/13.33 inference(rewrite,[status(thm)],[])).
% 13.18/13.33 tff(2010,plain,
% 13.18/13.33 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s17) | (~node3(c_bit1, s17, s18)) | m_counter_cell_v_value(c_bit1, s18))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s18) | node1(c_bit1, s17) | (~node3(c_bit1, s17, s18))))),
% 13.18/13.33 inference(monotonicity,[status(thm)],[2009])).
% 13.18/13.33 tff(2011,plain,
% 13.18/13.33 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s17) | (~node3(c_bit1, s17, s18)) | m_counter_cell_v_value(c_bit1, s18))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s18) | node1(c_bit1, s17) | (~node3(c_bit1, s17, s18)))),
% 13.18/13.33 inference(transitivity,[status(thm)],[2010, 2008])).
% 13.18/13.33 tff(2012,plain,
% 13.18/13.33 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s17) | (~node3(c_bit1, s17, s18)) | m_counter_cell_v_value(c_bit1, s18))),
% 13.18/13.33 inference(quant_inst,[status(thm)],[])).
% 13.18/13.33 tff(2013,plain,
% 13.18/13.33 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s18) | node1(c_bit1, s17) | (~node3(c_bit1, s17, s18))),
% 13.18/13.33 inference(modus_ponens,[status(thm)],[2012, 2011])).
% 13.18/13.33 tff(2014,plain,
% 13.18/13.33 (m_counter_cell_v_value(c_bit1, s18) | node1(c_bit1, s17)),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[2013, 73, 2007])).
% 13.18/13.33 tff(2015,plain,
% 13.18/13.33 (m_counter_cell_v_value(c_bit1, s18)),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[2014, 2003])).
% 13.18/13.33 tff(2016,plain,
% 13.18/13.33 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s18) | (~node4(c_bit0, s18)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s18) | (~node4(c_bit0, s18)))),
% 13.18/13.33 inference(rewrite,[status(thm)],[])).
% 13.18/13.33 tff(2017,plain,
% 13.18/13.33 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s18) | (~node4(c_bit0, s18)))),
% 13.18/13.33 inference(quant_inst,[status(thm)],[])).
% 13.18/13.33 tff(2018,plain,
% 13.18/13.33 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s18) | (~node4(c_bit0, s18))),
% 13.18/13.33 inference(modus_ponens,[status(thm)],[2017, 2016])).
% 13.18/13.33 tff(2019,plain,
% 13.18/13.33 (~node4(c_bit0, s18)),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[2018, 1344, 568])).
% 13.18/13.33 tff(2020,assumption,(m_counter_cell_v_carry_out(c_bit0, s18)), introduced(assumption)).
% 13.18/13.33 tff(2021,plain,
% 13.18/13.33 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s18)) | node4(c_bit0, s18))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s18)) | node4(c_bit0, s18))),
% 13.18/13.33 inference(rewrite,[status(thm)],[])).
% 13.18/13.33 tff(2022,plain,
% 13.18/13.33 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s18)) | node4(c_bit0, s18))),
% 13.18/13.33 inference(quant_inst,[status(thm)],[])).
% 13.18/13.33 tff(2023,plain,
% 13.18/13.33 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s18)) | node4(c_bit0, s18)),
% 13.18/13.33 inference(modus_ponens,[status(thm)],[2022, 2021])).
% 13.18/13.33 tff(2024,plain,
% 13.18/13.33 ($false),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[2023, 1359, 2020, 2019])).
% 13.18/13.33 tff(2025,plain,(~m_counter_cell_v_carry_out(c_bit0, s18)), inference(lemma,lemma(discharge,[]))).
% 13.18/13.33 tff(2026,plain,
% 13.18/13.33 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s18)) | m_counter_cell_v_carry_out(c_bit0, s18))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s18)) | m_counter_cell_v_carry_out(c_bit0, s18))),
% 13.18/13.33 inference(rewrite,[status(thm)],[])).
% 13.18/13.33 tff(2027,plain,
% 13.18/13.33 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s18)) | m_counter_cell_v_carry_out(c_bit0, s18))),
% 13.18/13.33 inference(quant_inst,[status(thm)],[])).
% 13.18/13.33 tff(2028,plain,
% 13.18/13.33 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s18)) | m_counter_cell_v_carry_out(c_bit0, s18)),
% 13.18/13.33 inference(modus_ponens,[status(thm)],[2027, 2026])).
% 13.18/13.33 tff(2029,plain,
% 13.18/13.33 (~m_counter_cell_v_carry_in(c_bit1, s18)),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[2028, 1374, 2025])).
% 13.18/13.33 tff(2030,assumption,(m_counter_cell_v_value(c_bit1, s18)), introduced(assumption)).
% 13.18/13.33 tff(2031,assumption,(node1(c_bit1, s18)), introduced(assumption)).
% 13.18/13.33 tff(2032,plain,
% 13.18/13.33 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s18) | (~m_counter_cell_v_value(c_bit1, s18)) | (~node1(c_bit1, s18)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s18) | (~m_counter_cell_v_value(c_bit1, s18)) | (~node1(c_bit1, s18)))),
% 13.18/13.33 inference(rewrite,[status(thm)],[])).
% 13.18/13.33 tff(2033,plain,
% 13.18/13.33 (((~node1(c_bit1, s18)) | m_counter_cell_v_carry_in(c_bit1, s18) | (~m_counter_cell_v_value(c_bit1, s18))) <=> (m_counter_cell_v_carry_in(c_bit1, s18) | (~m_counter_cell_v_value(c_bit1, s18)) | (~node1(c_bit1, s18)))),
% 13.18/13.33 inference(rewrite,[status(thm)],[])).
% 13.18/13.33 tff(2034,plain,
% 13.18/13.33 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s18)) | m_counter_cell_v_carry_in(c_bit1, s18) | (~m_counter_cell_v_value(c_bit1, s18)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s18) | (~m_counter_cell_v_value(c_bit1, s18)) | (~node1(c_bit1, s18))))),
% 13.18/13.33 inference(monotonicity,[status(thm)],[2033])).
% 13.18/13.33 tff(2035,plain,
% 13.18/13.33 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s18)) | m_counter_cell_v_carry_in(c_bit1, s18) | (~m_counter_cell_v_value(c_bit1, s18)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s18) | (~m_counter_cell_v_value(c_bit1, s18)) | (~node1(c_bit1, s18)))),
% 13.18/13.33 inference(transitivity,[status(thm)],[2034, 2032])).
% 13.18/13.33 tff(2036,plain,
% 13.18/13.33 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s18)) | m_counter_cell_v_carry_in(c_bit1, s18) | (~m_counter_cell_v_value(c_bit1, s18)))),
% 13.18/13.33 inference(quant_inst,[status(thm)],[])).
% 13.18/13.33 tff(2037,plain,
% 13.18/13.33 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s18) | (~m_counter_cell_v_value(c_bit1, s18)) | (~node1(c_bit1, s18))),
% 13.18/13.33 inference(modus_ponens,[status(thm)],[2036, 2035])).
% 13.18/13.33 tff(2038,plain,
% 13.18/13.33 ($false),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[2037, 1569, 2031, 2030, 2029])).
% 13.18/13.33 tff(2039,plain,((~m_counter_cell_v_value(c_bit1, s18)) | (~node1(c_bit1, s18))), inference(lemma,lemma(discharge,[]))).
% 13.18/13.33 tff(2040,plain,
% 13.18/13.33 (~node1(c_bit1, s18)),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[2039, 2015])).
% 13.18/13.33 tff(2041,plain,
% 13.18/13.33 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s18, s19)) | node3(c_bit1, s18, s19))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s18, s19)) | node3(c_bit1, s18, s19))),
% 13.18/13.33 inference(rewrite,[status(thm)],[])).
% 13.18/13.33 tff(2042,plain,
% 13.18/13.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s18, s19)) | node3(c_bit1, s18, s19))),
% 13.18/13.33 inference(quant_inst,[status(thm)],[])).
% 13.18/13.33 tff(2043,plain,
% 13.18/13.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s18, s19)) | node3(c_bit1, s18, s19)),
% 13.18/13.33 inference(modus_ponens,[status(thm)],[2042, 2041])).
% 13.18/13.33 tff(2044,plain,
% 13.18/13.33 (node3(c_bit1, s18, s19)),
% 13.18/13.33 inference(unit_resolution,[status(thm)],[2043, 59, 587])).
% 13.18/13.33 tff(2045,plain,
% 13.18/13.34 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s19) | node1(c_bit1, s18) | (~node3(c_bit1, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s19) | node1(c_bit1, s18) | (~node3(c_bit1, s18, s19)))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2046,plain,
% 13.18/13.34 ((node1(c_bit1, s18) | (~node3(c_bit1, s18, s19)) | m_counter_cell_v_value(c_bit1, s19)) <=> (m_counter_cell_v_value(c_bit1, s19) | node1(c_bit1, s18) | (~node3(c_bit1, s18, s19)))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2047,plain,
% 13.18/13.34 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s18) | (~node3(c_bit1, s18, s19)) | m_counter_cell_v_value(c_bit1, s19))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s19) | node1(c_bit1, s18) | (~node3(c_bit1, s18, s19))))),
% 13.18/13.34 inference(monotonicity,[status(thm)],[2046])).
% 13.18/13.34 tff(2048,plain,
% 13.18/13.34 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s18) | (~node3(c_bit1, s18, s19)) | m_counter_cell_v_value(c_bit1, s19))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s19) | node1(c_bit1, s18) | (~node3(c_bit1, s18, s19)))),
% 13.18/13.34 inference(transitivity,[status(thm)],[2047, 2045])).
% 13.18/13.34 tff(2049,plain,
% 13.18/13.34 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s18) | (~node3(c_bit1, s18, s19)) | m_counter_cell_v_value(c_bit1, s19))),
% 13.18/13.34 inference(quant_inst,[status(thm)],[])).
% 13.18/13.34 tff(2050,plain,
% 13.18/13.34 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s19) | node1(c_bit1, s18) | (~node3(c_bit1, s18, s19))),
% 13.18/13.34 inference(modus_ponens,[status(thm)],[2049, 2048])).
% 13.18/13.34 tff(2051,plain,
% 13.18/13.34 (m_counter_cell_v_value(c_bit1, s19) | node1(c_bit1, s18)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2050, 73, 2044])).
% 13.18/13.34 tff(2052,plain,
% 13.18/13.34 (m_counter_cell_v_value(c_bit1, s19)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2051, 2040])).
% 13.18/13.34 tff(2053,plain,
% 13.18/13.34 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s19)) | (~m_counter_cell_v_value(c_bit0, s19)) | m_counter_cell_v_carry_out(c_bit0, s19))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s19)) | (~m_counter_cell_v_value(c_bit0, s19)) | m_counter_cell_v_carry_out(c_bit0, s19))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2054,plain,
% 13.18/13.34 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s19)) | (~m_counter_cell_v_value(c_bit0, s19)) | m_counter_cell_v_carry_out(c_bit0, s19))),
% 13.18/13.34 inference(quant_inst,[status(thm)],[])).
% 13.18/13.34 tff(2055,plain,
% 13.18/13.34 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s19)) | (~m_counter_cell_v_value(c_bit0, s19)) | m_counter_cell_v_carry_out(c_bit0, s19)),
% 13.18/13.34 inference(modus_ponens,[status(thm)],[2054, 2053])).
% 13.18/13.34 tff(2056,plain,
% 13.18/13.34 ((~m_counter_cell_v_value(c_bit0, s19)) | m_counter_cell_v_carry_out(c_bit0, s19)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2055, 1390, 603])).
% 13.18/13.34 tff(2057,plain,
% 13.18/13.34 (m_counter_cell_v_carry_out(c_bit0, s19)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2056, 599])).
% 13.18/13.34 tff(2058,plain,
% 13.18/13.34 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s19)) | m_counter_cell_v_carry_in(c_bit1, s19))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s19)) | m_counter_cell_v_carry_in(c_bit1, s19))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2059,plain,
% 13.18/13.34 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s19)) | m_counter_cell_v_carry_in(c_bit1, s19))),
% 13.18/13.34 inference(quant_inst,[status(thm)],[])).
% 13.18/13.34 tff(2060,plain,
% 13.18/13.34 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s19)) | m_counter_cell_v_carry_in(c_bit1, s19)),
% 13.18/13.34 inference(modus_ponens,[status(thm)],[2059, 2058])).
% 13.18/13.34 tff(2061,plain,
% 13.18/13.34 (m_counter_cell_v_carry_in(c_bit1, s19)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2060, 1405, 2057])).
% 13.18/13.34 tff(2062,assumption,(m_counter_cell_v_value(c_bit1, s19)), introduced(assumption)).
% 13.18/13.34 tff(2063,assumption,(node2(c_bit1, s19)), introduced(assumption)).
% 13.18/13.34 tff(2064,plain,
% 13.18/13.34 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s19)) | (~m_counter_cell_v_value(c_bit1, s19)) | (~node2(c_bit1, s19)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s19)) | (~m_counter_cell_v_value(c_bit1, s19)) | (~node2(c_bit1, s19)))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2065,plain,
% 13.18/13.34 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s19)) | (~m_counter_cell_v_value(c_bit1, s19)) | (~node2(c_bit1, s19)))),
% 13.18/13.34 inference(quant_inst,[status(thm)],[])).
% 13.18/13.34 tff(2066,plain,
% 13.18/13.34 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s19)) | (~m_counter_cell_v_value(c_bit1, s19)) | (~node2(c_bit1, s19))),
% 13.18/13.34 inference(modus_ponens,[status(thm)],[2065, 2064])).
% 13.18/13.34 tff(2067,plain,
% 13.18/13.34 ($false),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2066, 93, 2063, 2062, 2061])).
% 13.18/13.34 tff(2068,plain,((~m_counter_cell_v_value(c_bit1, s19)) | (~node2(c_bit1, s19))), inference(lemma,lemma(discharge,[]))).
% 13.18/13.34 tff(2069,plain,
% 13.18/13.34 (~node2(c_bit1, s19)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2068, 2052])).
% 13.18/13.34 tff(2070,plain,
% 13.18/13.34 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s19, s20)) | node3(c_bit1, s19, s20))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s19, s20)) | node3(c_bit1, s19, s20))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2071,plain,
% 13.18/13.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s19, s20)) | node3(c_bit1, s19, s20))),
% 13.18/13.34 inference(quant_inst,[status(thm)],[])).
% 13.18/13.34 tff(2072,plain,
% 13.18/13.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s19, s20)) | node3(c_bit1, s19, s20)),
% 13.18/13.34 inference(modus_ponens,[status(thm)],[2071, 2070])).
% 13.18/13.34 tff(2073,plain,
% 13.18/13.34 (node3(c_bit1, s19, s20)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2072, 59, 615])).
% 13.18/13.34 tff(2074,plain,
% 13.18/13.34 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s20)) | node2(c_bit1, s19) | (~node3(c_bit1, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s20)) | node2(c_bit1, s19) | (~node3(c_bit1, s19, s20)))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2075,plain,
% 13.18/13.34 ((node2(c_bit1, s19) | (~node3(c_bit1, s19, s20)) | (~m_counter_cell_v_value(c_bit1, s20))) <=> ((~m_counter_cell_v_value(c_bit1, s20)) | node2(c_bit1, s19) | (~node3(c_bit1, s19, s20)))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2076,plain,
% 13.18/13.34 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s19) | (~node3(c_bit1, s19, s20)) | (~m_counter_cell_v_value(c_bit1, s20)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s20)) | node2(c_bit1, s19) | (~node3(c_bit1, s19, s20))))),
% 13.18/13.34 inference(monotonicity,[status(thm)],[2075])).
% 13.18/13.34 tff(2077,plain,
% 13.18/13.34 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s19) | (~node3(c_bit1, s19, s20)) | (~m_counter_cell_v_value(c_bit1, s20)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s20)) | node2(c_bit1, s19) | (~node3(c_bit1, s19, s20)))),
% 13.18/13.34 inference(transitivity,[status(thm)],[2076, 2074])).
% 13.18/13.34 tff(2078,plain,
% 13.18/13.34 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s19) | (~node3(c_bit1, s19, s20)) | (~m_counter_cell_v_value(c_bit1, s20)))),
% 13.18/13.34 inference(quant_inst,[status(thm)],[])).
% 13.18/13.34 tff(2079,plain,
% 13.18/13.34 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s20)) | node2(c_bit1, s19) | (~node3(c_bit1, s19, s20))),
% 13.18/13.34 inference(modus_ponens,[status(thm)],[2078, 2077])).
% 13.18/13.34 tff(2080,plain,
% 13.18/13.34 ((~m_counter_cell_v_value(c_bit1, s20)) | node2(c_bit1, s19)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2079, 121, 2073])).
% 13.18/13.34 tff(2081,plain,
% 13.18/13.34 (~m_counter_cell_v_value(c_bit1, s20)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2080, 2069])).
% 13.18/13.34 tff(2082,assumption,(node2(c_bit1, s20)), introduced(assumption)).
% 13.18/13.34 tff(2083,plain,
% 13.18/13.34 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s20) | m_counter_cell_v_value(c_bit1, s20) | (~node2(c_bit1, s20)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s20) | m_counter_cell_v_value(c_bit1, s20) | (~node2(c_bit1, s20)))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2084,plain,
% 13.18/13.34 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s20) | m_counter_cell_v_value(c_bit1, s20) | (~node2(c_bit1, s20)))),
% 13.18/13.34 inference(quant_inst,[status(thm)],[])).
% 13.18/13.34 tff(2085,plain,
% 13.18/13.34 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s20) | m_counter_cell_v_value(c_bit1, s20) | (~node2(c_bit1, s20))),
% 13.18/13.34 inference(modus_ponens,[status(thm)],[2084, 2083])).
% 13.18/13.34 tff(2086,plain,
% 13.18/13.34 ($false),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2085, 1498, 2082, 2081, 1462])).
% 13.18/13.34 tff(2087,plain,(~node2(c_bit1, s20)), inference(lemma,lemma(discharge,[]))).
% 13.18/13.34 tff(2088,plain,
% 13.18/13.34 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s20, s21)) | node3(c_bit1, s20, s21))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s20, s21)) | node3(c_bit1, s20, s21))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2089,plain,
% 13.18/13.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s20, s21)) | node3(c_bit1, s20, s21))),
% 13.18/13.34 inference(quant_inst,[status(thm)],[])).
% 13.18/13.34 tff(2090,plain,
% 13.18/13.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s20, s21)) | node3(c_bit1, s20, s21)),
% 13.18/13.34 inference(modus_ponens,[status(thm)],[2089, 2088])).
% 13.18/13.34 tff(2091,plain,
% 13.18/13.34 (node3(c_bit1, s20, s21)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2090, 59, 646])).
% 13.18/13.34 tff(2092,plain,
% 13.18/13.34 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s21)) | node2(c_bit1, s20) | (~node3(c_bit1, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s21)) | node2(c_bit1, s20) | (~node3(c_bit1, s20, s21)))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2093,plain,
% 13.18/13.34 ((node2(c_bit1, s20) | (~node3(c_bit1, s20, s21)) | (~m_counter_cell_v_value(c_bit1, s21))) <=> ((~m_counter_cell_v_value(c_bit1, s21)) | node2(c_bit1, s20) | (~node3(c_bit1, s20, s21)))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2094,plain,
% 13.18/13.34 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s20) | (~node3(c_bit1, s20, s21)) | (~m_counter_cell_v_value(c_bit1, s21)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s21)) | node2(c_bit1, s20) | (~node3(c_bit1, s20, s21))))),
% 13.18/13.34 inference(monotonicity,[status(thm)],[2093])).
% 13.18/13.34 tff(2095,plain,
% 13.18/13.34 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s20) | (~node3(c_bit1, s20, s21)) | (~m_counter_cell_v_value(c_bit1, s21)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s21)) | node2(c_bit1, s20) | (~node3(c_bit1, s20, s21)))),
% 13.18/13.34 inference(transitivity,[status(thm)],[2094, 2092])).
% 13.18/13.34 tff(2096,plain,
% 13.18/13.34 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s20) | (~node3(c_bit1, s20, s21)) | (~m_counter_cell_v_value(c_bit1, s21)))),
% 13.18/13.34 inference(quant_inst,[status(thm)],[])).
% 13.18/13.34 tff(2097,plain,
% 13.18/13.34 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s21)) | node2(c_bit1, s20) | (~node3(c_bit1, s20, s21))),
% 13.18/13.34 inference(modus_ponens,[status(thm)],[2096, 2095])).
% 13.18/13.34 tff(2098,plain,
% 13.18/13.34 ((~m_counter_cell_v_value(c_bit1, s21)) | node2(c_bit1, s20)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2097, 121, 2091])).
% 13.18/13.34 tff(2099,plain,
% 13.18/13.34 (~m_counter_cell_v_value(c_bit1, s21)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2098, 2087])).
% 13.18/13.34 tff(2100,plain,
% 13.18/13.34 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s21)) | (~m_counter_cell_v_value(c_bit0, s21)) | m_counter_cell_v_carry_out(c_bit0, s21))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s21)) | (~m_counter_cell_v_value(c_bit0, s21)) | m_counter_cell_v_carry_out(c_bit0, s21))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2101,plain,
% 13.18/13.34 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s21)) | (~m_counter_cell_v_value(c_bit0, s21)) | m_counter_cell_v_carry_out(c_bit0, s21))),
% 13.18/13.34 inference(quant_inst,[status(thm)],[])).
% 13.18/13.34 tff(2102,plain,
% 13.18/13.34 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s21)) | (~m_counter_cell_v_value(c_bit0, s21)) | m_counter_cell_v_carry_out(c_bit0, s21)),
% 13.18/13.34 inference(modus_ponens,[status(thm)],[2101, 2100])).
% 13.18/13.34 tff(2103,plain,
% 13.18/13.34 ((~m_counter_cell_v_value(c_bit0, s21)) | m_counter_cell_v_carry_out(c_bit0, s21)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2102, 1390, 662])).
% 13.18/13.34 tff(2104,plain,
% 13.18/13.34 (m_counter_cell_v_carry_out(c_bit0, s21)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2103, 658])).
% 13.18/13.34 tff(2105,plain,
% 13.18/13.34 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s21)) | m_counter_cell_v_carry_in(c_bit1, s21))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s21)) | m_counter_cell_v_carry_in(c_bit1, s21))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2106,plain,
% 13.18/13.34 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s21)) | m_counter_cell_v_carry_in(c_bit1, s21))),
% 13.18/13.34 inference(quant_inst,[status(thm)],[])).
% 13.18/13.34 tff(2107,plain,
% 13.18/13.34 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s21)) | m_counter_cell_v_carry_in(c_bit1, s21)),
% 13.18/13.34 inference(modus_ponens,[status(thm)],[2106, 2105])).
% 13.18/13.34 tff(2108,plain,
% 13.18/13.34 (m_counter_cell_v_carry_in(c_bit1, s21)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2107, 1405, 2104])).
% 13.18/13.34 tff(2109,assumption,(~m_counter_cell_v_value(c_bit1, s21)), introduced(assumption)).
% 13.18/13.34 tff(2110,assumption,(m_counter_cell_v_carry_in(c_bit1, s21)), introduced(assumption)).
% 13.18/13.34 tff(2111,assumption,(node1(c_bit1, s21)), introduced(assumption)).
% 13.18/13.34 tff(2112,plain,
% 13.18/13.34 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s21)) | m_counter_cell_v_value(c_bit1, s21) | (~node1(c_bit1, s21)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s21)) | m_counter_cell_v_value(c_bit1, s21) | (~node1(c_bit1, s21)))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2113,plain,
% 13.18/13.34 (((~node1(c_bit1, s21)) | (~m_counter_cell_v_carry_in(c_bit1, s21)) | m_counter_cell_v_value(c_bit1, s21)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s21)) | m_counter_cell_v_value(c_bit1, s21) | (~node1(c_bit1, s21)))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2114,plain,
% 13.18/13.34 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s21)) | (~m_counter_cell_v_carry_in(c_bit1, s21)) | m_counter_cell_v_value(c_bit1, s21))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s21)) | m_counter_cell_v_value(c_bit1, s21) | (~node1(c_bit1, s21))))),
% 13.18/13.34 inference(monotonicity,[status(thm)],[2113])).
% 13.18/13.34 tff(2115,plain,
% 13.18/13.34 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s21)) | (~m_counter_cell_v_carry_in(c_bit1, s21)) | m_counter_cell_v_value(c_bit1, s21))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s21)) | m_counter_cell_v_value(c_bit1, s21) | (~node1(c_bit1, s21)))),
% 13.18/13.34 inference(transitivity,[status(thm)],[2114, 2112])).
% 13.18/13.34 tff(2116,plain,
% 13.18/13.34 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s21)) | (~m_counter_cell_v_carry_in(c_bit1, s21)) | m_counter_cell_v_value(c_bit1, s21))),
% 13.18/13.34 inference(quant_inst,[status(thm)],[])).
% 13.18/13.34 tff(2117,plain,
% 13.18/13.34 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s21)) | m_counter_cell_v_value(c_bit1, s21) | (~node1(c_bit1, s21))),
% 13.18/13.34 inference(modus_ponens,[status(thm)],[2116, 2115])).
% 13.18/13.34 tff(2118,plain,
% 13.18/13.34 ($false),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2117, 30, 2111, 2110, 2109])).
% 13.18/13.34 tff(2119,plain,(m_counter_cell_v_value(c_bit1, s21) | (~node1(c_bit1, s21)) | (~m_counter_cell_v_carry_in(c_bit1, s21))), inference(lemma,lemma(discharge,[]))).
% 13.18/13.34 tff(2120,plain,
% 13.18/13.34 (m_counter_cell_v_value(c_bit1, s21) | (~node1(c_bit1, s21))),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2119, 2108])).
% 13.18/13.34 tff(2121,plain,
% 13.18/13.34 (~node1(c_bit1, s21)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2120, 2099])).
% 13.18/13.34 tff(2122,plain,
% 13.18/13.34 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s21, s22)) | node3(c_bit1, s21, s22))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s21, s22)) | node3(c_bit1, s21, s22))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2123,plain,
% 13.18/13.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s21, s22)) | node3(c_bit1, s21, s22))),
% 13.18/13.34 inference(quant_inst,[status(thm)],[])).
% 13.18/13.34 tff(2124,plain,
% 13.18/13.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s21, s22)) | node3(c_bit1, s21, s22)),
% 13.18/13.34 inference(modus_ponens,[status(thm)],[2123, 2122])).
% 13.18/13.34 tff(2125,plain,
% 13.18/13.34 (node3(c_bit1, s21, s22)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2124, 59, 674])).
% 13.18/13.34 tff(2126,plain,
% 13.18/13.34 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s22) | node1(c_bit1, s21) | (~node3(c_bit1, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s22) | node1(c_bit1, s21) | (~node3(c_bit1, s21, s22)))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2127,plain,
% 13.18/13.34 ((node1(c_bit1, s21) | (~node3(c_bit1, s21, s22)) | m_counter_cell_v_value(c_bit1, s22)) <=> (m_counter_cell_v_value(c_bit1, s22) | node1(c_bit1, s21) | (~node3(c_bit1, s21, s22)))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2128,plain,
% 13.18/13.34 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s21) | (~node3(c_bit1, s21, s22)) | m_counter_cell_v_value(c_bit1, s22))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s22) | node1(c_bit1, s21) | (~node3(c_bit1, s21, s22))))),
% 13.18/13.34 inference(monotonicity,[status(thm)],[2127])).
% 13.18/13.34 tff(2129,plain,
% 13.18/13.34 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s21) | (~node3(c_bit1, s21, s22)) | m_counter_cell_v_value(c_bit1, s22))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s22) | node1(c_bit1, s21) | (~node3(c_bit1, s21, s22)))),
% 13.18/13.34 inference(transitivity,[status(thm)],[2128, 2126])).
% 13.18/13.34 tff(2130,plain,
% 13.18/13.34 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s21) | (~node3(c_bit1, s21, s22)) | m_counter_cell_v_value(c_bit1, s22))),
% 13.18/13.34 inference(quant_inst,[status(thm)],[])).
% 13.18/13.34 tff(2131,plain,
% 13.18/13.34 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s22) | node1(c_bit1, s21) | (~node3(c_bit1, s21, s22))),
% 13.18/13.34 inference(modus_ponens,[status(thm)],[2130, 2129])).
% 13.18/13.34 tff(2132,plain,
% 13.18/13.34 (m_counter_cell_v_value(c_bit1, s22) | node1(c_bit1, s21)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2131, 73, 2125])).
% 13.18/13.34 tff(2133,plain,
% 13.18/13.34 (m_counter_cell_v_value(c_bit1, s22)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2132, 2121])).
% 13.18/13.34 tff(2134,plain,
% 13.18/13.34 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s22) | (~node4(c_bit0, s22)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s22) | (~node4(c_bit0, s22)))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2135,plain,
% 13.18/13.34 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s22) | (~node4(c_bit0, s22)))),
% 13.18/13.34 inference(quant_inst,[status(thm)],[])).
% 13.18/13.34 tff(2136,plain,
% 13.18/13.34 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s22) | (~node4(c_bit0, s22))),
% 13.18/13.34 inference(modus_ponens,[status(thm)],[2135, 2134])).
% 13.18/13.34 tff(2137,plain,
% 13.18/13.34 (~node4(c_bit0, s22)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2136, 1344, 686])).
% 13.18/13.34 tff(2138,assumption,(m_counter_cell_v_carry_out(c_bit0, s22)), introduced(assumption)).
% 13.18/13.34 tff(2139,plain,
% 13.18/13.34 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s22)) | node4(c_bit0, s22))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s22)) | node4(c_bit0, s22))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2140,plain,
% 13.18/13.34 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s22)) | node4(c_bit0, s22))),
% 13.18/13.34 inference(quant_inst,[status(thm)],[])).
% 13.18/13.34 tff(2141,plain,
% 13.18/13.34 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s22)) | node4(c_bit0, s22)),
% 13.18/13.34 inference(modus_ponens,[status(thm)],[2140, 2139])).
% 13.18/13.34 tff(2142,plain,
% 13.18/13.34 ($false),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2141, 1359, 2138, 2137])).
% 13.18/13.34 tff(2143,plain,(~m_counter_cell_v_carry_out(c_bit0, s22)), inference(lemma,lemma(discharge,[]))).
% 13.18/13.34 tff(2144,assumption,(m_counter_cell_v_carry_in(c_bit1, s22)), introduced(assumption)).
% 13.18/13.34 tff(2145,assumption,(~m_counter_cell_v_carry_out(c_bit0, s22)), introduced(assumption)).
% 13.18/13.34 tff(2146,plain,
% 13.18/13.34 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s22)) | m_counter_cell_v_carry_out(c_bit0, s22))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s22)) | m_counter_cell_v_carry_out(c_bit0, s22))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2147,plain,
% 13.18/13.34 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s22)) | m_counter_cell_v_carry_out(c_bit0, s22))),
% 13.18/13.34 inference(quant_inst,[status(thm)],[])).
% 13.18/13.34 tff(2148,plain,
% 13.18/13.34 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s22)) | m_counter_cell_v_carry_out(c_bit0, s22)),
% 13.18/13.34 inference(modus_ponens,[status(thm)],[2147, 2146])).
% 13.18/13.34 tff(2149,plain,
% 13.18/13.34 ($false),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2148, 1374, 2145, 2144])).
% 13.18/13.34 tff(2150,plain,((~m_counter_cell_v_carry_in(c_bit1, s22)) | m_counter_cell_v_carry_out(c_bit0, s22)), inference(lemma,lemma(discharge,[]))).
% 13.18/13.34 tff(2151,plain,
% 13.18/13.34 (~m_counter_cell_v_carry_in(c_bit1, s22)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2150, 2143])).
% 13.18/13.34 tff(2152,plain,
% 13.18/13.34 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s22) | (~m_counter_cell_v_value(c_bit1, s22)) | (~node1(c_bit1, s22)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s22) | (~m_counter_cell_v_value(c_bit1, s22)) | (~node1(c_bit1, s22)))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2153,plain,
% 13.18/13.34 (((~node1(c_bit1, s22)) | m_counter_cell_v_carry_in(c_bit1, s22) | (~m_counter_cell_v_value(c_bit1, s22))) <=> (m_counter_cell_v_carry_in(c_bit1, s22) | (~m_counter_cell_v_value(c_bit1, s22)) | (~node1(c_bit1, s22)))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2154,plain,
% 13.18/13.34 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s22)) | m_counter_cell_v_carry_in(c_bit1, s22) | (~m_counter_cell_v_value(c_bit1, s22)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s22) | (~m_counter_cell_v_value(c_bit1, s22)) | (~node1(c_bit1, s22))))),
% 13.18/13.34 inference(monotonicity,[status(thm)],[2153])).
% 13.18/13.34 tff(2155,plain,
% 13.18/13.34 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s22)) | m_counter_cell_v_carry_in(c_bit1, s22) | (~m_counter_cell_v_value(c_bit1, s22)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s22) | (~m_counter_cell_v_value(c_bit1, s22)) | (~node1(c_bit1, s22)))),
% 13.18/13.34 inference(transitivity,[status(thm)],[2154, 2152])).
% 13.18/13.34 tff(2156,plain,
% 13.18/13.34 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s22)) | m_counter_cell_v_carry_in(c_bit1, s22) | (~m_counter_cell_v_value(c_bit1, s22)))),
% 13.18/13.34 inference(quant_inst,[status(thm)],[])).
% 13.18/13.34 tff(2157,plain,
% 13.18/13.34 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s22) | (~m_counter_cell_v_value(c_bit1, s22)) | (~node1(c_bit1, s22))),
% 13.18/13.34 inference(modus_ponens,[status(thm)],[2156, 2155])).
% 13.18/13.34 tff(2158,plain,
% 13.18/13.34 ((~m_counter_cell_v_value(c_bit1, s22)) | (~node1(c_bit1, s22))),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2157, 1569, 2151])).
% 13.18/13.34 tff(2159,plain,
% 13.18/13.34 (~node1(c_bit1, s22)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2158, 2133])).
% 13.18/13.34 tff(2160,plain,
% 13.18/13.34 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s22, s23)) | node3(c_bit1, s22, s23))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s22, s23)) | node3(c_bit1, s22, s23))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2161,plain,
% 13.18/13.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s22, s23)) | node3(c_bit1, s22, s23))),
% 13.18/13.34 inference(quant_inst,[status(thm)],[])).
% 13.18/13.34 tff(2162,plain,
% 13.18/13.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s22, s23)) | node3(c_bit1, s22, s23)),
% 13.18/13.34 inference(modus_ponens,[status(thm)],[2161, 2160])).
% 13.18/13.34 tff(2163,plain,
% 13.18/13.34 (node3(c_bit1, s22, s23)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2162, 59, 705])).
% 13.18/13.34 tff(2164,plain,
% 13.18/13.34 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s23) | node1(c_bit1, s22) | (~node3(c_bit1, s22, s23)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s23) | node1(c_bit1, s22) | (~node3(c_bit1, s22, s23)))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2165,plain,
% 13.18/13.34 ((node1(c_bit1, s22) | (~node3(c_bit1, s22, s23)) | m_counter_cell_v_value(c_bit1, s23)) <=> (m_counter_cell_v_value(c_bit1, s23) | node1(c_bit1, s22) | (~node3(c_bit1, s22, s23)))),
% 13.18/13.34 inference(rewrite,[status(thm)],[])).
% 13.18/13.34 tff(2166,plain,
% 13.18/13.34 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s22) | (~node3(c_bit1, s22, s23)) | m_counter_cell_v_value(c_bit1, s23))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s23) | node1(c_bit1, s22) | (~node3(c_bit1, s22, s23))))),
% 13.18/13.34 inference(monotonicity,[status(thm)],[2165])).
% 13.18/13.34 tff(2167,plain,
% 13.18/13.34 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s22) | (~node3(c_bit1, s22, s23)) | m_counter_cell_v_value(c_bit1, s23))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s23) | node1(c_bit1, s22) | (~node3(c_bit1, s22, s23)))),
% 13.18/13.34 inference(transitivity,[status(thm)],[2166, 2164])).
% 13.18/13.34 tff(2168,plain,
% 13.18/13.34 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s22) | (~node3(c_bit1, s22, s23)) | m_counter_cell_v_value(c_bit1, s23))),
% 13.18/13.34 inference(quant_inst,[status(thm)],[])).
% 13.18/13.34 tff(2169,plain,
% 13.18/13.34 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s23) | node1(c_bit1, s22) | (~node3(c_bit1, s22, s23))),
% 13.18/13.34 inference(modus_ponens,[status(thm)],[2168, 2167])).
% 13.18/13.34 tff(2170,plain,
% 13.18/13.34 (m_counter_cell_v_value(c_bit1, s23) | node1(c_bit1, s22)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2169, 73, 2163])).
% 13.18/13.34 tff(2171,plain,
% 13.18/13.34 (m_counter_cell_v_value(c_bit1, s23)),
% 13.18/13.34 inference(unit_resolution,[status(thm)],[2170, 2159])).
% 13.18/13.34 tff(2172,plain,
% 13.18/13.34 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s23)) | (~m_counter_cell_v_value(c_bit0, s23)) | m_counter_cell_v_carry_out(c_bit0, s23))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s23)) | (~m_counter_cell_v_value(c_bit0, s23)) | m_counter_cell_v_carry_out(c_bit0, s23))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2173,plain,
% 13.18/13.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s23)) | (~m_counter_cell_v_value(c_bit0, s23)) | m_counter_cell_v_carry_out(c_bit0, s23))),
% 13.18/13.35 inference(quant_inst,[status(thm)],[])).
% 13.18/13.35 tff(2174,plain,
% 13.18/13.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s23)) | (~m_counter_cell_v_value(c_bit0, s23)) | m_counter_cell_v_carry_out(c_bit0, s23)),
% 13.18/13.35 inference(modus_ponens,[status(thm)],[2173, 2172])).
% 13.18/13.35 tff(2175,plain,
% 13.18/13.35 ((~m_counter_cell_v_value(c_bit0, s23)) | m_counter_cell_v_carry_out(c_bit0, s23)),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2174, 1390, 721])).
% 13.18/13.35 tff(2176,plain,
% 13.18/13.35 (m_counter_cell_v_carry_out(c_bit0, s23)),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2175, 717])).
% 13.18/13.35 tff(2177,plain,
% 13.18/13.35 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s23)) | m_counter_cell_v_carry_in(c_bit1, s23))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s23)) | m_counter_cell_v_carry_in(c_bit1, s23))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2178,plain,
% 13.18/13.35 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s23)) | m_counter_cell_v_carry_in(c_bit1, s23))),
% 13.18/13.35 inference(quant_inst,[status(thm)],[])).
% 13.18/13.35 tff(2179,plain,
% 13.18/13.35 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s23)) | m_counter_cell_v_carry_in(c_bit1, s23)),
% 13.18/13.35 inference(modus_ponens,[status(thm)],[2178, 2177])).
% 13.18/13.35 tff(2180,plain,
% 13.18/13.35 (m_counter_cell_v_carry_in(c_bit1, s23)),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2179, 1405, 2176])).
% 13.18/13.35 tff(2181,plain,
% 13.18/13.35 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s23)) | (~m_counter_cell_v_value(c_bit1, s23)) | (~node2(c_bit1, s23)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s23)) | (~m_counter_cell_v_value(c_bit1, s23)) | (~node2(c_bit1, s23)))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2182,plain,
% 13.18/13.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s23)) | (~m_counter_cell_v_value(c_bit1, s23)) | (~node2(c_bit1, s23)))),
% 13.18/13.35 inference(quant_inst,[status(thm)],[])).
% 13.18/13.35 tff(2183,plain,
% 13.18/13.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s23)) | (~m_counter_cell_v_value(c_bit1, s23)) | (~node2(c_bit1, s23))),
% 13.18/13.35 inference(modus_ponens,[status(thm)],[2182, 2181])).
% 13.18/13.35 tff(2184,plain,
% 13.18/13.35 ($false),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2183, 93, 2180, 2171, 1448])).
% 13.18/13.35 tff(2185,plain,(~node2(c_bit1, s23)), inference(lemma,lemma(discharge,[]))).
% 13.18/13.35 tff(2186,plain,
% 13.18/13.35 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s23, s24)) | node3(c_bit1, s23, s24))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s23, s24)) | node3(c_bit1, s23, s24))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2187,plain,
% 13.18/13.35 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s23, s24)) | node3(c_bit1, s23, s24))),
% 13.18/13.35 inference(quant_inst,[status(thm)],[])).
% 13.18/13.35 tff(2188,plain,
% 13.18/13.35 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s23, s24)) | node3(c_bit1, s23, s24)),
% 13.18/13.35 inference(modus_ponens,[status(thm)],[2187, 2186])).
% 13.18/13.35 tff(2189,plain,
% 13.18/13.35 (node3(c_bit1, s23, s24)),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2188, 59, 733])).
% 13.18/13.35 tff(2190,plain,
% 13.18/13.35 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s24)) | node2(c_bit1, s23) | (~node3(c_bit1, s23, s24)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s24)) | node2(c_bit1, s23) | (~node3(c_bit1, s23, s24)))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2191,plain,
% 13.18/13.35 ((node2(c_bit1, s23) | (~node3(c_bit1, s23, s24)) | (~m_counter_cell_v_value(c_bit1, s24))) <=> ((~m_counter_cell_v_value(c_bit1, s24)) | node2(c_bit1, s23) | (~node3(c_bit1, s23, s24)))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2192,plain,
% 13.18/13.35 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s23) | (~node3(c_bit1, s23, s24)) | (~m_counter_cell_v_value(c_bit1, s24)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s24)) | node2(c_bit1, s23) | (~node3(c_bit1, s23, s24))))),
% 13.18/13.35 inference(monotonicity,[status(thm)],[2191])).
% 13.18/13.35 tff(2193,plain,
% 13.18/13.35 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s23) | (~node3(c_bit1, s23, s24)) | (~m_counter_cell_v_value(c_bit1, s24)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s24)) | node2(c_bit1, s23) | (~node3(c_bit1, s23, s24)))),
% 13.18/13.35 inference(transitivity,[status(thm)],[2192, 2190])).
% 13.18/13.35 tff(2194,plain,
% 13.18/13.35 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s23) | (~node3(c_bit1, s23, s24)) | (~m_counter_cell_v_value(c_bit1, s24)))),
% 13.18/13.35 inference(quant_inst,[status(thm)],[])).
% 13.18/13.35 tff(2195,plain,
% 13.18/13.35 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s24)) | node2(c_bit1, s23) | (~node3(c_bit1, s23, s24))),
% 13.18/13.35 inference(modus_ponens,[status(thm)],[2194, 2193])).
% 13.18/13.35 tff(2196,plain,
% 13.18/13.35 ((~m_counter_cell_v_value(c_bit1, s24)) | node2(c_bit1, s23)),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2195, 121, 2189])).
% 13.18/13.35 tff(2197,plain,
% 13.18/13.35 (~m_counter_cell_v_value(c_bit1, s24)),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2196, 2185])).
% 13.18/13.35 tff(2198,assumption,(node2(c_bit1, s24)), introduced(assumption)).
% 13.18/13.35 tff(2199,plain,
% 13.18/13.35 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s24) | m_counter_cell_v_value(c_bit1, s24) | (~node2(c_bit1, s24)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s24) | m_counter_cell_v_value(c_bit1, s24) | (~node2(c_bit1, s24)))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2200,plain,
% 13.18/13.35 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s24) | m_counter_cell_v_value(c_bit1, s24) | (~node2(c_bit1, s24)))),
% 13.18/13.35 inference(quant_inst,[status(thm)],[])).
% 13.18/13.35 tff(2201,plain,
% 13.18/13.35 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s24) | m_counter_cell_v_value(c_bit1, s24) | (~node2(c_bit1, s24))),
% 13.18/13.35 inference(modus_ponens,[status(thm)],[2200, 2199])).
% 13.18/13.35 tff(2202,plain,
% 13.18/13.35 ($false),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2201, 1498, 2198, 2197, 1447])).
% 13.18/13.35 tff(2203,plain,(~node2(c_bit1, s24)), inference(lemma,lemma(discharge,[]))).
% 13.18/13.35 tff(2204,plain,
% 13.18/13.35 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s24, s25)) | node3(c_bit1, s24, s25))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s24, s25)) | node3(c_bit1, s24, s25))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2205,plain,
% 13.18/13.35 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s24, s25)) | node3(c_bit1, s24, s25))),
% 13.18/13.35 inference(quant_inst,[status(thm)],[])).
% 13.18/13.35 tff(2206,plain,
% 13.18/13.35 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s24, s25)) | node3(c_bit1, s24, s25)),
% 13.18/13.35 inference(modus_ponens,[status(thm)],[2205, 2204])).
% 13.18/13.35 tff(2207,plain,
% 13.18/13.35 (node3(c_bit1, s24, s25)),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2206, 59, 764])).
% 13.18/13.35 tff(2208,plain,
% 13.18/13.35 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s25)) | node2(c_bit1, s24) | (~node3(c_bit1, s24, s25)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s25)) | node2(c_bit1, s24) | (~node3(c_bit1, s24, s25)))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2209,plain,
% 13.18/13.35 ((node2(c_bit1, s24) | (~node3(c_bit1, s24, s25)) | (~m_counter_cell_v_value(c_bit1, s25))) <=> ((~m_counter_cell_v_value(c_bit1, s25)) | node2(c_bit1, s24) | (~node3(c_bit1, s24, s25)))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2210,plain,
% 13.18/13.35 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s24) | (~node3(c_bit1, s24, s25)) | (~m_counter_cell_v_value(c_bit1, s25)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s25)) | node2(c_bit1, s24) | (~node3(c_bit1, s24, s25))))),
% 13.18/13.35 inference(monotonicity,[status(thm)],[2209])).
% 13.18/13.35 tff(2211,plain,
% 13.18/13.35 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s24) | (~node3(c_bit1, s24, s25)) | (~m_counter_cell_v_value(c_bit1, s25)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s25)) | node2(c_bit1, s24) | (~node3(c_bit1, s24, s25)))),
% 13.18/13.35 inference(transitivity,[status(thm)],[2210, 2208])).
% 13.18/13.35 tff(2212,plain,
% 13.18/13.35 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s24) | (~node3(c_bit1, s24, s25)) | (~m_counter_cell_v_value(c_bit1, s25)))),
% 13.18/13.35 inference(quant_inst,[status(thm)],[])).
% 13.18/13.35 tff(2213,plain,
% 13.18/13.35 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s25)) | node2(c_bit1, s24) | (~node3(c_bit1, s24, s25))),
% 13.18/13.35 inference(modus_ponens,[status(thm)],[2212, 2211])).
% 13.18/13.35 tff(2214,plain,
% 13.18/13.35 ((~m_counter_cell_v_value(c_bit1, s25)) | node2(c_bit1, s24)),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2213, 121, 2207])).
% 13.18/13.35 tff(2215,plain,
% 13.18/13.35 (~m_counter_cell_v_value(c_bit1, s25)),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2214, 2203])).
% 13.18/13.35 tff(2216,assumption,(~m_counter_cell_v_value(c_bit1, s25)), introduced(assumption)).
% 13.18/13.35 tff(2217,plain,
% 13.18/13.35 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s25)) | (~m_counter_cell_v_value(c_bit0, s25)) | m_counter_cell_v_carry_out(c_bit0, s25))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s25)) | (~m_counter_cell_v_value(c_bit0, s25)) | m_counter_cell_v_carry_out(c_bit0, s25))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2218,plain,
% 13.18/13.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s25)) | (~m_counter_cell_v_value(c_bit0, s25)) | m_counter_cell_v_carry_out(c_bit0, s25))),
% 13.18/13.35 inference(quant_inst,[status(thm)],[])).
% 13.18/13.35 tff(2219,plain,
% 13.18/13.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s25)) | (~m_counter_cell_v_value(c_bit0, s25)) | m_counter_cell_v_carry_out(c_bit0, s25)),
% 13.18/13.35 inference(modus_ponens,[status(thm)],[2218, 2217])).
% 13.18/13.35 tff(2220,plain,
% 13.18/13.35 ((~m_counter_cell_v_value(c_bit0, s25)) | m_counter_cell_v_carry_out(c_bit0, s25)),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2219, 1390, 780])).
% 13.18/13.35 tff(2221,plain,
% 13.18/13.35 (m_counter_cell_v_carry_out(c_bit0, s25)),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2220, 776])).
% 13.18/13.35 tff(2222,plain,
% 13.18/13.35 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s25)) | m_counter_cell_v_carry_in(c_bit1, s25))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s25)) | m_counter_cell_v_carry_in(c_bit1, s25))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2223,plain,
% 13.18/13.35 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s25)) | m_counter_cell_v_carry_in(c_bit1, s25))),
% 13.18/13.35 inference(quant_inst,[status(thm)],[])).
% 13.18/13.35 tff(2224,plain,
% 13.18/13.35 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s25)) | m_counter_cell_v_carry_in(c_bit1, s25)),
% 13.18/13.35 inference(modus_ponens,[status(thm)],[2223, 2222])).
% 13.18/13.35 tff(2225,plain,
% 13.18/13.35 (m_counter_cell_v_carry_in(c_bit1, s25)),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2224, 1405, 2221])).
% 13.18/13.35 tff(2226,assumption,(node1(c_bit1, s25)), introduced(assumption)).
% 13.18/13.35 tff(2227,plain,
% 13.18/13.35 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s25)) | m_counter_cell_v_value(c_bit1, s25) | (~node1(c_bit1, s25)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s25)) | m_counter_cell_v_value(c_bit1, s25) | (~node1(c_bit1, s25)))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2228,plain,
% 13.18/13.35 (((~node1(c_bit1, s25)) | (~m_counter_cell_v_carry_in(c_bit1, s25)) | m_counter_cell_v_value(c_bit1, s25)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s25)) | m_counter_cell_v_value(c_bit1, s25) | (~node1(c_bit1, s25)))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2229,plain,
% 13.18/13.35 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s25)) | (~m_counter_cell_v_carry_in(c_bit1, s25)) | m_counter_cell_v_value(c_bit1, s25))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s25)) | m_counter_cell_v_value(c_bit1, s25) | (~node1(c_bit1, s25))))),
% 13.18/13.35 inference(monotonicity,[status(thm)],[2228])).
% 13.18/13.35 tff(2230,plain,
% 13.18/13.35 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s25)) | (~m_counter_cell_v_carry_in(c_bit1, s25)) | m_counter_cell_v_value(c_bit1, s25))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s25)) | m_counter_cell_v_value(c_bit1, s25) | (~node1(c_bit1, s25)))),
% 13.18/13.35 inference(transitivity,[status(thm)],[2229, 2227])).
% 13.18/13.35 tff(2231,plain,
% 13.18/13.35 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s25)) | (~m_counter_cell_v_carry_in(c_bit1, s25)) | m_counter_cell_v_value(c_bit1, s25))),
% 13.18/13.35 inference(quant_inst,[status(thm)],[])).
% 13.18/13.35 tff(2232,plain,
% 13.18/13.35 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s25)) | m_counter_cell_v_value(c_bit1, s25) | (~node1(c_bit1, s25))),
% 13.18/13.35 inference(modus_ponens,[status(thm)],[2231, 2230])).
% 13.18/13.35 tff(2233,plain,
% 13.18/13.35 ($false),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2232, 30, 2226, 2225, 2216])).
% 13.18/13.35 tff(2234,plain,(m_counter_cell_v_value(c_bit1, s25) | (~node1(c_bit1, s25))), inference(lemma,lemma(discharge,[]))).
% 13.18/13.35 tff(2235,plain,
% 13.18/13.35 (~node1(c_bit1, s25)),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2234, 2215])).
% 13.18/13.35 tff(2236,plain,
% 13.18/13.35 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s25, s26)) | node3(c_bit1, s25, s26))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s25, s26)) | node3(c_bit1, s25, s26))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2237,plain,
% 13.18/13.35 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s25, s26)) | node3(c_bit1, s25, s26))),
% 13.18/13.35 inference(quant_inst,[status(thm)],[])).
% 13.18/13.35 tff(2238,plain,
% 13.18/13.35 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s25, s26)) | node3(c_bit1, s25, s26)),
% 13.18/13.35 inference(modus_ponens,[status(thm)],[2237, 2236])).
% 13.18/13.35 tff(2239,plain,
% 13.18/13.35 (node3(c_bit1, s25, s26)),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2238, 59, 792])).
% 13.18/13.35 tff(2240,plain,
% 13.18/13.35 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s26) | node1(c_bit1, s25) | (~node3(c_bit1, s25, s26)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s26) | node1(c_bit1, s25) | (~node3(c_bit1, s25, s26)))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2241,plain,
% 13.18/13.35 ((node1(c_bit1, s25) | (~node3(c_bit1, s25, s26)) | m_counter_cell_v_value(c_bit1, s26)) <=> (m_counter_cell_v_value(c_bit1, s26) | node1(c_bit1, s25) | (~node3(c_bit1, s25, s26)))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2242,plain,
% 13.18/13.35 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s25) | (~node3(c_bit1, s25, s26)) | m_counter_cell_v_value(c_bit1, s26))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s26) | node1(c_bit1, s25) | (~node3(c_bit1, s25, s26))))),
% 13.18/13.35 inference(monotonicity,[status(thm)],[2241])).
% 13.18/13.35 tff(2243,plain,
% 13.18/13.35 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s25) | (~node3(c_bit1, s25, s26)) | m_counter_cell_v_value(c_bit1, s26))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s26) | node1(c_bit1, s25) | (~node3(c_bit1, s25, s26)))),
% 13.18/13.35 inference(transitivity,[status(thm)],[2242, 2240])).
% 13.18/13.35 tff(2244,plain,
% 13.18/13.35 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s25) | (~node3(c_bit1, s25, s26)) | m_counter_cell_v_value(c_bit1, s26))),
% 13.18/13.35 inference(quant_inst,[status(thm)],[])).
% 13.18/13.35 tff(2245,plain,
% 13.18/13.35 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s26) | node1(c_bit1, s25) | (~node3(c_bit1, s25, s26))),
% 13.18/13.35 inference(modus_ponens,[status(thm)],[2244, 2243])).
% 13.18/13.35 tff(2246,plain,
% 13.18/13.35 (m_counter_cell_v_value(c_bit1, s26) | node1(c_bit1, s25)),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2245, 73, 2239])).
% 13.18/13.35 tff(2247,plain,
% 13.18/13.35 (m_counter_cell_v_value(c_bit1, s26)),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2246, 2235])).
% 13.18/13.35 tff(2248,plain,
% 13.18/13.35 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s26) | (~node4(c_bit0, s26)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s26) | (~node4(c_bit0, s26)))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2249,plain,
% 13.18/13.35 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s26) | (~node4(c_bit0, s26)))),
% 13.18/13.35 inference(quant_inst,[status(thm)],[])).
% 13.18/13.35 tff(2250,plain,
% 13.18/13.35 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s26) | (~node4(c_bit0, s26))),
% 13.18/13.35 inference(modus_ponens,[status(thm)],[2249, 2248])).
% 13.18/13.35 tff(2251,plain,
% 13.18/13.35 (~node4(c_bit0, s26)),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2250, 1344, 804])).
% 13.18/13.35 tff(2252,assumption,(m_counter_cell_v_carry_out(c_bit0, s26)), introduced(assumption)).
% 13.18/13.35 tff(2253,plain,
% 13.18/13.35 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s26)) | node4(c_bit0, s26))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s26)) | node4(c_bit0, s26))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2254,plain,
% 13.18/13.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s26)) | node4(c_bit0, s26))),
% 13.18/13.35 inference(quant_inst,[status(thm)],[])).
% 13.18/13.35 tff(2255,plain,
% 13.18/13.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s26)) | node4(c_bit0, s26)),
% 13.18/13.35 inference(modus_ponens,[status(thm)],[2254, 2253])).
% 13.18/13.35 tff(2256,plain,
% 13.18/13.35 ($false),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2255, 1359, 2252, 2251])).
% 13.18/13.35 tff(2257,plain,(~m_counter_cell_v_carry_out(c_bit0, s26)), inference(lemma,lemma(discharge,[]))).
% 13.18/13.35 tff(2258,plain,
% 13.18/13.35 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s26)) | m_counter_cell_v_carry_out(c_bit0, s26))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s26)) | m_counter_cell_v_carry_out(c_bit0, s26))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2259,plain,
% 13.18/13.35 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s26)) | m_counter_cell_v_carry_out(c_bit0, s26))),
% 13.18/13.35 inference(quant_inst,[status(thm)],[])).
% 13.18/13.35 tff(2260,plain,
% 13.18/13.35 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s26)) | m_counter_cell_v_carry_out(c_bit0, s26)),
% 13.18/13.35 inference(modus_ponens,[status(thm)],[2259, 2258])).
% 13.18/13.35 tff(2261,plain,
% 13.18/13.35 (~m_counter_cell_v_carry_in(c_bit1, s26)),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2260, 1374, 2257])).
% 13.18/13.35 tff(2262,assumption,(node1(c_bit1, s26)), introduced(assumption)).
% 13.18/13.35 tff(2263,assumption,(m_counter_cell_v_value(c_bit1, s26)), introduced(assumption)).
% 13.18/13.35 tff(2264,plain,
% 13.18/13.35 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s26) | (~m_counter_cell_v_value(c_bit1, s26)) | (~node1(c_bit1, s26)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s26) | (~m_counter_cell_v_value(c_bit1, s26)) | (~node1(c_bit1, s26)))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2265,plain,
% 13.18/13.35 (((~node1(c_bit1, s26)) | m_counter_cell_v_carry_in(c_bit1, s26) | (~m_counter_cell_v_value(c_bit1, s26))) <=> (m_counter_cell_v_carry_in(c_bit1, s26) | (~m_counter_cell_v_value(c_bit1, s26)) | (~node1(c_bit1, s26)))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2266,plain,
% 13.18/13.35 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s26)) | m_counter_cell_v_carry_in(c_bit1, s26) | (~m_counter_cell_v_value(c_bit1, s26)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s26) | (~m_counter_cell_v_value(c_bit1, s26)) | (~node1(c_bit1, s26))))),
% 13.18/13.35 inference(monotonicity,[status(thm)],[2265])).
% 13.18/13.35 tff(2267,plain,
% 13.18/13.35 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s26)) | m_counter_cell_v_carry_in(c_bit1, s26) | (~m_counter_cell_v_value(c_bit1, s26)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s26) | (~m_counter_cell_v_value(c_bit1, s26)) | (~node1(c_bit1, s26)))),
% 13.18/13.35 inference(transitivity,[status(thm)],[2266, 2264])).
% 13.18/13.35 tff(2268,plain,
% 13.18/13.35 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s26)) | m_counter_cell_v_carry_in(c_bit1, s26) | (~m_counter_cell_v_value(c_bit1, s26)))),
% 13.18/13.35 inference(quant_inst,[status(thm)],[])).
% 13.18/13.35 tff(2269,plain,
% 13.18/13.35 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s26) | (~m_counter_cell_v_value(c_bit1, s26)) | (~node1(c_bit1, s26))),
% 13.18/13.35 inference(modus_ponens,[status(thm)],[2268, 2267])).
% 13.18/13.35 tff(2270,plain,
% 13.18/13.35 ($false),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2269, 1569, 2263, 2262, 2261])).
% 13.18/13.35 tff(2271,plain,((~m_counter_cell_v_value(c_bit1, s26)) | (~node1(c_bit1, s26))), inference(lemma,lemma(discharge,[]))).
% 13.18/13.35 tff(2272,plain,
% 13.18/13.35 (~node1(c_bit1, s26)),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2271, 2247])).
% 13.18/13.35 tff(2273,plain,
% 13.18/13.35 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s26, s27)) | node3(c_bit1, s26, s27))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s26, s27)) | node3(c_bit1, s26, s27))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2274,plain,
% 13.18/13.35 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s26, s27)) | node3(c_bit1, s26, s27))),
% 13.18/13.35 inference(quant_inst,[status(thm)],[])).
% 13.18/13.35 tff(2275,plain,
% 13.18/13.35 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s26, s27)) | node3(c_bit1, s26, s27)),
% 13.18/13.35 inference(modus_ponens,[status(thm)],[2274, 2273])).
% 13.18/13.35 tff(2276,plain,
% 13.18/13.35 (node3(c_bit1, s26, s27)),
% 13.18/13.35 inference(unit_resolution,[status(thm)],[2275, 59, 823])).
% 13.18/13.35 tff(2277,plain,
% 13.18/13.35 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s27) | node1(c_bit1, s26) | (~node3(c_bit1, s26, s27)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s27) | node1(c_bit1, s26) | (~node3(c_bit1, s26, s27)))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2278,plain,
% 13.18/13.35 ((node1(c_bit1, s26) | (~node3(c_bit1, s26, s27)) | m_counter_cell_v_value(c_bit1, s27)) <=> (m_counter_cell_v_value(c_bit1, s27) | node1(c_bit1, s26) | (~node3(c_bit1, s26, s27)))),
% 13.18/13.35 inference(rewrite,[status(thm)],[])).
% 13.18/13.35 tff(2279,plain,
% 13.18/13.35 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s26) | (~node3(c_bit1, s26, s27)) | m_counter_cell_v_value(c_bit1, s27))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s27) | node1(c_bit1, s26) | (~node3(c_bit1, s26, s27))))),
% 13.18/13.35 inference(monotonicity,[status(thm)],[2278])).
% 13.18/13.35 tff(2280,plain,
% 13.18/13.35 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s26) | (~node3(c_bit1, s26, s27)) | m_counter_cell_v_value(c_bit1, s27))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s27) | node1(c_bit1, s26) | (~node3(c_bit1, s26, s27)))),
% 13.18/13.35 inference(transitivity,[status(thm)],[2279, 2277])).
% 13.18/13.35 tff(2281,plain,
% 13.18/13.35 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s26) | (~node3(c_bit1, s26, s27)) | m_counter_cell_v_value(c_bit1, s27))),
% 13.18/13.36 inference(quant_inst,[status(thm)],[])).
% 13.18/13.36 tff(2282,plain,
% 13.18/13.36 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s27) | node1(c_bit1, s26) | (~node3(c_bit1, s26, s27))),
% 13.18/13.36 inference(modus_ponens,[status(thm)],[2281, 2280])).
% 13.18/13.36 tff(2283,plain,
% 13.18/13.36 (m_counter_cell_v_value(c_bit1, s27) | node1(c_bit1, s26)),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2282, 73, 2276])).
% 13.18/13.36 tff(2284,plain,
% 13.18/13.36 (m_counter_cell_v_value(c_bit1, s27)),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2283, 2272])).
% 13.18/13.36 tff(2285,assumption,(node2(c_bit1, s27)), introduced(assumption)).
% 13.18/13.36 tff(2286,plain,
% 13.18/13.36 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s27)) | (~m_counter_cell_v_value(c_bit1, s27)) | (~node2(c_bit1, s27)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s27)) | (~m_counter_cell_v_value(c_bit1, s27)) | (~node2(c_bit1, s27)))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2287,plain,
% 13.18/13.36 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s27)) | (~m_counter_cell_v_value(c_bit1, s27)) | (~node2(c_bit1, s27)))),
% 13.18/13.36 inference(quant_inst,[status(thm)],[])).
% 13.18/13.36 tff(2288,plain,
% 13.18/13.36 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s27)) | (~m_counter_cell_v_value(c_bit1, s27)) | (~node2(c_bit1, s27))),
% 13.18/13.36 inference(modus_ponens,[status(thm)],[2287, 2286])).
% 13.18/13.36 tff(2289,plain,
% 13.18/13.36 ($false),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2288, 93, 2285, 2284, 1433])).
% 13.18/13.36 tff(2290,plain,(~node2(c_bit1, s27)), inference(lemma,lemma(discharge,[]))).
% 13.18/13.36 tff(2291,plain,
% 13.18/13.36 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s27, s28)) | node3(c_bit1, s27, s28))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s27, s28)) | node3(c_bit1, s27, s28))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2292,plain,
% 13.18/13.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s27, s28)) | node3(c_bit1, s27, s28))),
% 13.18/13.36 inference(quant_inst,[status(thm)],[])).
% 13.18/13.36 tff(2293,plain,
% 13.18/13.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s27, s28)) | node3(c_bit1, s27, s28)),
% 13.18/13.36 inference(modus_ponens,[status(thm)],[2292, 2291])).
% 13.18/13.36 tff(2294,plain,
% 13.18/13.36 (node3(c_bit1, s27, s28)),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2293, 59, 851])).
% 13.18/13.36 tff(2295,plain,
% 13.18/13.36 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s28)) | node2(c_bit1, s27) | (~node3(c_bit1, s27, s28)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s28)) | node2(c_bit1, s27) | (~node3(c_bit1, s27, s28)))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2296,plain,
% 13.18/13.36 ((node2(c_bit1, s27) | (~node3(c_bit1, s27, s28)) | (~m_counter_cell_v_value(c_bit1, s28))) <=> ((~m_counter_cell_v_value(c_bit1, s28)) | node2(c_bit1, s27) | (~node3(c_bit1, s27, s28)))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2297,plain,
% 13.18/13.36 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s27) | (~node3(c_bit1, s27, s28)) | (~m_counter_cell_v_value(c_bit1, s28)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s28)) | node2(c_bit1, s27) | (~node3(c_bit1, s27, s28))))),
% 13.18/13.36 inference(monotonicity,[status(thm)],[2296])).
% 13.18/13.36 tff(2298,plain,
% 13.18/13.36 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s27) | (~node3(c_bit1, s27, s28)) | (~m_counter_cell_v_value(c_bit1, s28)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s28)) | node2(c_bit1, s27) | (~node3(c_bit1, s27, s28)))),
% 13.18/13.36 inference(transitivity,[status(thm)],[2297, 2295])).
% 13.18/13.36 tff(2299,plain,
% 13.18/13.36 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s27) | (~node3(c_bit1, s27, s28)) | (~m_counter_cell_v_value(c_bit1, s28)))),
% 13.18/13.36 inference(quant_inst,[status(thm)],[])).
% 13.18/13.36 tff(2300,plain,
% 13.18/13.36 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s28)) | node2(c_bit1, s27) | (~node3(c_bit1, s27, s28))),
% 13.18/13.36 inference(modus_ponens,[status(thm)],[2299, 2298])).
% 13.18/13.36 tff(2301,plain,
% 13.18/13.36 ((~m_counter_cell_v_value(c_bit1, s28)) | node2(c_bit1, s27)),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2300, 121, 2294])).
% 13.18/13.36 tff(2302,plain,
% 13.18/13.36 (~m_counter_cell_v_value(c_bit1, s28)),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2301, 2290])).
% 13.18/13.36 tff(2303,plain,
% 13.18/13.36 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s28) | (~node4(c_bit0, s28)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s28) | (~node4(c_bit0, s28)))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2304,plain,
% 13.18/13.36 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s28) | (~node4(c_bit0, s28)))),
% 13.18/13.36 inference(quant_inst,[status(thm)],[])).
% 13.18/13.36 tff(2305,plain,
% 13.18/13.36 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s28) | (~node4(c_bit0, s28))),
% 13.18/13.36 inference(modus_ponens,[status(thm)],[2304, 2303])).
% 13.18/13.36 tff(2306,plain,
% 13.18/13.36 (~node4(c_bit0, s28)),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2305, 1344, 863])).
% 13.18/13.36 tff(2307,assumption,(m_counter_cell_v_carry_out(c_bit0, s28)), introduced(assumption)).
% 13.18/13.36 tff(2308,plain,
% 13.18/13.36 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s28)) | node4(c_bit0, s28))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s28)) | node4(c_bit0, s28))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2309,plain,
% 13.18/13.36 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s28)) | node4(c_bit0, s28))),
% 13.18/13.36 inference(quant_inst,[status(thm)],[])).
% 13.18/13.36 tff(2310,plain,
% 13.18/13.36 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s28)) | node4(c_bit0, s28)),
% 13.18/13.36 inference(modus_ponens,[status(thm)],[2309, 2308])).
% 13.18/13.36 tff(2311,plain,
% 13.18/13.36 ($false),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2310, 1359, 2307, 2306])).
% 13.18/13.36 tff(2312,plain,(~m_counter_cell_v_carry_out(c_bit0, s28)), inference(lemma,lemma(discharge,[]))).
% 13.18/13.36 tff(2313,plain,
% 13.18/13.36 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s28)) | m_counter_cell_v_carry_out(c_bit0, s28))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s28)) | m_counter_cell_v_carry_out(c_bit0, s28))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2314,plain,
% 13.18/13.36 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s28)) | m_counter_cell_v_carry_out(c_bit0, s28))),
% 13.18/13.36 inference(quant_inst,[status(thm)],[])).
% 13.18/13.36 tff(2315,plain,
% 13.18/13.36 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s28)) | m_counter_cell_v_carry_out(c_bit0, s28)),
% 13.18/13.36 inference(modus_ponens,[status(thm)],[2314, 2313])).
% 13.18/13.36 tff(2316,plain,
% 13.18/13.36 (~m_counter_cell_v_carry_in(c_bit1, s28)),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2315, 1374, 2312])).
% 13.18/13.36 tff(2317,assumption,(node2(c_bit1, s28)), introduced(assumption)).
% 13.18/13.36 tff(2318,assumption,(~m_counter_cell_v_value(c_bit1, s28)), introduced(assumption)).
% 13.18/13.36 tff(2319,plain,
% 13.18/13.36 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s28) | m_counter_cell_v_value(c_bit1, s28) | (~node2(c_bit1, s28)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s28) | m_counter_cell_v_value(c_bit1, s28) | (~node2(c_bit1, s28)))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2320,plain,
% 13.18/13.36 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s28) | m_counter_cell_v_value(c_bit1, s28) | (~node2(c_bit1, s28)))),
% 13.18/13.36 inference(quant_inst,[status(thm)],[])).
% 13.18/13.36 tff(2321,plain,
% 13.18/13.36 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s28) | m_counter_cell_v_value(c_bit1, s28) | (~node2(c_bit1, s28))),
% 13.18/13.36 inference(modus_ponens,[status(thm)],[2320, 2319])).
% 13.18/13.36 tff(2322,plain,
% 13.18/13.36 ($false),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2321, 1498, 2318, 2317, 2316])).
% 13.18/13.36 tff(2323,plain,(m_counter_cell_v_value(c_bit1, s28) | (~node2(c_bit1, s28))), inference(lemma,lemma(discharge,[]))).
% 13.18/13.36 tff(2324,plain,
% 13.18/13.36 (~node2(c_bit1, s28)),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2323, 2302])).
% 13.18/13.36 tff(2325,plain,
% 13.18/13.36 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s28, s29)) | node3(c_bit1, s28, s29))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s28, s29)) | node3(c_bit1, s28, s29))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2326,plain,
% 13.18/13.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s28, s29)) | node3(c_bit1, s28, s29))),
% 13.18/13.36 inference(quant_inst,[status(thm)],[])).
% 13.18/13.36 tff(2327,plain,
% 13.18/13.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s28, s29)) | node3(c_bit1, s28, s29)),
% 13.18/13.36 inference(modus_ponens,[status(thm)],[2326, 2325])).
% 13.18/13.36 tff(2328,plain,
% 13.18/13.36 (node3(c_bit1, s28, s29)),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2327, 59, 882])).
% 13.18/13.36 tff(2329,plain,
% 13.18/13.36 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s29)) | node2(c_bit1, s28) | (~node3(c_bit1, s28, s29)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s29)) | node2(c_bit1, s28) | (~node3(c_bit1, s28, s29)))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2330,plain,
% 13.18/13.36 ((node2(c_bit1, s28) | (~node3(c_bit1, s28, s29)) | (~m_counter_cell_v_value(c_bit1, s29))) <=> ((~m_counter_cell_v_value(c_bit1, s29)) | node2(c_bit1, s28) | (~node3(c_bit1, s28, s29)))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2331,plain,
% 13.18/13.36 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s28) | (~node3(c_bit1, s28, s29)) | (~m_counter_cell_v_value(c_bit1, s29)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s29)) | node2(c_bit1, s28) | (~node3(c_bit1, s28, s29))))),
% 13.18/13.36 inference(monotonicity,[status(thm)],[2330])).
% 13.18/13.36 tff(2332,plain,
% 13.18/13.36 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s28) | (~node3(c_bit1, s28, s29)) | (~m_counter_cell_v_value(c_bit1, s29)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s29)) | node2(c_bit1, s28) | (~node3(c_bit1, s28, s29)))),
% 13.18/13.36 inference(transitivity,[status(thm)],[2331, 2329])).
% 13.18/13.36 tff(2333,plain,
% 13.18/13.36 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s28) | (~node3(c_bit1, s28, s29)) | (~m_counter_cell_v_value(c_bit1, s29)))),
% 13.18/13.36 inference(quant_inst,[status(thm)],[])).
% 13.18/13.36 tff(2334,plain,
% 13.18/13.36 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s29)) | node2(c_bit1, s28) | (~node3(c_bit1, s28, s29))),
% 13.18/13.36 inference(modus_ponens,[status(thm)],[2333, 2332])).
% 13.18/13.36 tff(2335,plain,
% 13.18/13.36 ((~m_counter_cell_v_value(c_bit1, s29)) | node2(c_bit1, s28)),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2334, 121, 2328])).
% 13.18/13.36 tff(2336,plain,
% 13.18/13.36 (~m_counter_cell_v_value(c_bit1, s29)),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2335, 2324])).
% 13.18/13.36 tff(2337,plain,
% 13.18/13.36 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s29)) | (~m_counter_cell_v_value(c_bit0, s29)) | m_counter_cell_v_carry_out(c_bit0, s29))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s29)) | (~m_counter_cell_v_value(c_bit0, s29)) | m_counter_cell_v_carry_out(c_bit0, s29))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2338,plain,
% 13.18/13.36 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s29)) | (~m_counter_cell_v_value(c_bit0, s29)) | m_counter_cell_v_carry_out(c_bit0, s29))),
% 13.18/13.36 inference(quant_inst,[status(thm)],[])).
% 13.18/13.36 tff(2339,plain,
% 13.18/13.36 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s29)) | (~m_counter_cell_v_value(c_bit0, s29)) | m_counter_cell_v_carry_out(c_bit0, s29)),
% 13.18/13.36 inference(modus_ponens,[status(thm)],[2338, 2337])).
% 13.18/13.36 tff(2340,plain,
% 13.18/13.36 ((~m_counter_cell_v_value(c_bit0, s29)) | m_counter_cell_v_carry_out(c_bit0, s29)),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2339, 1390, 898])).
% 13.18/13.36 tff(2341,plain,
% 13.18/13.36 (m_counter_cell_v_carry_out(c_bit0, s29)),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2340, 894])).
% 13.18/13.36 tff(2342,plain,
% 13.18/13.36 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s29)) | m_counter_cell_v_carry_in(c_bit1, s29))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s29)) | m_counter_cell_v_carry_in(c_bit1, s29))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2343,plain,
% 13.18/13.36 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s29)) | m_counter_cell_v_carry_in(c_bit1, s29))),
% 13.18/13.36 inference(quant_inst,[status(thm)],[])).
% 13.18/13.36 tff(2344,plain,
% 13.18/13.36 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s29)) | m_counter_cell_v_carry_in(c_bit1, s29)),
% 13.18/13.36 inference(modus_ponens,[status(thm)],[2343, 2342])).
% 13.18/13.36 tff(2345,plain,
% 13.18/13.36 (m_counter_cell_v_carry_in(c_bit1, s29)),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2344, 1405, 2341])).
% 13.18/13.36 tff(2346,assumption,(~m_counter_cell_v_value(c_bit1, s29)), introduced(assumption)).
% 13.18/13.36 tff(2347,assumption,(m_counter_cell_v_carry_in(c_bit1, s29)), introduced(assumption)).
% 13.18/13.36 tff(2348,assumption,(node1(c_bit1, s29)), introduced(assumption)).
% 13.18/13.36 tff(2349,plain,
% 13.18/13.36 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s29)) | m_counter_cell_v_value(c_bit1, s29) | (~node1(c_bit1, s29)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s29)) | m_counter_cell_v_value(c_bit1, s29) | (~node1(c_bit1, s29)))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2350,plain,
% 13.18/13.36 (((~node1(c_bit1, s29)) | (~m_counter_cell_v_carry_in(c_bit1, s29)) | m_counter_cell_v_value(c_bit1, s29)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s29)) | m_counter_cell_v_value(c_bit1, s29) | (~node1(c_bit1, s29)))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2351,plain,
% 13.18/13.36 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s29)) | (~m_counter_cell_v_carry_in(c_bit1, s29)) | m_counter_cell_v_value(c_bit1, s29))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s29)) | m_counter_cell_v_value(c_bit1, s29) | (~node1(c_bit1, s29))))),
% 13.18/13.36 inference(monotonicity,[status(thm)],[2350])).
% 13.18/13.36 tff(2352,plain,
% 13.18/13.36 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s29)) | (~m_counter_cell_v_carry_in(c_bit1, s29)) | m_counter_cell_v_value(c_bit1, s29))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s29)) | m_counter_cell_v_value(c_bit1, s29) | (~node1(c_bit1, s29)))),
% 13.18/13.36 inference(transitivity,[status(thm)],[2351, 2349])).
% 13.18/13.36 tff(2353,plain,
% 13.18/13.36 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s29)) | (~m_counter_cell_v_carry_in(c_bit1, s29)) | m_counter_cell_v_value(c_bit1, s29))),
% 13.18/13.36 inference(quant_inst,[status(thm)],[])).
% 13.18/13.36 tff(2354,plain,
% 13.18/13.36 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s29)) | m_counter_cell_v_value(c_bit1, s29) | (~node1(c_bit1, s29))),
% 13.18/13.36 inference(modus_ponens,[status(thm)],[2353, 2352])).
% 13.18/13.36 tff(2355,plain,
% 13.18/13.36 ($false),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2354, 30, 2348, 2347, 2346])).
% 13.18/13.36 tff(2356,plain,(m_counter_cell_v_value(c_bit1, s29) | (~node1(c_bit1, s29)) | (~m_counter_cell_v_carry_in(c_bit1, s29))), inference(lemma,lemma(discharge,[]))).
% 13.18/13.36 tff(2357,plain,
% 13.18/13.36 (m_counter_cell_v_value(c_bit1, s29) | (~node1(c_bit1, s29))),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2356, 2345])).
% 13.18/13.36 tff(2358,plain,
% 13.18/13.36 (~node1(c_bit1, s29)),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2357, 2336])).
% 13.18/13.36 tff(2359,plain,
% 13.18/13.36 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s29, s30)) | node3(c_bit1, s29, s30))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s29, s30)) | node3(c_bit1, s29, s30))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2360,plain,
% 13.18/13.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s29, s30)) | node3(c_bit1, s29, s30))),
% 13.18/13.36 inference(quant_inst,[status(thm)],[])).
% 13.18/13.36 tff(2361,plain,
% 13.18/13.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s29, s30)) | node3(c_bit1, s29, s30)),
% 13.18/13.36 inference(modus_ponens,[status(thm)],[2360, 2359])).
% 13.18/13.36 tff(2362,plain,
% 13.18/13.36 (node3(c_bit1, s29, s30)),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2361, 59, 910])).
% 13.18/13.36 tff(2363,plain,
% 13.18/13.36 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s30) | node1(c_bit1, s29) | (~node3(c_bit1, s29, s30)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s30) | node1(c_bit1, s29) | (~node3(c_bit1, s29, s30)))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2364,plain,
% 13.18/13.36 ((node1(c_bit1, s29) | (~node3(c_bit1, s29, s30)) | m_counter_cell_v_value(c_bit1, s30)) <=> (m_counter_cell_v_value(c_bit1, s30) | node1(c_bit1, s29) | (~node3(c_bit1, s29, s30)))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2365,plain,
% 13.18/13.36 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s29) | (~node3(c_bit1, s29, s30)) | m_counter_cell_v_value(c_bit1, s30))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s30) | node1(c_bit1, s29) | (~node3(c_bit1, s29, s30))))),
% 13.18/13.36 inference(monotonicity,[status(thm)],[2364])).
% 13.18/13.36 tff(2366,plain,
% 13.18/13.36 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s29) | (~node3(c_bit1, s29, s30)) | m_counter_cell_v_value(c_bit1, s30))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s30) | node1(c_bit1, s29) | (~node3(c_bit1, s29, s30)))),
% 13.18/13.36 inference(transitivity,[status(thm)],[2365, 2363])).
% 13.18/13.36 tff(2367,plain,
% 13.18/13.36 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s29) | (~node3(c_bit1, s29, s30)) | m_counter_cell_v_value(c_bit1, s30))),
% 13.18/13.36 inference(quant_inst,[status(thm)],[])).
% 13.18/13.36 tff(2368,plain,
% 13.18/13.36 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s30) | node1(c_bit1, s29) | (~node3(c_bit1, s29, s30))),
% 13.18/13.36 inference(modus_ponens,[status(thm)],[2367, 2366])).
% 13.18/13.36 tff(2369,plain,
% 13.18/13.36 (m_counter_cell_v_value(c_bit1, s30) | node1(c_bit1, s29)),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2368, 73, 2362])).
% 13.18/13.36 tff(2370,plain,
% 13.18/13.36 (m_counter_cell_v_value(c_bit1, s30)),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2369, 2358])).
% 13.18/13.36 tff(2371,plain,
% 13.18/13.36 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s30) | (~m_counter_cell_v_value(c_bit1, s30)) | (~node1(c_bit1, s30)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s30) | (~m_counter_cell_v_value(c_bit1, s30)) | (~node1(c_bit1, s30)))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2372,plain,
% 13.18/13.36 (((~node1(c_bit1, s30)) | m_counter_cell_v_carry_in(c_bit1, s30) | (~m_counter_cell_v_value(c_bit1, s30))) <=> (m_counter_cell_v_carry_in(c_bit1, s30) | (~m_counter_cell_v_value(c_bit1, s30)) | (~node1(c_bit1, s30)))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2373,plain,
% 13.18/13.36 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s30)) | m_counter_cell_v_carry_in(c_bit1, s30) | (~m_counter_cell_v_value(c_bit1, s30)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s30) | (~m_counter_cell_v_value(c_bit1, s30)) | (~node1(c_bit1, s30))))),
% 13.18/13.36 inference(monotonicity,[status(thm)],[2372])).
% 13.18/13.36 tff(2374,plain,
% 13.18/13.36 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s30)) | m_counter_cell_v_carry_in(c_bit1, s30) | (~m_counter_cell_v_value(c_bit1, s30)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s30) | (~m_counter_cell_v_value(c_bit1, s30)) | (~node1(c_bit1, s30)))),
% 13.18/13.36 inference(transitivity,[status(thm)],[2373, 2371])).
% 13.18/13.36 tff(2375,plain,
% 13.18/13.36 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s30)) | m_counter_cell_v_carry_in(c_bit1, s30) | (~m_counter_cell_v_value(c_bit1, s30)))),
% 13.18/13.36 inference(quant_inst,[status(thm)],[])).
% 13.18/13.36 tff(2376,plain,
% 13.18/13.36 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s30) | (~m_counter_cell_v_value(c_bit1, s30)) | (~node1(c_bit1, s30))),
% 13.18/13.36 inference(modus_ponens,[status(thm)],[2375, 2374])).
% 13.18/13.36 tff(2377,plain,
% 13.18/13.36 ($false),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2376, 1569, 2370, 1424, 1423])).
% 13.18/13.36 tff(2378,plain,(~node1(c_bit1, s30)), inference(lemma,lemma(discharge,[]))).
% 13.18/13.36 tff(2379,plain,
% 13.18/13.36 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s30, s31)) | node3(c_bit1, s30, s31))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s30, s31)) | node3(c_bit1, s30, s31))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2380,plain,
% 13.18/13.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s30, s31)) | node3(c_bit1, s30, s31))),
% 13.18/13.36 inference(quant_inst,[status(thm)],[])).
% 13.18/13.36 tff(2381,plain,
% 13.18/13.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s30, s31)) | node3(c_bit1, s30, s31)),
% 13.18/13.36 inference(modus_ponens,[status(thm)],[2380, 2379])).
% 13.18/13.36 tff(2382,plain,
% 13.18/13.36 (node3(c_bit1, s30, s31)),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2381, 59, 941])).
% 13.18/13.36 tff(2383,plain,
% 13.18/13.36 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s31) | node1(c_bit1, s30) | (~node3(c_bit1, s30, s31)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s31) | node1(c_bit1, s30) | (~node3(c_bit1, s30, s31)))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2384,plain,
% 13.18/13.36 ((node1(c_bit1, s30) | (~node3(c_bit1, s30, s31)) | m_counter_cell_v_value(c_bit1, s31)) <=> (m_counter_cell_v_value(c_bit1, s31) | node1(c_bit1, s30) | (~node3(c_bit1, s30, s31)))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2385,plain,
% 13.18/13.36 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s30) | (~node3(c_bit1, s30, s31)) | m_counter_cell_v_value(c_bit1, s31))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s31) | node1(c_bit1, s30) | (~node3(c_bit1, s30, s31))))),
% 13.18/13.36 inference(monotonicity,[status(thm)],[2384])).
% 13.18/13.36 tff(2386,plain,
% 13.18/13.36 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s30) | (~node3(c_bit1, s30, s31)) | m_counter_cell_v_value(c_bit1, s31))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s31) | node1(c_bit1, s30) | (~node3(c_bit1, s30, s31)))),
% 13.18/13.36 inference(transitivity,[status(thm)],[2385, 2383])).
% 13.18/13.36 tff(2387,plain,
% 13.18/13.36 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s30) | (~node3(c_bit1, s30, s31)) | m_counter_cell_v_value(c_bit1, s31))),
% 13.18/13.36 inference(quant_inst,[status(thm)],[])).
% 13.18/13.36 tff(2388,plain,
% 13.18/13.36 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s31) | node1(c_bit1, s30) | (~node3(c_bit1, s30, s31))),
% 13.18/13.36 inference(modus_ponens,[status(thm)],[2387, 2386])).
% 13.18/13.36 tff(2389,plain,
% 13.18/13.36 (m_counter_cell_v_value(c_bit1, s31) | node1(c_bit1, s30)),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2388, 73, 2382])).
% 13.18/13.36 tff(2390,plain,
% 13.18/13.36 (m_counter_cell_v_value(c_bit1, s31)),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2389, 2378])).
% 13.18/13.36 tff(2391,assumption,(node2(c_bit1, s31)), introduced(assumption)).
% 13.18/13.36 tff(2392,plain,
% 13.18/13.36 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s31)) | (~m_counter_cell_v_value(c_bit1, s31)) | (~node2(c_bit1, s31)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s31)) | (~m_counter_cell_v_value(c_bit1, s31)) | (~node2(c_bit1, s31)))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2393,plain,
% 13.18/13.36 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s31)) | (~m_counter_cell_v_value(c_bit1, s31)) | (~node2(c_bit1, s31)))),
% 13.18/13.36 inference(quant_inst,[status(thm)],[])).
% 13.18/13.36 tff(2394,plain,
% 13.18/13.36 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s31)) | (~m_counter_cell_v_value(c_bit1, s31)) | (~node2(c_bit1, s31))),
% 13.18/13.36 inference(modus_ponens,[status(thm)],[2393, 2392])).
% 13.18/13.36 tff(2395,plain,
% 13.18/13.36 ($false),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2394, 93, 2391, 2390, 1409])).
% 13.18/13.36 tff(2396,plain,(~node2(c_bit1, s31)), inference(lemma,lemma(discharge,[]))).
% 13.18/13.36 tff(2397,plain,
% 13.18/13.36 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s31, s32)) | node3(c_bit1, s31, s32))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s31, s32)) | node3(c_bit1, s31, s32))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2398,plain,
% 13.18/13.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s31, s32)) | node3(c_bit1, s31, s32))),
% 13.18/13.36 inference(quant_inst,[status(thm)],[])).
% 13.18/13.36 tff(2399,plain,
% 13.18/13.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s31, s32)) | node3(c_bit1, s31, s32)),
% 13.18/13.36 inference(modus_ponens,[status(thm)],[2398, 2397])).
% 13.18/13.36 tff(2400,plain,
% 13.18/13.36 (node3(c_bit1, s31, s32)),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2399, 59, 969])).
% 13.18/13.36 tff(2401,plain,
% 13.18/13.36 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s32)) | node2(c_bit1, s31) | (~node3(c_bit1, s31, s32)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s32)) | node2(c_bit1, s31) | (~node3(c_bit1, s31, s32)))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2402,plain,
% 13.18/13.36 ((node2(c_bit1, s31) | (~node3(c_bit1, s31, s32)) | (~m_counter_cell_v_value(c_bit1, s32))) <=> ((~m_counter_cell_v_value(c_bit1, s32)) | node2(c_bit1, s31) | (~node3(c_bit1, s31, s32)))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2403,plain,
% 13.18/13.36 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s31) | (~node3(c_bit1, s31, s32)) | (~m_counter_cell_v_value(c_bit1, s32)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s32)) | node2(c_bit1, s31) | (~node3(c_bit1, s31, s32))))),
% 13.18/13.36 inference(monotonicity,[status(thm)],[2402])).
% 13.18/13.36 tff(2404,plain,
% 13.18/13.36 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s31) | (~node3(c_bit1, s31, s32)) | (~m_counter_cell_v_value(c_bit1, s32)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s32)) | node2(c_bit1, s31) | (~node3(c_bit1, s31, s32)))),
% 13.18/13.36 inference(transitivity,[status(thm)],[2403, 2401])).
% 13.18/13.36 tff(2405,plain,
% 13.18/13.36 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s31) | (~node3(c_bit1, s31, s32)) | (~m_counter_cell_v_value(c_bit1, s32)))),
% 13.18/13.36 inference(quant_inst,[status(thm)],[])).
% 13.18/13.36 tff(2406,plain,
% 13.18/13.36 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s32)) | node2(c_bit1, s31) | (~node3(c_bit1, s31, s32))),
% 13.18/13.36 inference(modus_ponens,[status(thm)],[2405, 2404])).
% 13.18/13.36 tff(2407,plain,
% 13.18/13.36 ((~m_counter_cell_v_value(c_bit1, s32)) | node2(c_bit1, s31)),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2406, 121, 2400])).
% 13.18/13.36 tff(2408,plain,
% 13.18/13.36 (~m_counter_cell_v_value(c_bit1, s32)),
% 13.18/13.36 inference(unit_resolution,[status(thm)],[2407, 2396])).
% 13.18/13.36 tff(2409,plain,
% 13.18/13.36 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s32) | (~node4(c_bit0, s32)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s32) | (~node4(c_bit0, s32)))),
% 13.18/13.36 inference(rewrite,[status(thm)],[])).
% 13.18/13.36 tff(2410,plain,
% 13.18/13.36 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s32) | (~node4(c_bit0, s32)))),
% 13.18/13.37 inference(quant_inst,[status(thm)],[])).
% 13.18/13.37 tff(2411,plain,
% 13.18/13.37 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s32) | (~node4(c_bit0, s32))),
% 13.18/13.37 inference(modus_ponens,[status(thm)],[2410, 2409])).
% 13.18/13.37 tff(2412,plain,
% 13.18/13.37 (~node4(c_bit0, s32)),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2411, 1344, 981])).
% 13.18/13.37 tff(2413,assumption,(m_counter_cell_v_carry_out(c_bit0, s32)), introduced(assumption)).
% 13.18/13.37 tff(2414,plain,
% 13.18/13.37 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s32)) | node4(c_bit0, s32))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s32)) | node4(c_bit0, s32))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2415,plain,
% 13.18/13.37 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s32)) | node4(c_bit0, s32))),
% 13.18/13.37 inference(quant_inst,[status(thm)],[])).
% 13.18/13.37 tff(2416,plain,
% 13.18/13.37 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s32)) | node4(c_bit0, s32)),
% 13.18/13.37 inference(modus_ponens,[status(thm)],[2415, 2414])).
% 13.18/13.37 tff(2417,plain,
% 13.18/13.37 ($false),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2416, 1359, 2413, 2412])).
% 13.18/13.37 tff(2418,plain,(~m_counter_cell_v_carry_out(c_bit0, s32)), inference(lemma,lemma(discharge,[]))).
% 13.18/13.37 tff(2419,assumption,(m_counter_cell_v_carry_in(c_bit1, s32)), introduced(assumption)).
% 13.18/13.37 tff(2420,assumption,(~m_counter_cell_v_carry_out(c_bit0, s32)), introduced(assumption)).
% 13.18/13.37 tff(2421,plain,
% 13.18/13.37 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s32)) | m_counter_cell_v_carry_out(c_bit0, s32))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s32)) | m_counter_cell_v_carry_out(c_bit0, s32))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2422,plain,
% 13.18/13.37 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s32)) | m_counter_cell_v_carry_out(c_bit0, s32))),
% 13.18/13.37 inference(quant_inst,[status(thm)],[])).
% 13.18/13.37 tff(2423,plain,
% 13.18/13.37 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s32)) | m_counter_cell_v_carry_out(c_bit0, s32)),
% 13.18/13.37 inference(modus_ponens,[status(thm)],[2422, 2421])).
% 13.18/13.37 tff(2424,plain,
% 13.18/13.37 ($false),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2423, 1374, 2420, 2419])).
% 13.18/13.37 tff(2425,plain,((~m_counter_cell_v_carry_in(c_bit1, s32)) | m_counter_cell_v_carry_out(c_bit0, s32)), inference(lemma,lemma(discharge,[]))).
% 13.18/13.37 tff(2426,plain,
% 13.18/13.37 (~m_counter_cell_v_carry_in(c_bit1, s32)),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2425, 2418])).
% 13.18/13.37 tff(2427,plain,
% 13.18/13.37 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s32) | m_counter_cell_v_value(c_bit1, s32) | (~node2(c_bit1, s32)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s32) | m_counter_cell_v_value(c_bit1, s32) | (~node2(c_bit1, s32)))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2428,plain,
% 13.18/13.37 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s32) | m_counter_cell_v_value(c_bit1, s32) | (~node2(c_bit1, s32)))),
% 13.18/13.37 inference(quant_inst,[status(thm)],[])).
% 13.18/13.37 tff(2429,plain,
% 13.18/13.37 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s32) | m_counter_cell_v_value(c_bit1, s32) | (~node2(c_bit1, s32))),
% 13.18/13.37 inference(modus_ponens,[status(thm)],[2428, 2427])).
% 13.18/13.37 tff(2430,plain,
% 13.18/13.37 (m_counter_cell_v_value(c_bit1, s32) | (~node2(c_bit1, s32))),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2429, 1498, 2426])).
% 13.18/13.37 tff(2431,plain,
% 13.18/13.37 (~node2(c_bit1, s32)),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2430, 2408])).
% 13.18/13.37 tff(2432,plain,
% 13.18/13.37 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s32, s33)) | node3(c_bit1, s32, s33))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s32, s33)) | node3(c_bit1, s32, s33))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2433,plain,
% 13.18/13.37 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s32, s33)) | node3(c_bit1, s32, s33))),
% 13.18/13.37 inference(quant_inst,[status(thm)],[])).
% 13.18/13.37 tff(2434,plain,
% 13.18/13.37 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s32, s33)) | node3(c_bit1, s32, s33)),
% 13.18/13.37 inference(modus_ponens,[status(thm)],[2433, 2432])).
% 13.18/13.37 tff(2435,plain,
% 13.18/13.37 (node3(c_bit1, s32, s33)),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2434, 59, 1000])).
% 13.18/13.37 tff(2436,plain,
% 13.18/13.37 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s33)) | node2(c_bit1, s32) | (~node3(c_bit1, s32, s33)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s33)) | node2(c_bit1, s32) | (~node3(c_bit1, s32, s33)))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2437,plain,
% 13.18/13.37 ((node2(c_bit1, s32) | (~node3(c_bit1, s32, s33)) | (~m_counter_cell_v_value(c_bit1, s33))) <=> ((~m_counter_cell_v_value(c_bit1, s33)) | node2(c_bit1, s32) | (~node3(c_bit1, s32, s33)))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2438,plain,
% 13.18/13.37 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s32) | (~node3(c_bit1, s32, s33)) | (~m_counter_cell_v_value(c_bit1, s33)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s33)) | node2(c_bit1, s32) | (~node3(c_bit1, s32, s33))))),
% 13.18/13.37 inference(monotonicity,[status(thm)],[2437])).
% 13.18/13.37 tff(2439,plain,
% 13.18/13.37 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s32) | (~node3(c_bit1, s32, s33)) | (~m_counter_cell_v_value(c_bit1, s33)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s33)) | node2(c_bit1, s32) | (~node3(c_bit1, s32, s33)))),
% 13.18/13.37 inference(transitivity,[status(thm)],[2438, 2436])).
% 13.18/13.37 tff(2440,plain,
% 13.18/13.37 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s32) | (~node3(c_bit1, s32, s33)) | (~m_counter_cell_v_value(c_bit1, s33)))),
% 13.18/13.37 inference(quant_inst,[status(thm)],[])).
% 13.18/13.37 tff(2441,plain,
% 13.18/13.37 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s33)) | node2(c_bit1, s32) | (~node3(c_bit1, s32, s33))),
% 13.18/13.37 inference(modus_ponens,[status(thm)],[2440, 2439])).
% 13.18/13.37 tff(2442,plain,
% 13.18/13.37 ((~m_counter_cell_v_value(c_bit1, s33)) | node2(c_bit1, s32)),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2441, 121, 2435])).
% 13.18/13.37 tff(2443,plain,
% 13.18/13.37 (~m_counter_cell_v_value(c_bit1, s33)),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2442, 2431])).
% 13.18/13.37 tff(2444,assumption,(~m_counter_cell_v_value(c_bit1, s33)), introduced(assumption)).
% 13.18/13.37 tff(2445,assumption,(node1(c_bit1, s33)), introduced(assumption)).
% 13.18/13.37 tff(2446,plain,
% 13.18/13.37 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s33)) | (~m_counter_cell_v_value(c_bit0, s33)) | m_counter_cell_v_carry_out(c_bit0, s33))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s33)) | (~m_counter_cell_v_value(c_bit0, s33)) | m_counter_cell_v_carry_out(c_bit0, s33))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2447,plain,
% 13.18/13.37 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s33)) | (~m_counter_cell_v_value(c_bit0, s33)) | m_counter_cell_v_carry_out(c_bit0, s33))),
% 13.18/13.37 inference(quant_inst,[status(thm)],[])).
% 13.18/13.37 tff(2448,plain,
% 13.18/13.37 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s33)) | (~m_counter_cell_v_value(c_bit0, s33)) | m_counter_cell_v_carry_out(c_bit0, s33)),
% 13.18/13.37 inference(modus_ponens,[status(thm)],[2447, 2446])).
% 13.18/13.37 tff(2449,plain,
% 13.18/13.37 ((~m_counter_cell_v_value(c_bit0, s33)) | m_counter_cell_v_carry_out(c_bit0, s33)),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2448, 1390, 1016])).
% 13.18/13.37 tff(2450,plain,
% 13.18/13.37 (m_counter_cell_v_carry_out(c_bit0, s33)),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2449, 1012])).
% 13.18/13.37 tff(2451,plain,
% 13.18/13.37 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s33)) | m_counter_cell_v_carry_in(c_bit1, s33))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s33)) | m_counter_cell_v_carry_in(c_bit1, s33))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2452,plain,
% 13.18/13.37 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s33)) | m_counter_cell_v_carry_in(c_bit1, s33))),
% 13.18/13.37 inference(quant_inst,[status(thm)],[])).
% 13.18/13.37 tff(2453,plain,
% 13.18/13.37 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s33)) | m_counter_cell_v_carry_in(c_bit1, s33)),
% 13.18/13.37 inference(modus_ponens,[status(thm)],[2452, 2451])).
% 13.18/13.37 tff(2454,plain,
% 13.18/13.37 (m_counter_cell_v_carry_in(c_bit1, s33)),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2453, 1405, 2450])).
% 13.18/13.37 tff(2455,plain,
% 13.18/13.37 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_value(c_bit1, s33) | (~node1(c_bit1, s33)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_value(c_bit1, s33) | (~node1(c_bit1, s33)))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2456,plain,
% 13.18/13.37 (((~node1(c_bit1, s33)) | (~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_value(c_bit1, s33)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_value(c_bit1, s33) | (~node1(c_bit1, s33)))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2457,plain,
% 13.18/13.37 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s33)) | (~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_value(c_bit1, s33))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_value(c_bit1, s33) | (~node1(c_bit1, s33))))),
% 13.18/13.37 inference(monotonicity,[status(thm)],[2456])).
% 13.18/13.37 tff(2458,plain,
% 13.18/13.37 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s33)) | (~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_value(c_bit1, s33))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_value(c_bit1, s33) | (~node1(c_bit1, s33)))),
% 13.18/13.37 inference(transitivity,[status(thm)],[2457, 2455])).
% 13.18/13.37 tff(2459,plain,
% 13.18/13.37 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s33)) | (~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_value(c_bit1, s33))),
% 13.18/13.37 inference(quant_inst,[status(thm)],[])).
% 13.18/13.37 tff(2460,plain,
% 13.18/13.37 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_value(c_bit1, s33) | (~node1(c_bit1, s33))),
% 13.18/13.37 inference(modus_ponens,[status(thm)],[2459, 2458])).
% 13.18/13.37 tff(2461,plain,
% 13.18/13.37 ($false),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2460, 30, 2454, 2445, 2444])).
% 13.18/13.37 tff(2462,plain,((~node1(c_bit1, s33)) | m_counter_cell_v_value(c_bit1, s33)), inference(lemma,lemma(discharge,[]))).
% 13.18/13.37 tff(2463,plain,
% 13.18/13.37 (~node1(c_bit1, s33)),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2462, 2443])).
% 13.18/13.37 tff(2464,plain,
% 13.18/13.37 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s33, s34)) | node3(c_bit1, s33, s34))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s33, s34)) | node3(c_bit1, s33, s34))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2465,plain,
% 13.18/13.37 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s33, s34)) | node3(c_bit1, s33, s34))),
% 13.18/13.37 inference(quant_inst,[status(thm)],[])).
% 13.18/13.37 tff(2466,plain,
% 13.18/13.37 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s33, s34)) | node3(c_bit1, s33, s34)),
% 13.18/13.37 inference(modus_ponens,[status(thm)],[2465, 2464])).
% 13.18/13.37 tff(2467,plain,
% 13.18/13.37 (node3(c_bit1, s33, s34)),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2466, 59, 1028])).
% 13.18/13.37 tff(2468,plain,
% 13.18/13.37 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s34) | node1(c_bit1, s33) | (~node3(c_bit1, s33, s34)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s34) | node1(c_bit1, s33) | (~node3(c_bit1, s33, s34)))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2469,plain,
% 13.18/13.37 ((node1(c_bit1, s33) | (~node3(c_bit1, s33, s34)) | m_counter_cell_v_value(c_bit1, s34)) <=> (m_counter_cell_v_value(c_bit1, s34) | node1(c_bit1, s33) | (~node3(c_bit1, s33, s34)))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2470,plain,
% 13.18/13.37 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s33) | (~node3(c_bit1, s33, s34)) | m_counter_cell_v_value(c_bit1, s34))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s34) | node1(c_bit1, s33) | (~node3(c_bit1, s33, s34))))),
% 13.18/13.37 inference(monotonicity,[status(thm)],[2469])).
% 13.18/13.37 tff(2471,plain,
% 13.18/13.37 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s33) | (~node3(c_bit1, s33, s34)) | m_counter_cell_v_value(c_bit1, s34))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s34) | node1(c_bit1, s33) | (~node3(c_bit1, s33, s34)))),
% 13.18/13.37 inference(transitivity,[status(thm)],[2470, 2468])).
% 13.18/13.37 tff(2472,plain,
% 13.18/13.37 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s33) | (~node3(c_bit1, s33, s34)) | m_counter_cell_v_value(c_bit1, s34))),
% 13.18/13.37 inference(quant_inst,[status(thm)],[])).
% 13.18/13.37 tff(2473,plain,
% 13.18/13.37 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s34) | node1(c_bit1, s33) | (~node3(c_bit1, s33, s34))),
% 13.18/13.37 inference(modus_ponens,[status(thm)],[2472, 2471])).
% 13.18/13.37 tff(2474,plain,
% 13.18/13.37 (m_counter_cell_v_value(c_bit1, s34) | node1(c_bit1, s33)),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2473, 73, 2467])).
% 13.18/13.37 tff(2475,plain,
% 13.18/13.37 (m_counter_cell_v_value(c_bit1, s34)),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2474, 2463])).
% 13.18/13.37 tff(2476,plain,
% 13.18/13.37 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s34) | (~node4(c_bit0, s34)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s34) | (~node4(c_bit0, s34)))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2477,plain,
% 13.18/13.37 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s34) | (~node4(c_bit0, s34)))),
% 13.18/13.37 inference(quant_inst,[status(thm)],[])).
% 13.18/13.37 tff(2478,plain,
% 13.18/13.37 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s34) | (~node4(c_bit0, s34))),
% 13.18/13.37 inference(modus_ponens,[status(thm)],[2477, 2476])).
% 13.18/13.37 tff(2479,plain,
% 13.18/13.37 (~node4(c_bit0, s34)),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2478, 1344, 1040])).
% 13.18/13.37 tff(2480,assumption,(m_counter_cell_v_carry_out(c_bit0, s34)), introduced(assumption)).
% 13.18/13.37 tff(2481,plain,
% 13.18/13.37 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s34)) | node4(c_bit0, s34))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s34)) | node4(c_bit0, s34))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2482,plain,
% 13.18/13.37 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s34)) | node4(c_bit0, s34))),
% 13.18/13.37 inference(quant_inst,[status(thm)],[])).
% 13.18/13.37 tff(2483,plain,
% 13.18/13.37 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s34)) | node4(c_bit0, s34)),
% 13.18/13.37 inference(modus_ponens,[status(thm)],[2482, 2481])).
% 13.18/13.37 tff(2484,plain,
% 13.18/13.37 ($false),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2483, 1359, 2480, 2479])).
% 13.18/13.37 tff(2485,plain,(~m_counter_cell_v_carry_out(c_bit0, s34)), inference(lemma,lemma(discharge,[]))).
% 13.18/13.37 tff(2486,assumption,(m_counter_cell_v_carry_in(c_bit1, s34)), introduced(assumption)).
% 13.18/13.37 tff(2487,assumption,(~m_counter_cell_v_carry_out(c_bit0, s34)), introduced(assumption)).
% 13.18/13.37 tff(2488,plain,
% 13.18/13.37 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s34)) | m_counter_cell_v_carry_out(c_bit0, s34))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s34)) | m_counter_cell_v_carry_out(c_bit0, s34))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2489,plain,
% 13.18/13.37 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s34)) | m_counter_cell_v_carry_out(c_bit0, s34))),
% 13.18/13.37 inference(quant_inst,[status(thm)],[])).
% 13.18/13.37 tff(2490,plain,
% 13.18/13.37 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s34)) | m_counter_cell_v_carry_out(c_bit0, s34)),
% 13.18/13.37 inference(modus_ponens,[status(thm)],[2489, 2488])).
% 13.18/13.37 tff(2491,plain,
% 13.18/13.37 ($false),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2490, 1374, 2487, 2486])).
% 13.18/13.37 tff(2492,plain,((~m_counter_cell_v_carry_in(c_bit1, s34)) | m_counter_cell_v_carry_out(c_bit0, s34)), inference(lemma,lemma(discharge,[]))).
% 13.18/13.37 tff(2493,plain,
% 13.18/13.37 (~m_counter_cell_v_carry_in(c_bit1, s34)),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2492, 2485])).
% 13.18/13.37 tff(2494,plain,
% 13.18/13.37 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s34) | (~m_counter_cell_v_value(c_bit1, s34)) | (~node1(c_bit1, s34)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s34) | (~m_counter_cell_v_value(c_bit1, s34)) | (~node1(c_bit1, s34)))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2495,plain,
% 13.18/13.37 (((~node1(c_bit1, s34)) | m_counter_cell_v_carry_in(c_bit1, s34) | (~m_counter_cell_v_value(c_bit1, s34))) <=> (m_counter_cell_v_carry_in(c_bit1, s34) | (~m_counter_cell_v_value(c_bit1, s34)) | (~node1(c_bit1, s34)))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2496,plain,
% 13.18/13.37 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s34)) | m_counter_cell_v_carry_in(c_bit1, s34) | (~m_counter_cell_v_value(c_bit1, s34)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s34) | (~m_counter_cell_v_value(c_bit1, s34)) | (~node1(c_bit1, s34))))),
% 13.18/13.37 inference(monotonicity,[status(thm)],[2495])).
% 13.18/13.37 tff(2497,plain,
% 13.18/13.37 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s34)) | m_counter_cell_v_carry_in(c_bit1, s34) | (~m_counter_cell_v_value(c_bit1, s34)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s34) | (~m_counter_cell_v_value(c_bit1, s34)) | (~node1(c_bit1, s34)))),
% 13.18/13.37 inference(transitivity,[status(thm)],[2496, 2494])).
% 13.18/13.37 tff(2498,plain,
% 13.18/13.37 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s34)) | m_counter_cell_v_carry_in(c_bit1, s34) | (~m_counter_cell_v_value(c_bit1, s34)))),
% 13.18/13.37 inference(quant_inst,[status(thm)],[])).
% 13.18/13.37 tff(2499,plain,
% 13.18/13.37 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s34) | (~m_counter_cell_v_value(c_bit1, s34)) | (~node1(c_bit1, s34))),
% 13.18/13.37 inference(modus_ponens,[status(thm)],[2498, 2497])).
% 13.18/13.37 tff(2500,plain,
% 13.18/13.37 ((~m_counter_cell_v_value(c_bit1, s34)) | (~node1(c_bit1, s34))),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2499, 1569, 2493])).
% 13.18/13.37 tff(2501,plain,
% 13.18/13.37 (~node1(c_bit1, s34)),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2500, 2475])).
% 13.18/13.37 tff(2502,plain,
% 13.18/13.37 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s34, s35)) | node3(c_bit1, s34, s35))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s34, s35)) | node3(c_bit1, s34, s35))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2503,plain,
% 13.18/13.37 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s34, s35)) | node3(c_bit1, s34, s35))),
% 13.18/13.37 inference(quant_inst,[status(thm)],[])).
% 13.18/13.37 tff(2504,plain,
% 13.18/13.37 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s34, s35)) | node3(c_bit1, s34, s35)),
% 13.18/13.37 inference(modus_ponens,[status(thm)],[2503, 2502])).
% 13.18/13.37 tff(2505,plain,
% 13.18/13.37 (node3(c_bit1, s34, s35)),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2504, 59, 1059])).
% 13.18/13.37 tff(2506,plain,
% 13.18/13.37 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s35) | node1(c_bit1, s34) | (~node3(c_bit1, s34, s35)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s35) | node1(c_bit1, s34) | (~node3(c_bit1, s34, s35)))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2507,plain,
% 13.18/13.37 ((node1(c_bit1, s34) | (~node3(c_bit1, s34, s35)) | m_counter_cell_v_value(c_bit1, s35)) <=> (m_counter_cell_v_value(c_bit1, s35) | node1(c_bit1, s34) | (~node3(c_bit1, s34, s35)))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2508,plain,
% 13.18/13.37 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s34) | (~node3(c_bit1, s34, s35)) | m_counter_cell_v_value(c_bit1, s35))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s35) | node1(c_bit1, s34) | (~node3(c_bit1, s34, s35))))),
% 13.18/13.37 inference(monotonicity,[status(thm)],[2507])).
% 13.18/13.37 tff(2509,plain,
% 13.18/13.37 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s34) | (~node3(c_bit1, s34, s35)) | m_counter_cell_v_value(c_bit1, s35))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s35) | node1(c_bit1, s34) | (~node3(c_bit1, s34, s35)))),
% 13.18/13.37 inference(transitivity,[status(thm)],[2508, 2506])).
% 13.18/13.37 tff(2510,plain,
% 13.18/13.37 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s34) | (~node3(c_bit1, s34, s35)) | m_counter_cell_v_value(c_bit1, s35))),
% 13.18/13.37 inference(quant_inst,[status(thm)],[])).
% 13.18/13.37 tff(2511,plain,
% 13.18/13.37 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s35) | node1(c_bit1, s34) | (~node3(c_bit1, s34, s35))),
% 13.18/13.37 inference(modus_ponens,[status(thm)],[2510, 2509])).
% 13.18/13.37 tff(2512,plain,
% 13.18/13.37 (m_counter_cell_v_value(c_bit1, s35) | node1(c_bit1, s34)),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2511, 73, 2505])).
% 13.18/13.37 tff(2513,plain,
% 13.18/13.37 (m_counter_cell_v_value(c_bit1, s35)),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2512, 2501])).
% 13.18/13.37 tff(2514,plain,
% 13.18/13.37 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s35)) | (~m_counter_cell_v_value(c_bit0, s35)) | m_counter_cell_v_carry_out(c_bit0, s35))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s35)) | (~m_counter_cell_v_value(c_bit0, s35)) | m_counter_cell_v_carry_out(c_bit0, s35))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2515,plain,
% 13.18/13.37 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s35)) | (~m_counter_cell_v_value(c_bit0, s35)) | m_counter_cell_v_carry_out(c_bit0, s35))),
% 13.18/13.37 inference(quant_inst,[status(thm)],[])).
% 13.18/13.37 tff(2516,plain,
% 13.18/13.37 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s35)) | (~m_counter_cell_v_value(c_bit0, s35)) | m_counter_cell_v_carry_out(c_bit0, s35)),
% 13.18/13.37 inference(modus_ponens,[status(thm)],[2515, 2514])).
% 13.18/13.37 tff(2517,plain,
% 13.18/13.37 ((~m_counter_cell_v_value(c_bit0, s35)) | m_counter_cell_v_carry_out(c_bit0, s35)),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2516, 1390, 1075])).
% 13.18/13.37 tff(2518,plain,
% 13.18/13.37 (m_counter_cell_v_carry_out(c_bit0, s35)),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2517, 1071])).
% 13.18/13.37 tff(2519,plain,
% 13.18/13.37 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s35)) | m_counter_cell_v_carry_in(c_bit1, s35))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s35)) | m_counter_cell_v_carry_in(c_bit1, s35))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2520,plain,
% 13.18/13.37 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s35)) | m_counter_cell_v_carry_in(c_bit1, s35))),
% 13.18/13.37 inference(quant_inst,[status(thm)],[])).
% 13.18/13.37 tff(2521,plain,
% 13.18/13.37 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s35)) | m_counter_cell_v_carry_in(c_bit1, s35)),
% 13.18/13.37 inference(modus_ponens,[status(thm)],[2520, 2519])).
% 13.18/13.37 tff(2522,plain,
% 13.18/13.37 (m_counter_cell_v_carry_in(c_bit1, s35)),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2521, 1405, 2518])).
% 13.18/13.37 tff(2523,assumption,(m_counter_cell_v_value(c_bit1, s35)), introduced(assumption)).
% 13.18/13.37 tff(2524,assumption,(node2(c_bit1, s35)), introduced(assumption)).
% 13.18/13.37 tff(2525,plain,
% 13.18/13.37 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s35)) | (~m_counter_cell_v_value(c_bit1, s35)) | (~node2(c_bit1, s35)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s35)) | (~m_counter_cell_v_value(c_bit1, s35)) | (~node2(c_bit1, s35)))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2526,plain,
% 13.18/13.37 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s35)) | (~m_counter_cell_v_value(c_bit1, s35)) | (~node2(c_bit1, s35)))),
% 13.18/13.37 inference(quant_inst,[status(thm)],[])).
% 13.18/13.37 tff(2527,plain,
% 13.18/13.37 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s35)) | (~m_counter_cell_v_value(c_bit1, s35)) | (~node2(c_bit1, s35))),
% 13.18/13.37 inference(modus_ponens,[status(thm)],[2526, 2525])).
% 13.18/13.37 tff(2528,plain,
% 13.18/13.37 ($false),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2527, 93, 2524, 2523, 2522])).
% 13.18/13.37 tff(2529,plain,((~node2(c_bit1, s35)) | (~m_counter_cell_v_value(c_bit1, s35))), inference(lemma,lemma(discharge,[]))).
% 13.18/13.37 tff(2530,plain,
% 13.18/13.37 (~node2(c_bit1, s35)),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2529, 2513])).
% 13.18/13.37 tff(2531,plain,
% 13.18/13.37 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s35, s36)) | node3(c_bit1, s35, s36))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s35, s36)) | node3(c_bit1, s35, s36))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2532,plain,
% 13.18/13.37 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s35, s36)) | node3(c_bit1, s35, s36))),
% 13.18/13.37 inference(quant_inst,[status(thm)],[])).
% 13.18/13.37 tff(2533,plain,
% 13.18/13.37 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s35, s36)) | node3(c_bit1, s35, s36)),
% 13.18/13.37 inference(modus_ponens,[status(thm)],[2532, 2531])).
% 13.18/13.37 tff(2534,plain,
% 13.18/13.37 (node3(c_bit1, s35, s36)),
% 13.18/13.37 inference(unit_resolution,[status(thm)],[2533, 59, 1087])).
% 13.18/13.37 tff(2535,plain,
% 13.18/13.37 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s36)) | node2(c_bit1, s35) | (~node3(c_bit1, s35, s36)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s36)) | node2(c_bit1, s35) | (~node3(c_bit1, s35, s36)))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2536,plain,
% 13.18/13.37 ((node2(c_bit1, s35) | (~node3(c_bit1, s35, s36)) | (~m_counter_cell_v_value(c_bit1, s36))) <=> ((~m_counter_cell_v_value(c_bit1, s36)) | node2(c_bit1, s35) | (~node3(c_bit1, s35, s36)))),
% 13.18/13.37 inference(rewrite,[status(thm)],[])).
% 13.18/13.37 tff(2537,plain,
% 13.18/13.37 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s35) | (~node3(c_bit1, s35, s36)) | (~m_counter_cell_v_value(c_bit1, s36)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s36)) | node2(c_bit1, s35) | (~node3(c_bit1, s35, s36))))),
% 13.18/13.37 inference(monotonicity,[status(thm)],[2536])).
% 13.18/13.37 tff(2538,plain,
% 13.18/13.37 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s35) | (~node3(c_bit1, s35, s36)) | (~m_counter_cell_v_value(c_bit1, s36)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s36)) | node2(c_bit1, s35) | (~node3(c_bit1, s35, s36)))),
% 13.18/13.37 inference(transitivity,[status(thm)],[2537, 2535])).
% 13.18/13.37 tff(2539,plain,
% 13.18/13.37 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s35) | (~node3(c_bit1, s35, s36)) | (~m_counter_cell_v_value(c_bit1, s36)))),
% 13.18/13.37 inference(quant_inst,[status(thm)],[])).
% 13.18/13.37 tff(2540,plain,
% 13.18/13.37 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s36)) | node2(c_bit1, s35) | (~node3(c_bit1, s35, s36))),
% 13.18/13.37 inference(modus_ponens,[status(thm)],[2539, 2538])).
% 13.18/13.37 tff(2541,plain,
% 13.18/13.37 ((~m_counter_cell_v_value(c_bit1, s36)) | node2(c_bit1, s35)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2540, 121, 2534])).
% 13.18/13.38 tff(2542,plain,
% 13.18/13.38 (~m_counter_cell_v_value(c_bit1, s36)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2541, 2530])).
% 13.18/13.38 tff(2543,plain,
% 13.18/13.38 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s36) | (~node4(c_bit0, s36)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s36) | (~node4(c_bit0, s36)))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2544,plain,
% 13.18/13.38 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s36) | (~node4(c_bit0, s36)))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2545,plain,
% 13.18/13.38 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s36) | (~node4(c_bit0, s36))),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2544, 2543])).
% 13.18/13.38 tff(2546,plain,
% 13.18/13.38 (~node4(c_bit0, s36)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2545, 1344, 1099])).
% 13.18/13.38 tff(2547,assumption,(m_counter_cell_v_carry_out(c_bit0, s36)), introduced(assumption)).
% 13.18/13.38 tff(2548,plain,
% 13.18/13.38 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s36)) | node4(c_bit0, s36))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s36)) | node4(c_bit0, s36))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2549,plain,
% 13.18/13.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s36)) | node4(c_bit0, s36))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2550,plain,
% 13.18/13.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s36)) | node4(c_bit0, s36)),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2549, 2548])).
% 13.18/13.38 tff(2551,plain,
% 13.18/13.38 ($false),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2550, 1359, 2547, 2546])).
% 13.18/13.38 tff(2552,plain,(~m_counter_cell_v_carry_out(c_bit0, s36)), inference(lemma,lemma(discharge,[]))).
% 13.18/13.38 tff(2553,plain,
% 13.18/13.38 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s36)) | m_counter_cell_v_carry_out(c_bit0, s36))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s36)) | m_counter_cell_v_carry_out(c_bit0, s36))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2554,plain,
% 13.18/13.38 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s36)) | m_counter_cell_v_carry_out(c_bit0, s36))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2555,plain,
% 13.18/13.38 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s36)) | m_counter_cell_v_carry_out(c_bit0, s36)),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2554, 2553])).
% 13.18/13.38 tff(2556,plain,
% 13.18/13.38 (~m_counter_cell_v_carry_in(c_bit1, s36)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2555, 1374, 2552])).
% 13.18/13.38 tff(2557,assumption,(~m_counter_cell_v_value(c_bit1, s36)), introduced(assumption)).
% 13.18/13.38 tff(2558,assumption,(node2(c_bit1, s36)), introduced(assumption)).
% 13.18/13.38 tff(2559,plain,
% 13.18/13.38 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s36) | m_counter_cell_v_value(c_bit1, s36) | (~node2(c_bit1, s36)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s36) | m_counter_cell_v_value(c_bit1, s36) | (~node2(c_bit1, s36)))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2560,plain,
% 13.18/13.38 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s36) | m_counter_cell_v_value(c_bit1, s36) | (~node2(c_bit1, s36)))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2561,plain,
% 13.18/13.38 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s36) | m_counter_cell_v_value(c_bit1, s36) | (~node2(c_bit1, s36))),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2560, 2559])).
% 13.18/13.38 tff(2562,plain,
% 13.18/13.38 ($false),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2561, 1498, 2558, 2557, 2556])).
% 13.18/13.38 tff(2563,plain,(m_counter_cell_v_value(c_bit1, s36) | (~node2(c_bit1, s36))), inference(lemma,lemma(discharge,[]))).
% 13.18/13.38 tff(2564,plain,
% 13.18/13.38 (~node2(c_bit1, s36)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2563, 2542])).
% 13.18/13.38 tff(2565,plain,
% 13.18/13.38 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s36, s37)) | node3(c_bit1, s36, s37))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s36, s37)) | node3(c_bit1, s36, s37))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2566,plain,
% 13.18/13.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s36, s37)) | node3(c_bit1, s36, s37))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2567,plain,
% 13.18/13.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s36, s37)) | node3(c_bit1, s36, s37)),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2566, 2565])).
% 13.18/13.38 tff(2568,plain,
% 13.18/13.38 (node3(c_bit1, s36, s37)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2567, 59, 1118])).
% 13.18/13.38 tff(2569,plain,
% 13.18/13.38 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s37)) | node2(c_bit1, s36) | (~node3(c_bit1, s36, s37)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s37)) | node2(c_bit1, s36) | (~node3(c_bit1, s36, s37)))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2570,plain,
% 13.18/13.38 ((node2(c_bit1, s36) | (~node3(c_bit1, s36, s37)) | (~m_counter_cell_v_value(c_bit1, s37))) <=> ((~m_counter_cell_v_value(c_bit1, s37)) | node2(c_bit1, s36) | (~node3(c_bit1, s36, s37)))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2571,plain,
% 13.18/13.38 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s36) | (~node3(c_bit1, s36, s37)) | (~m_counter_cell_v_value(c_bit1, s37)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s37)) | node2(c_bit1, s36) | (~node3(c_bit1, s36, s37))))),
% 13.18/13.38 inference(monotonicity,[status(thm)],[2570])).
% 13.18/13.38 tff(2572,plain,
% 13.18/13.38 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s36) | (~node3(c_bit1, s36, s37)) | (~m_counter_cell_v_value(c_bit1, s37)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s37)) | node2(c_bit1, s36) | (~node3(c_bit1, s36, s37)))),
% 13.18/13.38 inference(transitivity,[status(thm)],[2571, 2569])).
% 13.18/13.38 tff(2573,plain,
% 13.18/13.38 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s36) | (~node3(c_bit1, s36, s37)) | (~m_counter_cell_v_value(c_bit1, s37)))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2574,plain,
% 13.18/13.38 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s37)) | node2(c_bit1, s36) | (~node3(c_bit1, s36, s37))),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2573, 2572])).
% 13.18/13.38 tff(2575,plain,
% 13.18/13.38 ((~m_counter_cell_v_value(c_bit1, s37)) | node2(c_bit1, s36)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2574, 121, 2568])).
% 13.18/13.38 tff(2576,plain,
% 13.18/13.38 (~m_counter_cell_v_value(c_bit1, s37)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2575, 2564])).
% 13.18/13.38 tff(2577,assumption,(~m_counter_cell_v_value(c_bit1, s37)), introduced(assumption)).
% 13.18/13.38 tff(2578,plain,
% 13.18/13.38 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s37)) | (~m_counter_cell_v_value(c_bit0, s37)) | m_counter_cell_v_carry_out(c_bit0, s37))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s37)) | (~m_counter_cell_v_value(c_bit0, s37)) | m_counter_cell_v_carry_out(c_bit0, s37))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2579,plain,
% 13.18/13.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s37)) | (~m_counter_cell_v_value(c_bit0, s37)) | m_counter_cell_v_carry_out(c_bit0, s37))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2580,plain,
% 13.18/13.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s37)) | (~m_counter_cell_v_value(c_bit0, s37)) | m_counter_cell_v_carry_out(c_bit0, s37)),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2579, 2578])).
% 13.18/13.38 tff(2581,plain,
% 13.18/13.38 ((~m_counter_cell_v_value(c_bit0, s37)) | m_counter_cell_v_carry_out(c_bit0, s37)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2580, 1390, 1134])).
% 13.18/13.38 tff(2582,plain,
% 13.18/13.38 (m_counter_cell_v_carry_out(c_bit0, s37)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2581, 1130])).
% 13.18/13.38 tff(2583,plain,
% 13.18/13.38 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s37)) | m_counter_cell_v_carry_in(c_bit1, s37))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s37)) | m_counter_cell_v_carry_in(c_bit1, s37))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2584,plain,
% 13.18/13.38 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s37)) | m_counter_cell_v_carry_in(c_bit1, s37))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2585,plain,
% 13.18/13.38 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s37)) | m_counter_cell_v_carry_in(c_bit1, s37)),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2584, 2583])).
% 13.18/13.38 tff(2586,plain,
% 13.18/13.38 (m_counter_cell_v_carry_in(c_bit1, s37)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2585, 1405, 2582])).
% 13.18/13.38 tff(2587,assumption,(node1(c_bit1, s37)), introduced(assumption)).
% 13.18/13.38 tff(2588,plain,
% 13.18/13.38 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s37)) | m_counter_cell_v_value(c_bit1, s37) | (~node1(c_bit1, s37)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s37)) | m_counter_cell_v_value(c_bit1, s37) | (~node1(c_bit1, s37)))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2589,plain,
% 13.18/13.38 (((~node1(c_bit1, s37)) | (~m_counter_cell_v_carry_in(c_bit1, s37)) | m_counter_cell_v_value(c_bit1, s37)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s37)) | m_counter_cell_v_value(c_bit1, s37) | (~node1(c_bit1, s37)))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2590,plain,
% 13.18/13.38 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s37)) | (~m_counter_cell_v_carry_in(c_bit1, s37)) | m_counter_cell_v_value(c_bit1, s37))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s37)) | m_counter_cell_v_value(c_bit1, s37) | (~node1(c_bit1, s37))))),
% 13.18/13.38 inference(monotonicity,[status(thm)],[2589])).
% 13.18/13.38 tff(2591,plain,
% 13.18/13.38 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s37)) | (~m_counter_cell_v_carry_in(c_bit1, s37)) | m_counter_cell_v_value(c_bit1, s37))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s37)) | m_counter_cell_v_value(c_bit1, s37) | (~node1(c_bit1, s37)))),
% 13.18/13.38 inference(transitivity,[status(thm)],[2590, 2588])).
% 13.18/13.38 tff(2592,plain,
% 13.18/13.38 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s37)) | (~m_counter_cell_v_carry_in(c_bit1, s37)) | m_counter_cell_v_value(c_bit1, s37))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2593,plain,
% 13.18/13.38 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s37)) | m_counter_cell_v_value(c_bit1, s37) | (~node1(c_bit1, s37))),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2592, 2591])).
% 13.18/13.38 tff(2594,plain,
% 13.18/13.38 ($false),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2593, 30, 2587, 2586, 2577])).
% 13.18/13.38 tff(2595,plain,(m_counter_cell_v_value(c_bit1, s37) | (~node1(c_bit1, s37))), inference(lemma,lemma(discharge,[]))).
% 13.18/13.38 tff(2596,plain,
% 13.18/13.38 (~node1(c_bit1, s37)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2595, 2576])).
% 13.18/13.38 tff(2597,plain,
% 13.18/13.38 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s37, s38)) | node3(c_bit1, s37, s38))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s37, s38)) | node3(c_bit1, s37, s38))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2598,plain,
% 13.18/13.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s37, s38)) | node3(c_bit1, s37, s38))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2599,plain,
% 13.18/13.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s37, s38)) | node3(c_bit1, s37, s38)),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2598, 2597])).
% 13.18/13.38 tff(2600,plain,
% 13.18/13.38 (node3(c_bit1, s37, s38)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2599, 59, 1146])).
% 13.18/13.38 tff(2601,plain,
% 13.18/13.38 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s38) | node1(c_bit1, s37) | (~node3(c_bit1, s37, s38)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s38) | node1(c_bit1, s37) | (~node3(c_bit1, s37, s38)))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2602,plain,
% 13.18/13.38 ((node1(c_bit1, s37) | (~node3(c_bit1, s37, s38)) | m_counter_cell_v_value(c_bit1, s38)) <=> (m_counter_cell_v_value(c_bit1, s38) | node1(c_bit1, s37) | (~node3(c_bit1, s37, s38)))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2603,plain,
% 13.18/13.38 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s37) | (~node3(c_bit1, s37, s38)) | m_counter_cell_v_value(c_bit1, s38))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s38) | node1(c_bit1, s37) | (~node3(c_bit1, s37, s38))))),
% 13.18/13.38 inference(monotonicity,[status(thm)],[2602])).
% 13.18/13.38 tff(2604,plain,
% 13.18/13.38 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s37) | (~node3(c_bit1, s37, s38)) | m_counter_cell_v_value(c_bit1, s38))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s38) | node1(c_bit1, s37) | (~node3(c_bit1, s37, s38)))),
% 13.18/13.38 inference(transitivity,[status(thm)],[2603, 2601])).
% 13.18/13.38 tff(2605,plain,
% 13.18/13.38 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s37) | (~node3(c_bit1, s37, s38)) | m_counter_cell_v_value(c_bit1, s38))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2606,plain,
% 13.18/13.38 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s38) | node1(c_bit1, s37) | (~node3(c_bit1, s37, s38))),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2605, 2604])).
% 13.18/13.38 tff(2607,plain,
% 13.18/13.38 (m_counter_cell_v_value(c_bit1, s38) | node1(c_bit1, s37)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2606, 73, 2600])).
% 13.18/13.38 tff(2608,plain,
% 13.18/13.38 (m_counter_cell_v_value(c_bit1, s38)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2607, 2596])).
% 13.18/13.38 tff(2609,plain,
% 13.18/13.38 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s38) | (~node4(c_bit0, s38)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s38) | (~node4(c_bit0, s38)))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2610,plain,
% 13.18/13.38 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s38) | (~node4(c_bit0, s38)))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2611,plain,
% 13.18/13.38 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s38) | (~node4(c_bit0, s38))),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2610, 2609])).
% 13.18/13.38 tff(2612,plain,
% 13.18/13.38 (~node4(c_bit0, s38)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2611, 1344, 1158])).
% 13.18/13.38 tff(2613,assumption,(m_counter_cell_v_carry_out(c_bit0, s38)), introduced(assumption)).
% 13.18/13.38 tff(2614,plain,
% 13.18/13.38 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s38)) | node4(c_bit0, s38))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s38)) | node4(c_bit0, s38))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2615,plain,
% 13.18/13.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s38)) | node4(c_bit0, s38))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2616,plain,
% 13.18/13.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s38)) | node4(c_bit0, s38)),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2615, 2614])).
% 13.18/13.38 tff(2617,plain,
% 13.18/13.38 ($false),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2616, 1359, 2613, 2612])).
% 13.18/13.38 tff(2618,plain,(~m_counter_cell_v_carry_out(c_bit0, s38)), inference(lemma,lemma(discharge,[]))).
% 13.18/13.38 tff(2619,plain,
% 13.18/13.38 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s38)) | m_counter_cell_v_carry_out(c_bit0, s38))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s38)) | m_counter_cell_v_carry_out(c_bit0, s38))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2620,plain,
% 13.18/13.38 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s38)) | m_counter_cell_v_carry_out(c_bit0, s38))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2621,plain,
% 13.18/13.38 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s38)) | m_counter_cell_v_carry_out(c_bit0, s38)),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2620, 2619])).
% 13.18/13.38 tff(2622,plain,
% 13.18/13.38 (~m_counter_cell_v_carry_in(c_bit1, s38)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2621, 1374, 2618])).
% 13.18/13.38 tff(2623,assumption,(node1(c_bit1, s38)), introduced(assumption)).
% 13.18/13.38 tff(2624,assumption,(m_counter_cell_v_value(c_bit1, s38)), introduced(assumption)).
% 13.18/13.38 tff(2625,plain,
% 13.18/13.38 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s38) | (~m_counter_cell_v_value(c_bit1, s38)) | (~node1(c_bit1, s38)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s38) | (~m_counter_cell_v_value(c_bit1, s38)) | (~node1(c_bit1, s38)))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2626,plain,
% 13.18/13.38 (((~node1(c_bit1, s38)) | m_counter_cell_v_carry_in(c_bit1, s38) | (~m_counter_cell_v_value(c_bit1, s38))) <=> (m_counter_cell_v_carry_in(c_bit1, s38) | (~m_counter_cell_v_value(c_bit1, s38)) | (~node1(c_bit1, s38)))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2627,plain,
% 13.18/13.38 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s38)) | m_counter_cell_v_carry_in(c_bit1, s38) | (~m_counter_cell_v_value(c_bit1, s38)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s38) | (~m_counter_cell_v_value(c_bit1, s38)) | (~node1(c_bit1, s38))))),
% 13.18/13.38 inference(monotonicity,[status(thm)],[2626])).
% 13.18/13.38 tff(2628,plain,
% 13.18/13.38 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s38)) | m_counter_cell_v_carry_in(c_bit1, s38) | (~m_counter_cell_v_value(c_bit1, s38)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s38) | (~m_counter_cell_v_value(c_bit1, s38)) | (~node1(c_bit1, s38)))),
% 13.18/13.38 inference(transitivity,[status(thm)],[2627, 2625])).
% 13.18/13.38 tff(2629,plain,
% 13.18/13.38 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s38)) | m_counter_cell_v_carry_in(c_bit1, s38) | (~m_counter_cell_v_value(c_bit1, s38)))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2630,plain,
% 13.18/13.38 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s38) | (~m_counter_cell_v_value(c_bit1, s38)) | (~node1(c_bit1, s38))),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2629, 2628])).
% 13.18/13.38 tff(2631,plain,
% 13.18/13.38 ($false),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2630, 1569, 2624, 2623, 2622])).
% 13.18/13.38 tff(2632,plain,((~node1(c_bit1, s38)) | (~m_counter_cell_v_value(c_bit1, s38))), inference(lemma,lemma(discharge,[]))).
% 13.18/13.38 tff(2633,plain,
% 13.18/13.38 (~node1(c_bit1, s38)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2632, 2608])).
% 13.18/13.38 tff(2634,plain,
% 13.18/13.38 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s38, s39)) | node3(c_bit1, s38, s39))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s38, s39)) | node3(c_bit1, s38, s39))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2635,plain,
% 13.18/13.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s38, s39)) | node3(c_bit1, s38, s39))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2636,plain,
% 13.18/13.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s38, s39)) | node3(c_bit1, s38, s39)),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2635, 2634])).
% 13.18/13.38 tff(2637,plain,
% 13.18/13.38 (node3(c_bit1, s38, s39)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2636, 59, 1177])).
% 13.18/13.38 tff(2638,plain,
% 13.18/13.38 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s39) | node1(c_bit1, s38) | (~node3(c_bit1, s38, s39)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s39) | node1(c_bit1, s38) | (~node3(c_bit1, s38, s39)))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2639,plain,
% 13.18/13.38 ((node1(c_bit1, s38) | (~node3(c_bit1, s38, s39)) | m_counter_cell_v_value(c_bit1, s39)) <=> (m_counter_cell_v_value(c_bit1, s39) | node1(c_bit1, s38) | (~node3(c_bit1, s38, s39)))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2640,plain,
% 13.18/13.38 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s38) | (~node3(c_bit1, s38, s39)) | m_counter_cell_v_value(c_bit1, s39))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s39) | node1(c_bit1, s38) | (~node3(c_bit1, s38, s39))))),
% 13.18/13.38 inference(monotonicity,[status(thm)],[2639])).
% 13.18/13.38 tff(2641,plain,
% 13.18/13.38 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s38) | (~node3(c_bit1, s38, s39)) | m_counter_cell_v_value(c_bit1, s39))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s39) | node1(c_bit1, s38) | (~node3(c_bit1, s38, s39)))),
% 13.18/13.38 inference(transitivity,[status(thm)],[2640, 2638])).
% 13.18/13.38 tff(2642,plain,
% 13.18/13.38 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s38) | (~node3(c_bit1, s38, s39)) | m_counter_cell_v_value(c_bit1, s39))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2643,plain,
% 13.18/13.38 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s39) | node1(c_bit1, s38) | (~node3(c_bit1, s38, s39))),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2642, 2641])).
% 13.18/13.38 tff(2644,plain,
% 13.18/13.38 (m_counter_cell_v_value(c_bit1, s39) | node1(c_bit1, s38)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2643, 73, 2637])).
% 13.18/13.38 tff(2645,plain,
% 13.18/13.38 (m_counter_cell_v_value(c_bit1, s39)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2644, 2633])).
% 13.18/13.38 tff(2646,assumption,(m_counter_cell_v_value(c_bit1, s39)), introduced(assumption)).
% 13.18/13.38 tff(2647,plain,
% 13.18/13.38 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s39)) | (~m_counter_cell_v_value(c_bit0, s39)) | m_counter_cell_v_carry_out(c_bit0, s39))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s39)) | (~m_counter_cell_v_value(c_bit0, s39)) | m_counter_cell_v_carry_out(c_bit0, s39))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2648,plain,
% 13.18/13.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s39)) | (~m_counter_cell_v_value(c_bit0, s39)) | m_counter_cell_v_carry_out(c_bit0, s39))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2649,plain,
% 13.18/13.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s39)) | (~m_counter_cell_v_value(c_bit0, s39)) | m_counter_cell_v_carry_out(c_bit0, s39)),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2648, 2647])).
% 13.18/13.38 tff(2650,plain,
% 13.18/13.38 ((~m_counter_cell_v_value(c_bit0, s39)) | m_counter_cell_v_carry_out(c_bit0, s39)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2649, 1390, 1193])).
% 13.18/13.38 tff(2651,plain,
% 13.18/13.38 (m_counter_cell_v_carry_out(c_bit0, s39)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2650, 1189])).
% 13.18/13.38 tff(2652,plain,
% 13.18/13.38 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s39)) | m_counter_cell_v_carry_in(c_bit1, s39))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s39)) | m_counter_cell_v_carry_in(c_bit1, s39))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2653,plain,
% 13.18/13.38 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s39)) | m_counter_cell_v_carry_in(c_bit1, s39))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2654,plain,
% 13.18/13.38 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s39)) | m_counter_cell_v_carry_in(c_bit1, s39)),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2653, 2652])).
% 13.18/13.38 tff(2655,plain,
% 13.18/13.38 (m_counter_cell_v_carry_in(c_bit1, s39)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2654, 1405, 2651])).
% 13.18/13.38 tff(2656,assumption,(node2(c_bit1, s39)), introduced(assumption)).
% 13.18/13.38 tff(2657,plain,
% 13.18/13.38 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s39)) | (~m_counter_cell_v_value(c_bit1, s39)) | (~node2(c_bit1, s39)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s39)) | (~m_counter_cell_v_value(c_bit1, s39)) | (~node2(c_bit1, s39)))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2658,plain,
% 13.18/13.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s39)) | (~m_counter_cell_v_value(c_bit1, s39)) | (~node2(c_bit1, s39)))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2659,plain,
% 13.18/13.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s39)) | (~m_counter_cell_v_value(c_bit1, s39)) | (~node2(c_bit1, s39))),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2658, 2657])).
% 13.18/13.38 tff(2660,plain,
% 13.18/13.38 ($false),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2659, 93, 2656, 2655, 2646])).
% 13.18/13.38 tff(2661,plain,((~node2(c_bit1, s39)) | (~m_counter_cell_v_value(c_bit1, s39))), inference(lemma,lemma(discharge,[]))).
% 13.18/13.38 tff(2662,plain,
% 13.18/13.38 (~node2(c_bit1, s39)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2661, 2645])).
% 13.18/13.38 tff(2663,plain,
% 13.18/13.38 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s39, s40)) | node3(c_bit1, s39, s40))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s39, s40)) | node3(c_bit1, s39, s40))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2664,plain,
% 13.18/13.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s39, s40)) | node3(c_bit1, s39, s40))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2665,plain,
% 13.18/13.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s39, s40)) | node3(c_bit1, s39, s40)),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2664, 2663])).
% 13.18/13.38 tff(2666,plain,
% 13.18/13.38 (node3(c_bit1, s39, s40)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2665, 59, 1205])).
% 13.18/13.38 tff(2667,plain,
% 13.18/13.38 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s40)) | node2(c_bit1, s39) | (~node3(c_bit1, s39, s40)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s40)) | node2(c_bit1, s39) | (~node3(c_bit1, s39, s40)))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2668,plain,
% 13.18/13.38 ((node2(c_bit1, s39) | (~node3(c_bit1, s39, s40)) | (~m_counter_cell_v_value(c_bit1, s40))) <=> ((~m_counter_cell_v_value(c_bit1, s40)) | node2(c_bit1, s39) | (~node3(c_bit1, s39, s40)))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2669,plain,
% 13.18/13.38 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s39) | (~node3(c_bit1, s39, s40)) | (~m_counter_cell_v_value(c_bit1, s40)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s40)) | node2(c_bit1, s39) | (~node3(c_bit1, s39, s40))))),
% 13.18/13.38 inference(monotonicity,[status(thm)],[2668])).
% 13.18/13.38 tff(2670,plain,
% 13.18/13.38 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s39) | (~node3(c_bit1, s39, s40)) | (~m_counter_cell_v_value(c_bit1, s40)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s40)) | node2(c_bit1, s39) | (~node3(c_bit1, s39, s40)))),
% 13.18/13.38 inference(transitivity,[status(thm)],[2669, 2667])).
% 13.18/13.38 tff(2671,plain,
% 13.18/13.38 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s39) | (~node3(c_bit1, s39, s40)) | (~m_counter_cell_v_value(c_bit1, s40)))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2672,plain,
% 13.18/13.38 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s40)) | node2(c_bit1, s39) | (~node3(c_bit1, s39, s40))),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2671, 2670])).
% 13.18/13.38 tff(2673,plain,
% 13.18/13.38 ((~m_counter_cell_v_value(c_bit1, s40)) | node2(c_bit1, s39)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2672, 121, 2666])).
% 13.18/13.38 tff(2674,plain,
% 13.18/13.38 (~m_counter_cell_v_value(c_bit1, s40)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2673, 2662])).
% 13.18/13.38 tff(2675,plain,
% 13.18/13.38 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s40) | (~node4(c_bit0, s40)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s40) | (~node4(c_bit0, s40)))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2676,plain,
% 13.18/13.38 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s40) | (~node4(c_bit0, s40)))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2677,plain,
% 13.18/13.38 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s40) | (~node4(c_bit0, s40))),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2676, 2675])).
% 13.18/13.38 tff(2678,plain,
% 13.18/13.38 (~node4(c_bit0, s40)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2677, 1344, 1217])).
% 13.18/13.38 tff(2679,assumption,(m_counter_cell_v_carry_out(c_bit0, s40)), introduced(assumption)).
% 13.18/13.38 tff(2680,plain,
% 13.18/13.38 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s40)) | node4(c_bit0, s40))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s40)) | node4(c_bit0, s40))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2681,plain,
% 13.18/13.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s40)) | node4(c_bit0, s40))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2682,plain,
% 13.18/13.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s40)) | node4(c_bit0, s40)),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2681, 2680])).
% 13.18/13.38 tff(2683,plain,
% 13.18/13.38 ($false),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2682, 1359, 2679, 2678])).
% 13.18/13.38 tff(2684,plain,(~m_counter_cell_v_carry_out(c_bit0, s40)), inference(lemma,lemma(discharge,[]))).
% 13.18/13.38 tff(2685,assumption,(m_counter_cell_v_carry_in(c_bit1, s40)), introduced(assumption)).
% 13.18/13.38 tff(2686,assumption,(~m_counter_cell_v_carry_out(c_bit0, s40)), introduced(assumption)).
% 13.18/13.38 tff(2687,plain,
% 13.18/13.38 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s40)) | m_counter_cell_v_carry_out(c_bit0, s40))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s40)) | m_counter_cell_v_carry_out(c_bit0, s40))),
% 13.18/13.38 inference(rewrite,[status(thm)],[])).
% 13.18/13.38 tff(2688,plain,
% 13.18/13.38 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s40)) | m_counter_cell_v_carry_out(c_bit0, s40))),
% 13.18/13.38 inference(quant_inst,[status(thm)],[])).
% 13.18/13.38 tff(2689,plain,
% 13.18/13.38 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s40)) | m_counter_cell_v_carry_out(c_bit0, s40)),
% 13.18/13.38 inference(modus_ponens,[status(thm)],[2688, 2687])).
% 13.18/13.38 tff(2690,plain,
% 13.18/13.38 ($false),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2689, 1374, 2686, 2685])).
% 13.18/13.38 tff(2691,plain,((~m_counter_cell_v_carry_in(c_bit1, s40)) | m_counter_cell_v_carry_out(c_bit0, s40)), inference(lemma,lemma(discharge,[]))).
% 13.18/13.38 tff(2692,plain,
% 13.18/13.38 (~m_counter_cell_v_carry_in(c_bit1, s40)),
% 13.18/13.38 inference(unit_resolution,[status(thm)],[2691, 2684])).
% 13.18/13.38 tff(2693,plain,
% 13.18/13.38 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s40) | m_counter_cell_v_value(c_bit1, s40) | (~node2(c_bit1, s40)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s40) | m_counter_cell_v_value(c_bit1, s40) | (~node2(c_bit1, s40)))),
% 13.18/13.39 inference(rewrite,[status(thm)],[])).
% 13.18/13.39 tff(2694,plain,
% 13.18/13.39 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s40) | m_counter_cell_v_value(c_bit1, s40) | (~node2(c_bit1, s40)))),
% 13.18/13.39 inference(quant_inst,[status(thm)],[])).
% 13.18/13.39 tff(2695,plain,
% 13.18/13.39 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s40) | m_counter_cell_v_value(c_bit1, s40) | (~node2(c_bit1, s40))),
% 13.18/13.39 inference(modus_ponens,[status(thm)],[2694, 2693])).
% 13.18/13.39 tff(2696,plain,
% 13.18/13.39 (m_counter_cell_v_value(c_bit1, s40) | (~node2(c_bit1, s40))),
% 13.18/13.39 inference(unit_resolution,[status(thm)],[2695, 1498, 2692])).
% 13.18/13.39 tff(2697,plain,
% 13.18/13.39 (~node2(c_bit1, s40)),
% 13.18/13.39 inference(unit_resolution,[status(thm)],[2696, 2674])).
% 13.18/13.39 tff(2698,plain,
% 13.18/13.39 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s40, s41)) | node3(c_bit1, s40, s41))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s40, s41)) | node3(c_bit1, s40, s41))),
% 13.18/13.39 inference(rewrite,[status(thm)],[])).
% 13.18/13.39 tff(2699,plain,
% 13.18/13.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s40, s41)) | node3(c_bit1, s40, s41))),
% 13.18/13.39 inference(quant_inst,[status(thm)],[])).
% 13.18/13.39 tff(2700,plain,
% 13.18/13.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s40, s41)) | node3(c_bit1, s40, s41)),
% 13.18/13.39 inference(modus_ponens,[status(thm)],[2699, 2698])).
% 13.18/13.39 tff(2701,plain,
% 13.18/13.39 (node3(c_bit1, s40, s41)),
% 13.18/13.39 inference(unit_resolution,[status(thm)],[2700, 59, 1236])).
% 13.18/13.39 tff(2702,plain,
% 13.18/13.39 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s41)) | node2(c_bit1, s40) | (~node3(c_bit1, s40, s41)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s41)) | node2(c_bit1, s40) | (~node3(c_bit1, s40, s41)))),
% 13.18/13.39 inference(rewrite,[status(thm)],[])).
% 13.18/13.39 tff(2703,plain,
% 13.18/13.39 ((node2(c_bit1, s40) | (~node3(c_bit1, s40, s41)) | (~m_counter_cell_v_value(c_bit1, s41))) <=> ((~m_counter_cell_v_value(c_bit1, s41)) | node2(c_bit1, s40) | (~node3(c_bit1, s40, s41)))),
% 13.18/13.39 inference(rewrite,[status(thm)],[])).
% 13.18/13.39 tff(2704,plain,
% 13.18/13.39 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s40) | (~node3(c_bit1, s40, s41)) | (~m_counter_cell_v_value(c_bit1, s41)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s41)) | node2(c_bit1, s40) | (~node3(c_bit1, s40, s41))))),
% 13.18/13.39 inference(monotonicity,[status(thm)],[2703])).
% 13.18/13.39 tff(2705,plain,
% 13.18/13.39 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s40) | (~node3(c_bit1, s40, s41)) | (~m_counter_cell_v_value(c_bit1, s41)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s41)) | node2(c_bit1, s40) | (~node3(c_bit1, s40, s41)))),
% 13.18/13.39 inference(transitivity,[status(thm)],[2704, 2702])).
% 13.18/13.39 tff(2706,plain,
% 13.18/13.39 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s40) | (~node3(c_bit1, s40, s41)) | (~m_counter_cell_v_value(c_bit1, s41)))),
% 13.18/13.39 inference(quant_inst,[status(thm)],[])).
% 13.18/13.39 tff(2707,plain,
% 13.18/13.39 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s41)) | node2(c_bit1, s40) | (~node3(c_bit1, s40, s41))),
% 13.18/13.39 inference(modus_ponens,[status(thm)],[2706, 2705])).
% 13.18/13.39 tff(2708,plain,
% 13.18/13.39 ((~m_counter_cell_v_value(c_bit1, s41)) | node2(c_bit1, s40)),
% 13.18/13.39 inference(unit_resolution,[status(thm)],[2707, 121, 2701])).
% 13.18/13.39 tff(2709,plain,
% 13.18/13.39 (~m_counter_cell_v_value(c_bit1, s41)),
% 13.18/13.39 inference(unit_resolution,[status(thm)],[2708, 2697])).
% 13.18/13.39 tff(2710,plain,
% 13.18/13.39 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s41)) | (~m_counter_cell_v_value(c_bit0, s41)) | m_counter_cell_v_carry_out(c_bit0, s41))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s41)) | (~m_counter_cell_v_value(c_bit0, s41)) | m_counter_cell_v_carry_out(c_bit0, s41))),
% 13.18/13.39 inference(rewrite,[status(thm)],[])).
% 13.18/13.39 tff(2711,plain,
% 13.18/13.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s41)) | (~m_counter_cell_v_value(c_bit0, s41)) | m_counter_cell_v_carry_out(c_bit0, s41))),
% 13.18/13.39 inference(quant_inst,[status(thm)],[])).
% 13.18/13.39 tff(2712,plain,
% 13.18/13.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s41)) | (~m_counter_cell_v_value(c_bit0, s41)) | m_counter_cell_v_carry_out(c_bit0, s41)),
% 13.18/13.39 inference(modus_ponens,[status(thm)],[2711, 2710])).
% 13.18/13.39 tff(2713,plain,
% 13.18/13.39 ((~m_counter_cell_v_value(c_bit0, s41)) | m_counter_cell_v_carry_out(c_bit0, s41)),
% 13.18/13.39 inference(unit_resolution,[status(thm)],[2712, 1390, 1252])).
% 13.18/13.39 tff(2714,plain,
% 13.18/13.39 (m_counter_cell_v_carry_out(c_bit0, s41)),
% 13.18/13.39 inference(unit_resolution,[status(thm)],[2713, 1248])).
% 13.18/13.39 tff(2715,plain,
% 13.18/13.39 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s41)) | m_counter_cell_v_carry_in(c_bit1, s41))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s41)) | m_counter_cell_v_carry_in(c_bit1, s41))),
% 13.18/13.39 inference(rewrite,[status(thm)],[])).
% 13.18/13.39 tff(2716,plain,
% 13.18/13.39 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s41)) | m_counter_cell_v_carry_in(c_bit1, s41))),
% 13.18/13.39 inference(quant_inst,[status(thm)],[])).
% 13.18/13.39 tff(2717,plain,
% 13.18/13.39 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s41)) | m_counter_cell_v_carry_in(c_bit1, s41)),
% 13.18/13.39 inference(modus_ponens,[status(thm)],[2716, 2715])).
% 13.18/13.39 tff(2718,plain,
% 13.18/13.39 (m_counter_cell_v_carry_in(c_bit1, s41)),
% 13.18/13.39 inference(unit_resolution,[status(thm)],[2717, 1405, 2714])).
% 13.18/13.39 tff(2719,assumption,(m_counter_cell_v_carry_in(c_bit1, s41)), introduced(assumption)).
% 13.18/13.39 tff(2720,assumption,(node1(c_bit1, s41)), introduced(assumption)).
% 13.18/13.39 tff(2721,assumption,(~m_counter_cell_v_value(c_bit1, s41)), introduced(assumption)).
% 13.18/13.39 tff(2722,plain,
% 13.18/13.39 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s41)) | m_counter_cell_v_value(c_bit1, s41) | (~node1(c_bit1, s41)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s41)) | m_counter_cell_v_value(c_bit1, s41) | (~node1(c_bit1, s41)))),
% 13.18/13.39 inference(rewrite,[status(thm)],[])).
% 13.18/13.39 tff(2723,plain,
% 13.18/13.39 (((~node1(c_bit1, s41)) | (~m_counter_cell_v_carry_in(c_bit1, s41)) | m_counter_cell_v_value(c_bit1, s41)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s41)) | m_counter_cell_v_value(c_bit1, s41) | (~node1(c_bit1, s41)))),
% 13.18/13.39 inference(rewrite,[status(thm)],[])).
% 13.18/13.39 tff(2724,plain,
% 13.18/13.39 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s41)) | (~m_counter_cell_v_carry_in(c_bit1, s41)) | m_counter_cell_v_value(c_bit1, s41))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s41)) | m_counter_cell_v_value(c_bit1, s41) | (~node1(c_bit1, s41))))),
% 13.18/13.39 inference(monotonicity,[status(thm)],[2723])).
% 13.18/13.39 tff(2725,plain,
% 13.18/13.39 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s41)) | (~m_counter_cell_v_carry_in(c_bit1, s41)) | m_counter_cell_v_value(c_bit1, s41))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s41)) | m_counter_cell_v_value(c_bit1, s41) | (~node1(c_bit1, s41)))),
% 13.18/13.39 inference(transitivity,[status(thm)],[2724, 2722])).
% 13.18/13.39 tff(2726,plain,
% 13.18/13.39 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s41)) | (~m_counter_cell_v_carry_in(c_bit1, s41)) | m_counter_cell_v_value(c_bit1, s41))),
% 13.18/13.39 inference(quant_inst,[status(thm)],[])).
% 13.18/13.39 tff(2727,plain,
% 13.18/13.39 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s41)) | m_counter_cell_v_value(c_bit1, s41) | (~node1(c_bit1, s41))),
% 13.18/13.39 inference(modus_ponens,[status(thm)],[2726, 2725])).
% 13.18/13.39 tff(2728,plain,
% 13.18/13.39 ($false),
% 13.18/13.39 inference(unit_resolution,[status(thm)],[2727, 30, 2721, 2720, 2719])).
% 13.18/13.39 tff(2729,plain,(m_counter_cell_v_value(c_bit1, s41) | (~node1(c_bit1, s41)) | (~m_counter_cell_v_carry_in(c_bit1, s41))), inference(lemma,lemma(discharge,[]))).
% 13.18/13.39 tff(2730,plain,
% 13.18/13.39 (m_counter_cell_v_value(c_bit1, s41) | (~node1(c_bit1, s41))),
% 13.18/13.39 inference(unit_resolution,[status(thm)],[2729, 2718])).
% 13.18/13.39 tff(2731,plain,
% 13.18/13.39 (~node1(c_bit1, s41)),
% 13.18/13.39 inference(unit_resolution,[status(thm)],[2730, 2709])).
% 13.18/13.39 tff(2732,plain,
% 13.18/13.39 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s41, s42)) | node3(c_bit1, s41, s42))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s41, s42)) | node3(c_bit1, s41, s42))),
% 13.18/13.39 inference(rewrite,[status(thm)],[])).
% 13.18/13.39 tff(2733,plain,
% 13.18/13.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s41, s42)) | node3(c_bit1, s41, s42))),
% 13.18/13.39 inference(quant_inst,[status(thm)],[])).
% 13.18/13.39 tff(2734,plain,
% 13.18/13.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s41, s42)) | node3(c_bit1, s41, s42)),
% 13.18/13.39 inference(modus_ponens,[status(thm)],[2733, 2732])).
% 13.18/13.39 tff(2735,plain,
% 13.18/13.39 (node3(c_bit1, s41, s42)),
% 13.18/13.39 inference(unit_resolution,[status(thm)],[2734, 59, 1264])).
% 13.18/13.39 tff(2736,plain,
% 13.18/13.39 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s42) | node1(c_bit1, s41) | (~node3(c_bit1, s41, s42)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s42) | node1(c_bit1, s41) | (~node3(c_bit1, s41, s42)))),
% 13.18/13.39 inference(rewrite,[status(thm)],[])).
% 13.18/13.39 tff(2737,plain,
% 13.18/13.39 ((node1(c_bit1, s41) | (~node3(c_bit1, s41, s42)) | m_counter_cell_v_value(c_bit1, s42)) <=> (m_counter_cell_v_value(c_bit1, s42) | node1(c_bit1, s41) | (~node3(c_bit1, s41, s42)))),
% 13.18/13.39 inference(rewrite,[status(thm)],[])).
% 13.18/13.39 tff(2738,plain,
% 13.18/13.39 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s41) | (~node3(c_bit1, s41, s42)) | m_counter_cell_v_value(c_bit1, s42))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s42) | node1(c_bit1, s41) | (~node3(c_bit1, s41, s42))))),
% 13.18/13.39 inference(monotonicity,[status(thm)],[2737])).
% 13.18/13.39 tff(2739,plain,
% 13.18/13.39 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s41) | (~node3(c_bit1, s41, s42)) | m_counter_cell_v_value(c_bit1, s42))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s42) | node1(c_bit1, s41) | (~node3(c_bit1, s41, s42)))),
% 13.18/13.39 inference(transitivity,[status(thm)],[2738, 2736])).
% 13.18/13.39 tff(2740,plain,
% 13.18/13.39 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s41) | (~node3(c_bit1, s41, s42)) | m_counter_cell_v_value(c_bit1, s42))),
% 13.18/13.39 inference(quant_inst,[status(thm)],[])).
% 13.18/13.39 tff(2741,plain,
% 13.18/13.39 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s42) | node1(c_bit1, s41) | (~node3(c_bit1, s41, s42))),
% 13.18/13.39 inference(modus_ponens,[status(thm)],[2740, 2739])).
% 13.18/13.39 tff(2742,plain,
% 13.18/13.39 (m_counter_cell_v_value(c_bit1, s42) | node1(c_bit1, s41)),
% 13.18/13.39 inference(unit_resolution,[status(thm)],[2741, 73, 2735])).
% 13.18/13.39 tff(2743,plain,
% 13.18/13.39 (m_counter_cell_v_value(c_bit1, s42)),
% 13.18/13.39 inference(unit_resolution,[status(thm)],[2742, 2731])).
% 13.18/13.39 tff(2744,plain,
% 13.18/13.39 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s42) | (~node4(c_bit0, s42)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s42) | (~node4(c_bit0, s42)))),
% 13.18/13.39 inference(rewrite,[status(thm)],[])).
% 13.18/13.39 tff(2745,plain,
% 13.18/13.39 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s42) | (~node4(c_bit0, s42)))),
% 13.18/13.39 inference(quant_inst,[status(thm)],[])).
% 13.18/13.39 tff(2746,plain,
% 13.18/13.39 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s42) | (~node4(c_bit0, s42))),
% 13.18/13.39 inference(modus_ponens,[status(thm)],[2745, 2744])).
% 13.18/13.39 tff(2747,plain,
% 13.18/13.39 (~node4(c_bit0, s42)),
% 13.18/13.39 inference(unit_resolution,[status(thm)],[2746, 1344, 1276])).
% 13.18/13.39 tff(2748,assumption,(m_counter_cell_v_carry_out(c_bit0, s42)), introduced(assumption)).
% 13.18/13.39 tff(2749,plain,
% 13.18/13.39 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s42)) | node4(c_bit0, s42))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s42)) | node4(c_bit0, s42))),
% 13.18/13.39 inference(rewrite,[status(thm)],[])).
% 13.18/13.39 tff(2750,plain,
% 13.18/13.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s42)) | node4(c_bit0, s42))),
% 13.18/13.39 inference(quant_inst,[status(thm)],[])).
% 13.18/13.39 tff(2751,plain,
% 13.18/13.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s42)) | node4(c_bit0, s42)),
% 13.18/13.39 inference(modus_ponens,[status(thm)],[2750, 2749])).
% 13.18/13.39 tff(2752,plain,
% 13.18/13.39 ($false),
% 13.18/13.39 inference(unit_resolution,[status(thm)],[2751, 1359, 2748, 2747])).
% 13.18/13.39 tff(2753,plain,(~m_counter_cell_v_carry_out(c_bit0, s42)), inference(lemma,lemma(discharge,[]))).
% 13.18/13.39 tff(2754,plain,
% 13.18/13.39 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s42)) | m_counter_cell_v_carry_out(c_bit0, s42))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s42)) | m_counter_cell_v_carry_out(c_bit0, s42))),
% 13.18/13.39 inference(rewrite,[status(thm)],[])).
% 13.18/13.39 tff(2755,plain,
% 13.18/13.39 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s42)) | m_counter_cell_v_carry_out(c_bit0, s42))),
% 13.18/13.39 inference(quant_inst,[status(thm)],[])).
% 13.18/13.39 tff(2756,plain,
% 13.18/13.39 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s42)) | m_counter_cell_v_carry_out(c_bit0, s42)),
% 13.18/13.39 inference(modus_ponens,[status(thm)],[2755, 2754])).
% 13.18/13.39 tff(2757,plain,
% 13.18/13.39 (~m_counter_cell_v_carry_in(c_bit1, s42)),
% 13.18/13.39 inference(unit_resolution,[status(thm)],[2756, 1374, 2753])).
% 13.18/13.39 tff(2758,assumption,(node1(c_bit1, s42)), introduced(assumption)).
% 13.18/13.39 tff(2759,assumption,(m_counter_cell_v_value(c_bit1, s42)), introduced(assumption)).
% 13.18/13.39 tff(2760,plain,
% 13.18/13.39 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s42) | (~m_counter_cell_v_value(c_bit1, s42)) | (~node1(c_bit1, s42)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s42) | (~m_counter_cell_v_value(c_bit1, s42)) | (~node1(c_bit1, s42)))),
% 13.18/13.39 inference(rewrite,[status(thm)],[])).
% 13.18/13.39 tff(2761,plain,
% 13.18/13.39 (((~node1(c_bit1, s42)) | m_counter_cell_v_carry_in(c_bit1, s42) | (~m_counter_cell_v_value(c_bit1, s42))) <=> (m_counter_cell_v_carry_in(c_bit1, s42) | (~m_counter_cell_v_value(c_bit1, s42)) | (~node1(c_bit1, s42)))),
% 13.18/13.39 inference(rewrite,[status(thm)],[])).
% 13.18/13.39 tff(2762,plain,
% 13.18/13.39 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s42)) | m_counter_cell_v_carry_in(c_bit1, s42) | (~m_counter_cell_v_value(c_bit1, s42)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s42) | (~m_counter_cell_v_value(c_bit1, s42)) | (~node1(c_bit1, s42))))),
% 13.18/13.39 inference(monotonicity,[status(thm)],[2761])).
% 13.18/13.39 tff(2763,plain,
% 13.18/13.39 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s42)) | m_counter_cell_v_carry_in(c_bit1, s42) | (~m_counter_cell_v_value(c_bit1, s42)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s42) | (~m_counter_cell_v_value(c_bit1, s42)) | (~node1(c_bit1, s42)))),
% 13.18/13.39 inference(transitivity,[status(thm)],[2762, 2760])).
% 13.18/13.39 tff(2764,plain,
% 13.18/13.39 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s42)) | m_counter_cell_v_carry_in(c_bit1, s42) | (~m_counter_cell_v_value(c_bit1, s42)))),
% 13.18/13.39 inference(quant_inst,[status(thm)],[])).
% 13.18/13.39 tff(2765,plain,
% 13.18/13.39 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s42) | (~m_counter_cell_v_value(c_bit1, s42)) | (~node1(c_bit1, s42))),
% 13.18/13.39 inference(modus_ponens,[status(thm)],[2764, 2763])).
% 13.18/13.39 tff(2766,plain,
% 13.18/13.39 ($false),
% 13.18/13.39 inference(unit_resolution,[status(thm)],[2765, 1569, 2759, 2758, 2757])).
% 13.18/13.39 tff(2767,plain,((~m_counter_cell_v_value(c_bit1, s42)) | (~node1(c_bit1, s42))), inference(lemma,lemma(discharge,[]))).
% 13.18/13.39 tff(2768,plain,
% 13.18/13.39 (~node1(c_bit1, s42)),
% 13.18/13.39 inference(unit_resolution,[status(thm)],[2767, 2743])).
% 13.18/13.39 tff(2769,plain,
% 13.18/13.39 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s42, s43)) | node3(c_bit1, s42, s43))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s42, s43)) | node3(c_bit1, s42, s43))),
% 13.18/13.39 inference(rewrite,[status(thm)],[])).
% 13.18/13.39 tff(2770,plain,
% 13.18/13.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s42, s43)) | node3(c_bit1, s42, s43))),
% 13.18/13.39 inference(quant_inst,[status(thm)],[])).
% 13.18/13.39 tff(2771,plain,
% 13.18/13.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s42, s43)) | node3(c_bit1, s42, s43)),
% 13.18/13.39 inference(modus_ponens,[status(thm)],[2770, 2769])).
% 13.18/13.39 tff(2772,plain,
% 13.18/13.39 (node3(c_bit1, s42, s43)),
% 13.18/13.39 inference(unit_resolution,[status(thm)],[2771, 59, 1295])).
% 13.18/13.39 tff(2773,plain,
% 13.18/13.39 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s43) | node1(c_bit1, s42) | (~node3(c_bit1, s42, s43)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s43) | node1(c_bit1, s42) | (~node3(c_bit1, s42, s43)))),
% 13.18/13.39 inference(rewrite,[status(thm)],[])).
% 13.25/13.39 tff(2774,plain,
% 13.25/13.39 ((node1(c_bit1, s42) | (~node3(c_bit1, s42, s43)) | m_counter_cell_v_value(c_bit1, s43)) <=> (m_counter_cell_v_value(c_bit1, s43) | node1(c_bit1, s42) | (~node3(c_bit1, s42, s43)))),
% 13.25/13.39 inference(rewrite,[status(thm)],[])).
% 13.25/13.39 tff(2775,plain,
% 13.25/13.39 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s42) | (~node3(c_bit1, s42, s43)) | m_counter_cell_v_value(c_bit1, s43))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s43) | node1(c_bit1, s42) | (~node3(c_bit1, s42, s43))))),
% 13.25/13.39 inference(monotonicity,[status(thm)],[2774])).
% 13.25/13.39 tff(2776,plain,
% 13.25/13.39 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s42) | (~node3(c_bit1, s42, s43)) | m_counter_cell_v_value(c_bit1, s43))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s43) | node1(c_bit1, s42) | (~node3(c_bit1, s42, s43)))),
% 13.25/13.39 inference(transitivity,[status(thm)],[2775, 2773])).
% 13.25/13.39 tff(2777,plain,
% 13.25/13.39 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s42) | (~node3(c_bit1, s42, s43)) | m_counter_cell_v_value(c_bit1, s43))),
% 13.25/13.39 inference(quant_inst,[status(thm)],[])).
% 13.25/13.39 tff(2778,plain,
% 13.25/13.39 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s43) | node1(c_bit1, s42) | (~node3(c_bit1, s42, s43))),
% 13.25/13.39 inference(modus_ponens,[status(thm)],[2777, 2776])).
% 13.25/13.39 tff(2779,plain,
% 13.25/13.39 (m_counter_cell_v_value(c_bit1, s43) | node1(c_bit1, s42)),
% 13.25/13.39 inference(unit_resolution,[status(thm)],[2778, 73, 2772])).
% 13.25/13.39 tff(2780,plain,
% 13.25/13.39 (m_counter_cell_v_value(c_bit1, s43)),
% 13.25/13.39 inference(unit_resolution,[status(thm)],[2779, 2768])).
% 13.25/13.39 tff(2781,plain,
% 13.25/13.39 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s43)) | (~m_counter_cell_v_value(c_bit0, s43)) | m_counter_cell_v_carry_out(c_bit0, s43))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s43)) | (~m_counter_cell_v_value(c_bit0, s43)) | m_counter_cell_v_carry_out(c_bit0, s43))),
% 13.25/13.39 inference(rewrite,[status(thm)],[])).
% 13.25/13.39 tff(2782,plain,
% 13.25/13.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s43)) | (~m_counter_cell_v_value(c_bit0, s43)) | m_counter_cell_v_carry_out(c_bit0, s43))),
% 13.25/13.39 inference(quant_inst,[status(thm)],[])).
% 13.25/13.39 tff(2783,plain,
% 13.25/13.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s43)) | (~m_counter_cell_v_value(c_bit0, s43)) | m_counter_cell_v_carry_out(c_bit0, s43)),
% 13.25/13.39 inference(modus_ponens,[status(thm)],[2782, 2781])).
% 13.25/13.39 tff(2784,plain,
% 13.25/13.39 ((~m_counter_cell_v_value(c_bit0, s43)) | m_counter_cell_v_carry_out(c_bit0, s43)),
% 13.25/13.39 inference(unit_resolution,[status(thm)],[2783, 1390, 1311])).
% 13.25/13.39 tff(2785,plain,
% 13.25/13.39 (m_counter_cell_v_carry_out(c_bit0, s43)),
% 13.25/13.39 inference(unit_resolution,[status(thm)],[2784, 1307])).
% 13.25/13.39 tff(2786,plain,
% 13.25/13.39 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s43)) | m_counter_cell_v_carry_in(c_bit1, s43))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s43)) | m_counter_cell_v_carry_in(c_bit1, s43))),
% 13.25/13.39 inference(rewrite,[status(thm)],[])).
% 13.25/13.39 tff(2787,plain,
% 13.25/13.39 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s43)) | m_counter_cell_v_carry_in(c_bit1, s43))),
% 13.25/13.39 inference(quant_inst,[status(thm)],[])).
% 13.25/13.39 tff(2788,plain,
% 13.25/13.39 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s43)) | m_counter_cell_v_carry_in(c_bit1, s43)),
% 13.25/13.39 inference(modus_ponens,[status(thm)],[2787, 2786])).
% 13.25/13.39 tff(2789,plain,
% 13.25/13.39 (m_counter_cell_v_carry_in(c_bit1, s43)),
% 13.25/13.39 inference(unit_resolution,[status(thm)],[2788, 1405, 2785])).
% 13.25/13.39 tff(2790,assumption,(m_counter_cell_v_value(c_bit1, s43)), introduced(assumption)).
% 13.25/13.39 tff(2791,assumption,(node2(c_bit1, s43)), introduced(assumption)).
% 13.25/13.39 tff(2792,plain,
% 13.25/13.39 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s43)) | (~m_counter_cell_v_value(c_bit1, s43)) | (~node2(c_bit1, s43)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s43)) | (~m_counter_cell_v_value(c_bit1, s43)) | (~node2(c_bit1, s43)))),
% 13.25/13.39 inference(rewrite,[status(thm)],[])).
% 13.25/13.39 tff(2793,plain,
% 13.25/13.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s43)) | (~m_counter_cell_v_value(c_bit1, s43)) | (~node2(c_bit1, s43)))),
% 13.25/13.39 inference(quant_inst,[status(thm)],[])).
% 13.25/13.39 tff(2794,plain,
% 13.25/13.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s43)) | (~m_counter_cell_v_value(c_bit1, s43)) | (~node2(c_bit1, s43))),
% 13.25/13.39 inference(modus_ponens,[status(thm)],[2793, 2792])).
% 13.25/13.39 tff(2795,plain,
% 13.25/13.39 ($false),
% 13.25/13.39 inference(unit_resolution,[status(thm)],[2794, 93, 2791, 2790, 2789])).
% 13.25/13.39 tff(2796,plain,((~m_counter_cell_v_value(c_bit1, s43)) | (~node2(c_bit1, s43))), inference(lemma,lemma(discharge,[]))).
% 13.25/13.39 tff(2797,plain,
% 13.25/13.39 (~node2(c_bit1, s43)),
% 13.25/13.39 inference(unit_resolution,[status(thm)],[2796, 2780])).
% 13.25/13.39 tff(2798,plain,
% 13.25/13.39 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s43, s44)) | node3(c_bit1, s43, s44))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s43, s44)) | node3(c_bit1, s43, s44))),
% 13.25/13.39 inference(rewrite,[status(thm)],[])).
% 13.25/13.39 tff(2799,plain,
% 13.25/13.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s43, s44)) | node3(c_bit1, s43, s44))),
% 13.25/13.39 inference(quant_inst,[status(thm)],[])).
% 13.25/13.39 tff(2800,plain,
% 13.25/13.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s43, s44)) | node3(c_bit1, s43, s44)),
% 13.25/13.39 inference(modus_ponens,[status(thm)],[2799, 2798])).
% 13.25/13.39 tff(2801,plain,
% 13.25/13.39 (node3(c_bit1, s43, s44)),
% 13.25/13.39 inference(unit_resolution,[status(thm)],[2800, 59, 1323])).
% 13.25/13.39 tff(2802,plain,
% 13.25/13.39 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s44)) | node2(c_bit1, s43) | (~node3(c_bit1, s43, s44)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s44)) | node2(c_bit1, s43) | (~node3(c_bit1, s43, s44)))),
% 13.25/13.39 inference(rewrite,[status(thm)],[])).
% 13.25/13.39 tff(2803,plain,
% 13.25/13.39 ((node2(c_bit1, s43) | (~node3(c_bit1, s43, s44)) | (~m_counter_cell_v_value(c_bit1, s44))) <=> ((~m_counter_cell_v_value(c_bit1, s44)) | node2(c_bit1, s43) | (~node3(c_bit1, s43, s44)))),
% 13.25/13.39 inference(rewrite,[status(thm)],[])).
% 13.25/13.39 tff(2804,plain,
% 13.25/13.39 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s43) | (~node3(c_bit1, s43, s44)) | (~m_counter_cell_v_value(c_bit1, s44)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s44)) | node2(c_bit1, s43) | (~node3(c_bit1, s43, s44))))),
% 13.25/13.39 inference(monotonicity,[status(thm)],[2803])).
% 13.25/13.39 tff(2805,plain,
% 13.25/13.39 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s43) | (~node3(c_bit1, s43, s44)) | (~m_counter_cell_v_value(c_bit1, s44)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s44)) | node2(c_bit1, s43) | (~node3(c_bit1, s43, s44)))),
% 13.25/13.40 inference(transitivity,[status(thm)],[2804, 2802])).
% 13.25/13.40 tff(2806,plain,
% 13.25/13.40 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s43) | (~node3(c_bit1, s43, s44)) | (~m_counter_cell_v_value(c_bit1, s44)))),
% 13.25/13.40 inference(quant_inst,[status(thm)],[])).
% 13.25/13.40 tff(2807,plain,
% 13.25/13.40 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s44)) | node2(c_bit1, s43) | (~node3(c_bit1, s43, s44))),
% 13.25/13.40 inference(modus_ponens,[status(thm)],[2806, 2805])).
% 13.25/13.40 tff(2808,plain,
% 13.25/13.40 ((~m_counter_cell_v_value(c_bit1, s44)) | node2(c_bit1, s43)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2807, 121, 2801])).
% 13.25/13.40 tff(2809,plain,
% 13.25/13.40 (~m_counter_cell_v_value(c_bit1, s44)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2808, 2797])).
% 13.25/13.40 tff(2810,plain,
% 13.25/13.40 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s44) | m_counter_cell_v_value(c_bit1, s44) | (~node2(c_bit1, s44)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s44) | m_counter_cell_v_value(c_bit1, s44) | (~node2(c_bit1, s44)))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2811,plain,
% 13.25/13.40 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s44) | m_counter_cell_v_value(c_bit1, s44) | (~node2(c_bit1, s44)))),
% 13.25/13.40 inference(quant_inst,[status(thm)],[])).
% 13.25/13.40 tff(2812,plain,
% 13.25/13.40 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s44) | m_counter_cell_v_value(c_bit1, s44) | (~node2(c_bit1, s44))),
% 13.25/13.40 inference(modus_ponens,[status(thm)],[2811, 2810])).
% 13.25/13.40 tff(2813,plain,
% 13.25/13.40 (~node2(c_bit1, s44)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2812, 1498, 2809, 1380])).
% 13.25/13.40 tff(2814,plain,
% 13.25/13.40 (succ(s44, s45) <=> succ(s44, s45)),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2815,axiom,(succ(s44, s45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound45')).
% 13.25/13.40 tff(2816,plain,
% 13.25/13.40 (succ(s44, s45)),
% 13.25/13.40 inference(modus_ponens,[status(thm)],[2815, 2814])).
% 13.25/13.40 tff(2817,plain,
% 13.25/13.40 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s44, s45)) | trans(s44, s45))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s44, s45)) | trans(s44, s45))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2818,plain,
% 13.25/13.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s44, s45)) | trans(s44, s45))),
% 13.25/13.40 inference(quant_inst,[status(thm)],[])).
% 13.25/13.40 tff(2819,plain,
% 13.25/13.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s44, s45)) | trans(s44, s45)),
% 13.25/13.40 inference(modus_ponens,[status(thm)],[2818, 2817])).
% 13.25/13.40 tff(2820,plain,
% 13.25/13.40 (trans(s44, s45)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2819, 2816, 45])).
% 13.25/13.40 tff(2821,plain,
% 13.25/13.40 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s44, s45)) | node3(c_bit1, s44, s45))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s44, s45)) | node3(c_bit1, s44, s45))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2822,plain,
% 13.25/13.40 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s44, s45)) | node3(c_bit1, s44, s45))),
% 13.25/13.40 inference(quant_inst,[status(thm)],[])).
% 13.25/13.40 tff(2823,plain,
% 13.25/13.40 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s44, s45)) | node3(c_bit1, s44, s45)),
% 13.25/13.40 inference(modus_ponens,[status(thm)],[2822, 2821])).
% 13.25/13.40 tff(2824,plain,
% 13.25/13.40 (node3(c_bit1, s44, s45)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2823, 59, 2820])).
% 13.25/13.40 tff(2825,plain,
% 13.25/13.40 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s45)) | node2(c_bit1, s44) | (~node3(c_bit1, s44, s45)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s45)) | node2(c_bit1, s44) | (~node3(c_bit1, s44, s45)))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2826,plain,
% 13.25/13.40 ((node2(c_bit1, s44) | (~node3(c_bit1, s44, s45)) | (~m_counter_cell_v_value(c_bit1, s45))) <=> ((~m_counter_cell_v_value(c_bit1, s45)) | node2(c_bit1, s44) | (~node3(c_bit1, s44, s45)))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2827,plain,
% 13.25/13.40 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s44) | (~node3(c_bit1, s44, s45)) | (~m_counter_cell_v_value(c_bit1, s45)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s45)) | node2(c_bit1, s44) | (~node3(c_bit1, s44, s45))))),
% 13.25/13.40 inference(monotonicity,[status(thm)],[2826])).
% 13.25/13.40 tff(2828,plain,
% 13.25/13.40 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s44) | (~node3(c_bit1, s44, s45)) | (~m_counter_cell_v_value(c_bit1, s45)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s45)) | node2(c_bit1, s44) | (~node3(c_bit1, s44, s45)))),
% 13.25/13.40 inference(transitivity,[status(thm)],[2827, 2825])).
% 13.25/13.40 tff(2829,plain,
% 13.25/13.40 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s44) | (~node3(c_bit1, s44, s45)) | (~m_counter_cell_v_value(c_bit1, s45)))),
% 13.25/13.40 inference(quant_inst,[status(thm)],[])).
% 13.25/13.40 tff(2830,plain,
% 13.25/13.40 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s45)) | node2(c_bit1, s44) | (~node3(c_bit1, s44, s45))),
% 13.25/13.40 inference(modus_ponens,[status(thm)],[2829, 2828])).
% 13.25/13.40 tff(2831,plain,
% 13.25/13.40 ((~m_counter_cell_v_value(c_bit1, s45)) | node2(c_bit1, s44)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2830, 121, 2824])).
% 13.25/13.40 tff(2832,plain,
% 13.25/13.40 (~m_counter_cell_v_value(c_bit1, s45)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2831, 2813])).
% 13.25/13.40 tff(2833,assumption,(node1(c_bit1, s45)), introduced(assumption)).
% 13.25/13.40 tff(2834,assumption,(~m_counter_cell_v_carry_in(c_bit0, s44)), introduced(assumption)).
% 13.25/13.40 tff(2835,plain,
% 13.25/13.40 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s44)),
% 13.25/13.40 inference(quant_inst,[status(thm)],[])).
% 13.25/13.40 tff(2836,plain,
% 13.25/13.40 ($false),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2835, 18, 2834])).
% 13.25/13.40 tff(2837,plain,(m_counter_cell_v_carry_in(c_bit0, s44)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.40 tff(2838,plain,
% 13.25/13.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s44)) | m_counter_cell_v_value(c_bit0, s44) | (~node1(c_bit0, s44)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s44)) | m_counter_cell_v_value(c_bit0, s44) | (~node1(c_bit0, s44)))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2839,plain,
% 13.25/13.40 (((~node1(c_bit0, s44)) | (~m_counter_cell_v_carry_in(c_bit0, s44)) | m_counter_cell_v_value(c_bit0, s44)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s44)) | m_counter_cell_v_value(c_bit0, s44) | (~node1(c_bit0, s44)))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2840,plain,
% 13.25/13.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s44)) | (~m_counter_cell_v_carry_in(c_bit0, s44)) | m_counter_cell_v_value(c_bit0, s44))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s44)) | m_counter_cell_v_value(c_bit0, s44) | (~node1(c_bit0, s44))))),
% 13.25/13.40 inference(monotonicity,[status(thm)],[2839])).
% 13.25/13.40 tff(2841,plain,
% 13.25/13.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s44)) | (~m_counter_cell_v_carry_in(c_bit0, s44)) | m_counter_cell_v_value(c_bit0, s44))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s44)) | m_counter_cell_v_value(c_bit0, s44) | (~node1(c_bit0, s44)))),
% 13.25/13.40 inference(transitivity,[status(thm)],[2840, 2838])).
% 13.25/13.40 tff(2842,plain,
% 13.25/13.40 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s44)) | (~m_counter_cell_v_carry_in(c_bit0, s44)) | m_counter_cell_v_value(c_bit0, s44))),
% 13.25/13.40 inference(quant_inst,[status(thm)],[])).
% 13.25/13.40 tff(2843,plain,
% 13.25/13.40 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s44)) | m_counter_cell_v_value(c_bit0, s44) | (~node1(c_bit0, s44))),
% 13.25/13.40 inference(modus_ponens,[status(thm)],[2842, 2841])).
% 13.25/13.40 tff(2844,plain,
% 13.25/13.40 (m_counter_cell_v_value(c_bit0, s44) | (~node1(c_bit0, s44))),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2843, 30, 2837])).
% 13.25/13.40 tff(2845,plain,
% 13.25/13.40 (~node1(c_bit0, s44)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2844, 1335])).
% 13.25/13.40 tff(2846,plain,
% 13.25/13.40 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s44, s45)) | node3(c_bit0, s44, s45))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s44, s45)) | node3(c_bit0, s44, s45))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2847,plain,
% 13.25/13.40 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s44, s45)) | node3(c_bit0, s44, s45))),
% 13.25/13.40 inference(quant_inst,[status(thm)],[])).
% 13.25/13.40 tff(2848,plain,
% 13.25/13.40 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s44, s45)) | node3(c_bit0, s44, s45)),
% 13.25/13.40 inference(modus_ponens,[status(thm)],[2847, 2846])).
% 13.25/13.40 tff(2849,plain,
% 13.25/13.40 (node3(c_bit0, s44, s45)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2848, 59, 2820])).
% 13.25/13.40 tff(2850,plain,
% 13.25/13.40 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s45) | node1(c_bit0, s44) | (~node3(c_bit0, s44, s45)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s45) | node1(c_bit0, s44) | (~node3(c_bit0, s44, s45)))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2851,plain,
% 13.25/13.40 ((node1(c_bit0, s44) | (~node3(c_bit0, s44, s45)) | m_counter_cell_v_value(c_bit0, s45)) <=> (m_counter_cell_v_value(c_bit0, s45) | node1(c_bit0, s44) | (~node3(c_bit0, s44, s45)))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2852,plain,
% 13.25/13.40 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s44) | (~node3(c_bit0, s44, s45)) | m_counter_cell_v_value(c_bit0, s45))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s45) | node1(c_bit0, s44) | (~node3(c_bit0, s44, s45))))),
% 13.25/13.40 inference(monotonicity,[status(thm)],[2851])).
% 13.25/13.40 tff(2853,plain,
% 13.25/13.40 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s44) | (~node3(c_bit0, s44, s45)) | m_counter_cell_v_value(c_bit0, s45))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s45) | node1(c_bit0, s44) | (~node3(c_bit0, s44, s45)))),
% 13.25/13.40 inference(transitivity,[status(thm)],[2852, 2850])).
% 13.25/13.40 tff(2854,plain,
% 13.25/13.40 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s44) | (~node3(c_bit0, s44, s45)) | m_counter_cell_v_value(c_bit0, s45))),
% 13.25/13.40 inference(quant_inst,[status(thm)],[])).
% 13.25/13.40 tff(2855,plain,
% 13.25/13.40 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s45) | node1(c_bit0, s44) | (~node3(c_bit0, s44, s45))),
% 13.25/13.40 inference(modus_ponens,[status(thm)],[2854, 2853])).
% 13.25/13.40 tff(2856,plain,
% 13.25/13.40 (m_counter_cell_v_value(c_bit0, s45) | node1(c_bit0, s44)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2855, 73, 2849])).
% 13.25/13.40 tff(2857,plain,
% 13.25/13.40 (m_counter_cell_v_value(c_bit0, s45)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2856, 2845])).
% 13.25/13.40 tff(2858,assumption,(~m_counter_cell_v_carry_in(c_bit0, s45)), introduced(assumption)).
% 13.25/13.40 tff(2859,plain,
% 13.25/13.40 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s45)),
% 13.25/13.40 inference(quant_inst,[status(thm)],[])).
% 13.25/13.40 tff(2860,plain,
% 13.25/13.40 ($false),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2859, 18, 2858])).
% 13.25/13.40 tff(2861,plain,(m_counter_cell_v_carry_in(c_bit0, s45)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.40 tff(2862,plain,
% 13.25/13.40 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s45)) | (~m_counter_cell_v_value(c_bit0, s45)) | m_counter_cell_v_carry_out(c_bit0, s45))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s45)) | (~m_counter_cell_v_value(c_bit0, s45)) | m_counter_cell_v_carry_out(c_bit0, s45))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2863,plain,
% 13.25/13.40 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s45)) | (~m_counter_cell_v_value(c_bit0, s45)) | m_counter_cell_v_carry_out(c_bit0, s45))),
% 13.25/13.40 inference(quant_inst,[status(thm)],[])).
% 13.25/13.40 tff(2864,plain,
% 13.25/13.40 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s45)) | (~m_counter_cell_v_value(c_bit0, s45)) | m_counter_cell_v_carry_out(c_bit0, s45)),
% 13.25/13.40 inference(modus_ponens,[status(thm)],[2863, 2862])).
% 13.25/13.40 tff(2865,plain,
% 13.25/13.40 ((~m_counter_cell_v_value(c_bit0, s45)) | m_counter_cell_v_carry_out(c_bit0, s45)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2864, 1390, 2861])).
% 13.25/13.40 tff(2866,plain,
% 13.25/13.40 (m_counter_cell_v_carry_out(c_bit0, s45)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2865, 2857])).
% 13.25/13.40 tff(2867,plain,
% 13.25/13.40 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s45)) | m_counter_cell_v_carry_in(c_bit1, s45))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s45)) | m_counter_cell_v_carry_in(c_bit1, s45))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2868,plain,
% 13.25/13.40 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s45)) | m_counter_cell_v_carry_in(c_bit1, s45))),
% 13.25/13.40 inference(quant_inst,[status(thm)],[])).
% 13.25/13.40 tff(2869,plain,
% 13.25/13.40 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s45)) | m_counter_cell_v_carry_in(c_bit1, s45)),
% 13.25/13.40 inference(modus_ponens,[status(thm)],[2868, 2867])).
% 13.25/13.40 tff(2870,plain,
% 13.25/13.40 (m_counter_cell_v_carry_in(c_bit1, s45)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2869, 1405, 2866])).
% 13.25/13.40 tff(2871,assumption,(~m_counter_cell_v_value(c_bit1, s45)), introduced(assumption)).
% 13.25/13.40 tff(2872,plain,
% 13.25/13.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s45)) | m_counter_cell_v_value(c_bit1, s45) | (~node1(c_bit1, s45)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s45)) | m_counter_cell_v_value(c_bit1, s45) | (~node1(c_bit1, s45)))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2873,plain,
% 13.25/13.40 (((~node1(c_bit1, s45)) | (~m_counter_cell_v_carry_in(c_bit1, s45)) | m_counter_cell_v_value(c_bit1, s45)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s45)) | m_counter_cell_v_value(c_bit1, s45) | (~node1(c_bit1, s45)))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2874,plain,
% 13.25/13.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s45)) | (~m_counter_cell_v_carry_in(c_bit1, s45)) | m_counter_cell_v_value(c_bit1, s45))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s45)) | m_counter_cell_v_value(c_bit1, s45) | (~node1(c_bit1, s45))))),
% 13.25/13.40 inference(monotonicity,[status(thm)],[2873])).
% 13.25/13.40 tff(2875,plain,
% 13.25/13.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s45)) | (~m_counter_cell_v_carry_in(c_bit1, s45)) | m_counter_cell_v_value(c_bit1, s45))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s45)) | m_counter_cell_v_value(c_bit1, s45) | (~node1(c_bit1, s45)))),
% 13.25/13.40 inference(transitivity,[status(thm)],[2874, 2872])).
% 13.25/13.40 tff(2876,plain,
% 13.25/13.40 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s45)) | (~m_counter_cell_v_carry_in(c_bit1, s45)) | m_counter_cell_v_value(c_bit1, s45))),
% 13.25/13.40 inference(quant_inst,[status(thm)],[])).
% 13.25/13.40 tff(2877,plain,
% 13.25/13.40 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s45)) | m_counter_cell_v_value(c_bit1, s45) | (~node1(c_bit1, s45))),
% 13.25/13.40 inference(modus_ponens,[status(thm)],[2876, 2875])).
% 13.25/13.40 tff(2878,plain,
% 13.25/13.40 ($false),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2877, 30, 2871, 2870, 2833])).
% 13.25/13.40 tff(2879,plain,(m_counter_cell_v_value(c_bit1, s45) | (~node1(c_bit1, s45))), inference(lemma,lemma(discharge,[]))).
% 13.25/13.40 tff(2880,plain,
% 13.25/13.40 (~node1(c_bit1, s45)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2879, 2832])).
% 13.25/13.40 tff(2881,plain,
% 13.25/13.40 (succ(s45, s46) <=> succ(s45, s46)),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2882,axiom,(succ(s45, s46)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound46')).
% 13.25/13.40 tff(2883,plain,
% 13.25/13.40 (succ(s45, s46)),
% 13.25/13.40 inference(modus_ponens,[status(thm)],[2882, 2881])).
% 13.25/13.40 tff(2884,plain,
% 13.25/13.40 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s45, s46)) | trans(s45, s46))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s45, s46)) | trans(s45, s46))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2885,plain,
% 13.25/13.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s45, s46)) | trans(s45, s46))),
% 13.25/13.40 inference(quant_inst,[status(thm)],[])).
% 13.25/13.40 tff(2886,plain,
% 13.25/13.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s45, s46)) | trans(s45, s46)),
% 13.25/13.40 inference(modus_ponens,[status(thm)],[2885, 2884])).
% 13.25/13.40 tff(2887,plain,
% 13.25/13.40 (trans(s45, s46)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2886, 2883, 45])).
% 13.25/13.40 tff(2888,plain,
% 13.25/13.40 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s45, s46)) | node3(c_bit1, s45, s46))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s45, s46)) | node3(c_bit1, s45, s46))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2889,plain,
% 13.25/13.40 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s45, s46)) | node3(c_bit1, s45, s46))),
% 13.25/13.40 inference(quant_inst,[status(thm)],[])).
% 13.25/13.40 tff(2890,plain,
% 13.25/13.40 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s45, s46)) | node3(c_bit1, s45, s46)),
% 13.25/13.40 inference(modus_ponens,[status(thm)],[2889, 2888])).
% 13.25/13.40 tff(2891,plain,
% 13.25/13.40 (node3(c_bit1, s45, s46)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2890, 59, 2887])).
% 13.25/13.40 tff(2892,plain,
% 13.25/13.40 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s46) | node1(c_bit1, s45) | (~node3(c_bit1, s45, s46)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s46) | node1(c_bit1, s45) | (~node3(c_bit1, s45, s46)))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2893,plain,
% 13.25/13.40 ((node1(c_bit1, s45) | (~node3(c_bit1, s45, s46)) | m_counter_cell_v_value(c_bit1, s46)) <=> (m_counter_cell_v_value(c_bit1, s46) | node1(c_bit1, s45) | (~node3(c_bit1, s45, s46)))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2894,plain,
% 13.25/13.40 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s45) | (~node3(c_bit1, s45, s46)) | m_counter_cell_v_value(c_bit1, s46))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s46) | node1(c_bit1, s45) | (~node3(c_bit1, s45, s46))))),
% 13.25/13.40 inference(monotonicity,[status(thm)],[2893])).
% 13.25/13.40 tff(2895,plain,
% 13.25/13.40 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s45) | (~node3(c_bit1, s45, s46)) | m_counter_cell_v_value(c_bit1, s46))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s46) | node1(c_bit1, s45) | (~node3(c_bit1, s45, s46)))),
% 13.25/13.40 inference(transitivity,[status(thm)],[2894, 2892])).
% 13.25/13.40 tff(2896,plain,
% 13.25/13.40 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s45) | (~node3(c_bit1, s45, s46)) | m_counter_cell_v_value(c_bit1, s46))),
% 13.25/13.40 inference(quant_inst,[status(thm)],[])).
% 13.25/13.40 tff(2897,plain,
% 13.25/13.40 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s46) | node1(c_bit1, s45) | (~node3(c_bit1, s45, s46))),
% 13.25/13.40 inference(modus_ponens,[status(thm)],[2896, 2895])).
% 13.25/13.40 tff(2898,plain,
% 13.25/13.40 (m_counter_cell_v_value(c_bit1, s46) | node1(c_bit1, s45)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2897, 73, 2891])).
% 13.25/13.40 tff(2899,plain,
% 13.25/13.40 (m_counter_cell_v_value(c_bit1, s46)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2898, 2880])).
% 13.25/13.40 tff(2900,plain,
% 13.25/13.40 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s45)) | (~m_counter_cell_v_value(c_bit0, s45)) | (~node2(c_bit0, s45)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s45)) | (~m_counter_cell_v_value(c_bit0, s45)) | (~node2(c_bit0, s45)))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2901,plain,
% 13.25/13.40 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s45)) | (~m_counter_cell_v_value(c_bit0, s45)) | (~node2(c_bit0, s45)))),
% 13.25/13.40 inference(quant_inst,[status(thm)],[])).
% 13.25/13.40 tff(2902,plain,
% 13.25/13.40 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s45)) | (~m_counter_cell_v_value(c_bit0, s45)) | (~node2(c_bit0, s45))),
% 13.25/13.40 inference(modus_ponens,[status(thm)],[2901, 2900])).
% 13.25/13.40 tff(2903,plain,
% 13.25/13.40 ((~m_counter_cell_v_value(c_bit0, s45)) | (~node2(c_bit0, s45))),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2902, 93, 2861])).
% 13.25/13.40 tff(2904,plain,
% 13.25/13.40 (~node2(c_bit0, s45)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2903, 2857])).
% 13.25/13.40 tff(2905,plain,
% 13.25/13.40 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s45, s46)) | node3(c_bit0, s45, s46))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s45, s46)) | node3(c_bit0, s45, s46))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2906,plain,
% 13.25/13.40 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s45, s46)) | node3(c_bit0, s45, s46))),
% 13.25/13.40 inference(quant_inst,[status(thm)],[])).
% 13.25/13.40 tff(2907,plain,
% 13.25/13.40 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s45, s46)) | node3(c_bit0, s45, s46)),
% 13.25/13.40 inference(modus_ponens,[status(thm)],[2906, 2905])).
% 13.25/13.40 tff(2908,plain,
% 13.25/13.40 (node3(c_bit0, s45, s46)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2907, 59, 2887])).
% 13.25/13.40 tff(2909,plain,
% 13.25/13.40 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s46)) | node2(c_bit0, s45) | (~node3(c_bit0, s45, s46)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s46)) | node2(c_bit0, s45) | (~node3(c_bit0, s45, s46)))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2910,plain,
% 13.25/13.40 ((node2(c_bit0, s45) | (~node3(c_bit0, s45, s46)) | (~m_counter_cell_v_value(c_bit0, s46))) <=> ((~m_counter_cell_v_value(c_bit0, s46)) | node2(c_bit0, s45) | (~node3(c_bit0, s45, s46)))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2911,plain,
% 13.25/13.40 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s45) | (~node3(c_bit0, s45, s46)) | (~m_counter_cell_v_value(c_bit0, s46)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s46)) | node2(c_bit0, s45) | (~node3(c_bit0, s45, s46))))),
% 13.25/13.40 inference(monotonicity,[status(thm)],[2910])).
% 13.25/13.40 tff(2912,plain,
% 13.25/13.40 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s45) | (~node3(c_bit0, s45, s46)) | (~m_counter_cell_v_value(c_bit0, s46)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s46)) | node2(c_bit0, s45) | (~node3(c_bit0, s45, s46)))),
% 13.25/13.40 inference(transitivity,[status(thm)],[2911, 2909])).
% 13.25/13.40 tff(2913,plain,
% 13.25/13.40 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s45) | (~node3(c_bit0, s45, s46)) | (~m_counter_cell_v_value(c_bit0, s46)))),
% 13.25/13.40 inference(quant_inst,[status(thm)],[])).
% 13.25/13.40 tff(2914,plain,
% 13.25/13.40 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s46)) | node2(c_bit0, s45) | (~node3(c_bit0, s45, s46))),
% 13.25/13.40 inference(modus_ponens,[status(thm)],[2913, 2912])).
% 13.25/13.40 tff(2915,plain,
% 13.25/13.40 ((~m_counter_cell_v_value(c_bit0, s46)) | node2(c_bit0, s45)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2914, 121, 2908])).
% 13.25/13.40 tff(2916,plain,
% 13.25/13.40 (~m_counter_cell_v_value(c_bit0, s46)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2915, 2904])).
% 13.25/13.40 tff(2917,plain,
% 13.25/13.40 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s46) | (~node4(c_bit0, s46)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s46) | (~node4(c_bit0, s46)))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2918,plain,
% 13.25/13.40 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s46) | (~node4(c_bit0, s46)))),
% 13.25/13.40 inference(quant_inst,[status(thm)],[])).
% 13.25/13.40 tff(2919,plain,
% 13.25/13.40 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s46) | (~node4(c_bit0, s46))),
% 13.25/13.40 inference(modus_ponens,[status(thm)],[2918, 2917])).
% 13.25/13.40 tff(2920,plain,
% 13.25/13.40 (~node4(c_bit0, s46)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2919, 1344, 2916])).
% 13.25/13.40 tff(2921,assumption,(m_counter_cell_v_carry_out(c_bit0, s46)), introduced(assumption)).
% 13.25/13.40 tff(2922,plain,
% 13.25/13.40 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s46)) | node4(c_bit0, s46))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s46)) | node4(c_bit0, s46))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2923,plain,
% 13.25/13.40 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s46)) | node4(c_bit0, s46))),
% 13.25/13.40 inference(quant_inst,[status(thm)],[])).
% 13.25/13.40 tff(2924,plain,
% 13.25/13.40 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s46)) | node4(c_bit0, s46)),
% 13.25/13.40 inference(modus_ponens,[status(thm)],[2923, 2922])).
% 13.25/13.40 tff(2925,plain,
% 13.25/13.40 ($false),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2924, 1359, 2921, 2920])).
% 13.25/13.40 tff(2926,plain,(~m_counter_cell_v_carry_out(c_bit0, s46)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.40 tff(2927,assumption,(m_counter_cell_v_carry_in(c_bit1, s46)), introduced(assumption)).
% 13.25/13.40 tff(2928,assumption,(~m_counter_cell_v_carry_out(c_bit0, s46)), introduced(assumption)).
% 13.25/13.40 tff(2929,plain,
% 13.25/13.40 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s46)) | m_counter_cell_v_carry_out(c_bit0, s46))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s46)) | m_counter_cell_v_carry_out(c_bit0, s46))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2930,plain,
% 13.25/13.40 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s46)) | m_counter_cell_v_carry_out(c_bit0, s46))),
% 13.25/13.40 inference(quant_inst,[status(thm)],[])).
% 13.25/13.40 tff(2931,plain,
% 13.25/13.40 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s46)) | m_counter_cell_v_carry_out(c_bit0, s46)),
% 13.25/13.40 inference(modus_ponens,[status(thm)],[2930, 2929])).
% 13.25/13.40 tff(2932,plain,
% 13.25/13.40 ($false),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2931, 1374, 2928, 2927])).
% 13.25/13.40 tff(2933,plain,((~m_counter_cell_v_carry_in(c_bit1, s46)) | m_counter_cell_v_carry_out(c_bit0, s46)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.40 tff(2934,plain,
% 13.25/13.40 (~m_counter_cell_v_carry_in(c_bit1, s46)),
% 13.25/13.40 inference(unit_resolution,[status(thm)],[2933, 2926])).
% 13.25/13.40 tff(2935,plain,
% 13.25/13.40 (^[I0: $i, X: $i] : refl((m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X))) <=> (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X))))),
% 13.25/13.40 inference(bind,[status(th)],[])).
% 13.25/13.40 tff(2936,plain,
% 13.25/13.40 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X))) <=> ![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))),
% 13.25/13.40 inference(quant_intro,[status(thm)],[2935])).
% 13.25/13.40 tff(2937,plain,
% 13.25/13.40 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X))) <=> ![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2938,axiom,(![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_counter_cell_10')).
% 13.25/13.40 tff(2939,plain,
% 13.25/13.40 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))),
% 13.25/13.40 inference(modus_ponens,[status(thm)],[2938, 2937])).
% 13.25/13.40 tff(2940,plain,(
% 13.25/13.40 ![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))),
% 13.25/13.40 inference(skolemize,[status(sab)],[2939])).
% 13.25/13.40 tff(2941,plain,
% 13.25/13.40 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))),
% 13.25/13.40 inference(modus_ponens,[status(thm)],[2940, 2936])).
% 13.25/13.40 tff(2942,plain,
% 13.25/13.40 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s46) | (~node4(c_bit1, s46)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s46) | (~node4(c_bit1, s46)))),
% 13.25/13.40 inference(rewrite,[status(thm)],[])).
% 13.25/13.40 tff(2943,plain,
% 13.25/13.40 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s46) | (~node4(c_bit1, s46)))),
% 13.25/13.41 inference(quant_inst,[status(thm)],[])).
% 13.25/13.41 tff(2944,plain,
% 13.25/13.41 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s46) | (~node4(c_bit1, s46))),
% 13.25/13.41 inference(modus_ponens,[status(thm)],[2943, 2942])).
% 13.25/13.41 tff(2945,plain,
% 13.25/13.41 (~node4(c_bit1, s46)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[2944, 2941, 2934])).
% 13.25/13.41 tff(2946,plain,
% 13.25/13.41 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s46)) | node4(c_bit1, s46))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s46)) | node4(c_bit1, s46))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(2947,plain,
% 13.25/13.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s46)) | node4(c_bit1, s46))),
% 13.25/13.41 inference(quant_inst,[status(thm)],[])).
% 13.25/13.41 tff(2948,plain,
% 13.25/13.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s46)) | node4(c_bit1, s46)),
% 13.25/13.41 inference(modus_ponens,[status(thm)],[2947, 2946])).
% 13.25/13.41 tff(2949,plain,
% 13.25/13.41 (~m_counter_cell_v_carry_out(c_bit1, s46)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[2948, 1359, 2945])).
% 13.25/13.41 tff(2950,assumption,(m_counter_cell_v_value(c_bit1, s46)), introduced(assumption)).
% 13.25/13.41 tff(2951,assumption,(node1(c_bit1, s46)), introduced(assumption)).
% 13.25/13.41 tff(2952,plain,
% 13.25/13.41 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s46) | (~m_counter_cell_v_value(c_bit1, s46)) | (~node1(c_bit1, s46)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s46) | (~m_counter_cell_v_value(c_bit1, s46)) | (~node1(c_bit1, s46)))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(2953,plain,
% 13.25/13.41 (((~node1(c_bit1, s46)) | m_counter_cell_v_carry_in(c_bit1, s46) | (~m_counter_cell_v_value(c_bit1, s46))) <=> (m_counter_cell_v_carry_in(c_bit1, s46) | (~m_counter_cell_v_value(c_bit1, s46)) | (~node1(c_bit1, s46)))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(2954,plain,
% 13.25/13.41 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s46)) | m_counter_cell_v_carry_in(c_bit1, s46) | (~m_counter_cell_v_value(c_bit1, s46)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s46) | (~m_counter_cell_v_value(c_bit1, s46)) | (~node1(c_bit1, s46))))),
% 13.25/13.41 inference(monotonicity,[status(thm)],[2953])).
% 13.25/13.41 tff(2955,plain,
% 13.25/13.41 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s46)) | m_counter_cell_v_carry_in(c_bit1, s46) | (~m_counter_cell_v_value(c_bit1, s46)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s46) | (~m_counter_cell_v_value(c_bit1, s46)) | (~node1(c_bit1, s46)))),
% 13.25/13.41 inference(transitivity,[status(thm)],[2954, 2952])).
% 13.25/13.41 tff(2956,plain,
% 13.25/13.41 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s46)) | m_counter_cell_v_carry_in(c_bit1, s46) | (~m_counter_cell_v_value(c_bit1, s46)))),
% 13.25/13.41 inference(quant_inst,[status(thm)],[])).
% 13.25/13.41 tff(2957,plain,
% 13.25/13.41 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s46) | (~m_counter_cell_v_value(c_bit1, s46)) | (~node1(c_bit1, s46))),
% 13.25/13.41 inference(modus_ponens,[status(thm)],[2956, 2955])).
% 13.25/13.41 tff(2958,plain,
% 13.25/13.41 (m_counter_cell_v_carry_in(c_bit1, s46) | (~m_counter_cell_v_value(c_bit1, s46))),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[2957, 1569, 2951])).
% 13.25/13.41 tff(2959,plain,
% 13.25/13.41 (m_counter_cell_v_carry_in(c_bit1, s46)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[2958, 2950])).
% 13.25/13.41 tff(2960,assumption,(~m_counter_cell_v_carry_out(c_bit1, s46)), introduced(assumption)).
% 13.25/13.41 tff(2961,plain,
% 13.25/13.41 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s46)) | (~m_counter_cell_v_value(c_bit1, s46)) | m_counter_cell_v_carry_out(c_bit1, s46))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s46)) | (~m_counter_cell_v_value(c_bit1, s46)) | m_counter_cell_v_carry_out(c_bit1, s46))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(2962,plain,
% 13.25/13.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s46)) | (~m_counter_cell_v_value(c_bit1, s46)) | m_counter_cell_v_carry_out(c_bit1, s46))),
% 13.25/13.41 inference(quant_inst,[status(thm)],[])).
% 13.25/13.41 tff(2963,plain,
% 13.25/13.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s46)) | (~m_counter_cell_v_value(c_bit1, s46)) | m_counter_cell_v_carry_out(c_bit1, s46)),
% 13.25/13.41 inference(modus_ponens,[status(thm)],[2962, 2961])).
% 13.25/13.41 tff(2964,plain,
% 13.25/13.41 ((~m_counter_cell_v_carry_in(c_bit1, s46)) | (~m_counter_cell_v_value(c_bit1, s46))),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[2963, 1390, 2960])).
% 13.25/13.41 tff(2965,plain,
% 13.25/13.41 ($false),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[2964, 2959, 2950])).
% 13.25/13.41 tff(2966,plain,((~m_counter_cell_v_value(c_bit1, s46)) | m_counter_cell_v_carry_out(c_bit1, s46) | (~node1(c_bit1, s46))), inference(lemma,lemma(discharge,[]))).
% 13.25/13.41 tff(2967,plain,
% 13.25/13.41 ((~m_counter_cell_v_value(c_bit1, s46)) | (~node1(c_bit1, s46))),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[2966, 2949])).
% 13.25/13.41 tff(2968,plain,
% 13.25/13.41 (~node1(c_bit1, s46)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[2967, 2899])).
% 13.25/13.41 tff(2969,plain,
% 13.25/13.41 (succ(s46, s47) <=> succ(s46, s47)),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(2970,axiom,(succ(s46, s47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound47')).
% 13.25/13.41 tff(2971,plain,
% 13.25/13.41 (succ(s46, s47)),
% 13.25/13.41 inference(modus_ponens,[status(thm)],[2970, 2969])).
% 13.25/13.41 tff(2972,plain,
% 13.25/13.41 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s46, s47)) | trans(s46, s47))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s46, s47)) | trans(s46, s47))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(2973,plain,
% 13.25/13.41 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s46, s47)) | trans(s46, s47))),
% 13.25/13.41 inference(quant_inst,[status(thm)],[])).
% 13.25/13.41 tff(2974,plain,
% 13.25/13.41 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s46, s47)) | trans(s46, s47)),
% 13.25/13.41 inference(modus_ponens,[status(thm)],[2973, 2972])).
% 13.25/13.41 tff(2975,plain,
% 13.25/13.41 (trans(s46, s47)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[2974, 2971, 45])).
% 13.25/13.41 tff(2976,plain,
% 13.25/13.41 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s46, s47)) | node3(c_bit1, s46, s47))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s46, s47)) | node3(c_bit1, s46, s47))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(2977,plain,
% 13.25/13.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s46, s47)) | node3(c_bit1, s46, s47))),
% 13.25/13.41 inference(quant_inst,[status(thm)],[])).
% 13.25/13.41 tff(2978,plain,
% 13.25/13.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s46, s47)) | node3(c_bit1, s46, s47)),
% 13.25/13.41 inference(modus_ponens,[status(thm)],[2977, 2976])).
% 13.25/13.41 tff(2979,plain,
% 13.25/13.41 (node3(c_bit1, s46, s47)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[2978, 59, 2975])).
% 13.25/13.41 tff(2980,plain,
% 13.25/13.41 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s47) | node1(c_bit1, s46) | (~node3(c_bit1, s46, s47)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s47) | node1(c_bit1, s46) | (~node3(c_bit1, s46, s47)))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(2981,plain,
% 13.25/13.41 ((node1(c_bit1, s46) | (~node3(c_bit1, s46, s47)) | m_counter_cell_v_value(c_bit1, s47)) <=> (m_counter_cell_v_value(c_bit1, s47) | node1(c_bit1, s46) | (~node3(c_bit1, s46, s47)))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(2982,plain,
% 13.25/13.41 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s46) | (~node3(c_bit1, s46, s47)) | m_counter_cell_v_value(c_bit1, s47))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s47) | node1(c_bit1, s46) | (~node3(c_bit1, s46, s47))))),
% 13.25/13.41 inference(monotonicity,[status(thm)],[2981])).
% 13.25/13.41 tff(2983,plain,
% 13.25/13.41 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s46) | (~node3(c_bit1, s46, s47)) | m_counter_cell_v_value(c_bit1, s47))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s47) | node1(c_bit1, s46) | (~node3(c_bit1, s46, s47)))),
% 13.25/13.41 inference(transitivity,[status(thm)],[2982, 2980])).
% 13.25/13.41 tff(2984,plain,
% 13.25/13.41 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s46) | (~node3(c_bit1, s46, s47)) | m_counter_cell_v_value(c_bit1, s47))),
% 13.25/13.41 inference(quant_inst,[status(thm)],[])).
% 13.25/13.41 tff(2985,plain,
% 13.25/13.41 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s47) | node1(c_bit1, s46) | (~node3(c_bit1, s46, s47))),
% 13.25/13.41 inference(modus_ponens,[status(thm)],[2984, 2983])).
% 13.25/13.41 tff(2986,plain,
% 13.25/13.41 (m_counter_cell_v_value(c_bit1, s47) | node1(c_bit1, s46)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[2985, 73, 2979])).
% 13.25/13.41 tff(2987,plain,
% 13.25/13.41 (m_counter_cell_v_value(c_bit1, s47)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[2986, 2968])).
% 13.25/13.41 tff(2988,assumption,(node2(c_bit1, s47)), introduced(assumption)).
% 13.25/13.41 tff(2989,assumption,(~m_counter_cell_v_carry_in(c_bit0, s46)), introduced(assumption)).
% 13.25/13.41 tff(2990,plain,
% 13.25/13.41 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s46)),
% 13.25/13.41 inference(quant_inst,[status(thm)],[])).
% 13.25/13.41 tff(2991,plain,
% 13.25/13.41 ($false),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[2990, 18, 2989])).
% 13.25/13.41 tff(2992,plain,(m_counter_cell_v_carry_in(c_bit0, s46)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.41 tff(2993,plain,
% 13.25/13.41 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s46)) | m_counter_cell_v_value(c_bit0, s46) | (~node1(c_bit0, s46)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s46)) | m_counter_cell_v_value(c_bit0, s46) | (~node1(c_bit0, s46)))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(2994,plain,
% 13.25/13.41 (((~node1(c_bit0, s46)) | (~m_counter_cell_v_carry_in(c_bit0, s46)) | m_counter_cell_v_value(c_bit0, s46)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s46)) | m_counter_cell_v_value(c_bit0, s46) | (~node1(c_bit0, s46)))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(2995,plain,
% 13.25/13.41 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s46)) | (~m_counter_cell_v_carry_in(c_bit0, s46)) | m_counter_cell_v_value(c_bit0, s46))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s46)) | m_counter_cell_v_value(c_bit0, s46) | (~node1(c_bit0, s46))))),
% 13.25/13.41 inference(monotonicity,[status(thm)],[2994])).
% 13.25/13.41 tff(2996,plain,
% 13.25/13.41 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s46)) | (~m_counter_cell_v_carry_in(c_bit0, s46)) | m_counter_cell_v_value(c_bit0, s46))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s46)) | m_counter_cell_v_value(c_bit0, s46) | (~node1(c_bit0, s46)))),
% 13.25/13.41 inference(transitivity,[status(thm)],[2995, 2993])).
% 13.25/13.41 tff(2997,plain,
% 13.25/13.41 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s46)) | (~m_counter_cell_v_carry_in(c_bit0, s46)) | m_counter_cell_v_value(c_bit0, s46))),
% 13.25/13.41 inference(quant_inst,[status(thm)],[])).
% 13.25/13.41 tff(2998,plain,
% 13.25/13.41 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s46)) | m_counter_cell_v_value(c_bit0, s46) | (~node1(c_bit0, s46))),
% 13.25/13.41 inference(modus_ponens,[status(thm)],[2997, 2996])).
% 13.25/13.41 tff(2999,plain,
% 13.25/13.41 (m_counter_cell_v_value(c_bit0, s46) | (~node1(c_bit0, s46))),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[2998, 30, 2992])).
% 13.25/13.41 tff(3000,plain,
% 13.25/13.41 (~node1(c_bit0, s46)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[2999, 2916])).
% 13.25/13.41 tff(3001,plain,
% 13.25/13.41 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s46, s47)) | node3(c_bit0, s46, s47))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s46, s47)) | node3(c_bit0, s46, s47))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(3002,plain,
% 13.25/13.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s46, s47)) | node3(c_bit0, s46, s47))),
% 13.25/13.41 inference(quant_inst,[status(thm)],[])).
% 13.25/13.41 tff(3003,plain,
% 13.25/13.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s46, s47)) | node3(c_bit0, s46, s47)),
% 13.25/13.41 inference(modus_ponens,[status(thm)],[3002, 3001])).
% 13.25/13.41 tff(3004,plain,
% 13.25/13.41 (node3(c_bit0, s46, s47)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[3003, 59, 2975])).
% 13.25/13.41 tff(3005,plain,
% 13.25/13.41 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s47) | node1(c_bit0, s46) | (~node3(c_bit0, s46, s47)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s47) | node1(c_bit0, s46) | (~node3(c_bit0, s46, s47)))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(3006,plain,
% 13.25/13.41 ((node1(c_bit0, s46) | (~node3(c_bit0, s46, s47)) | m_counter_cell_v_value(c_bit0, s47)) <=> (m_counter_cell_v_value(c_bit0, s47) | node1(c_bit0, s46) | (~node3(c_bit0, s46, s47)))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(3007,plain,
% 13.25/13.41 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s46) | (~node3(c_bit0, s46, s47)) | m_counter_cell_v_value(c_bit0, s47))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s47) | node1(c_bit0, s46) | (~node3(c_bit0, s46, s47))))),
% 13.25/13.41 inference(monotonicity,[status(thm)],[3006])).
% 13.25/13.41 tff(3008,plain,
% 13.25/13.41 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s46) | (~node3(c_bit0, s46, s47)) | m_counter_cell_v_value(c_bit0, s47))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s47) | node1(c_bit0, s46) | (~node3(c_bit0, s46, s47)))),
% 13.25/13.41 inference(transitivity,[status(thm)],[3007, 3005])).
% 13.25/13.41 tff(3009,plain,
% 13.25/13.41 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s46) | (~node3(c_bit0, s46, s47)) | m_counter_cell_v_value(c_bit0, s47))),
% 13.25/13.41 inference(quant_inst,[status(thm)],[])).
% 13.25/13.41 tff(3010,plain,
% 13.25/13.41 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s47) | node1(c_bit0, s46) | (~node3(c_bit0, s46, s47))),
% 13.25/13.41 inference(modus_ponens,[status(thm)],[3009, 3008])).
% 13.25/13.41 tff(3011,plain,
% 13.25/13.41 (m_counter_cell_v_value(c_bit0, s47) | node1(c_bit0, s46)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[3010, 73, 3004])).
% 13.25/13.41 tff(3012,plain,
% 13.25/13.41 (m_counter_cell_v_value(c_bit0, s47)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[3011, 3000])).
% 13.25/13.41 tff(3013,assumption,(~m_counter_cell_v_carry_in(c_bit0, s47)), introduced(assumption)).
% 13.25/13.41 tff(3014,plain,
% 13.25/13.41 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s47)),
% 13.25/13.41 inference(quant_inst,[status(thm)],[])).
% 13.25/13.41 tff(3015,plain,
% 13.25/13.41 ($false),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[3014, 18, 3013])).
% 13.25/13.41 tff(3016,plain,(m_counter_cell_v_carry_in(c_bit0, s47)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.41 tff(3017,plain,
% 13.25/13.41 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s47)) | (~m_counter_cell_v_value(c_bit0, s47)) | m_counter_cell_v_carry_out(c_bit0, s47))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s47)) | (~m_counter_cell_v_value(c_bit0, s47)) | m_counter_cell_v_carry_out(c_bit0, s47))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(3018,plain,
% 13.25/13.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s47)) | (~m_counter_cell_v_value(c_bit0, s47)) | m_counter_cell_v_carry_out(c_bit0, s47))),
% 13.25/13.41 inference(quant_inst,[status(thm)],[])).
% 13.25/13.41 tff(3019,plain,
% 13.25/13.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s47)) | (~m_counter_cell_v_value(c_bit0, s47)) | m_counter_cell_v_carry_out(c_bit0, s47)),
% 13.25/13.41 inference(modus_ponens,[status(thm)],[3018, 3017])).
% 13.25/13.41 tff(3020,plain,
% 13.25/13.41 ((~m_counter_cell_v_value(c_bit0, s47)) | m_counter_cell_v_carry_out(c_bit0, s47)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[3019, 1390, 3016])).
% 13.25/13.41 tff(3021,plain,
% 13.25/13.41 (m_counter_cell_v_carry_out(c_bit0, s47)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[3020, 3012])).
% 13.25/13.41 tff(3022,plain,
% 13.25/13.41 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s47)) | m_counter_cell_v_carry_in(c_bit1, s47))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s47)) | m_counter_cell_v_carry_in(c_bit1, s47))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(3023,plain,
% 13.25/13.41 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s47)) | m_counter_cell_v_carry_in(c_bit1, s47))),
% 13.25/13.41 inference(quant_inst,[status(thm)],[])).
% 13.25/13.41 tff(3024,plain,
% 13.25/13.41 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s47)) | m_counter_cell_v_carry_in(c_bit1, s47)),
% 13.25/13.41 inference(modus_ponens,[status(thm)],[3023, 3022])).
% 13.25/13.41 tff(3025,plain,
% 13.25/13.41 (m_counter_cell_v_carry_in(c_bit1, s47)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[3024, 1405, 3021])).
% 13.25/13.41 tff(3026,assumption,(m_counter_cell_v_value(c_bit1, s47)), introduced(assumption)).
% 13.25/13.41 tff(3027,plain,
% 13.25/13.41 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s47)) | (~m_counter_cell_v_value(c_bit1, s47)) | (~node2(c_bit1, s47)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s47)) | (~m_counter_cell_v_value(c_bit1, s47)) | (~node2(c_bit1, s47)))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(3028,plain,
% 13.25/13.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s47)) | (~m_counter_cell_v_value(c_bit1, s47)) | (~node2(c_bit1, s47)))),
% 13.25/13.41 inference(quant_inst,[status(thm)],[])).
% 13.25/13.41 tff(3029,plain,
% 13.25/13.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s47)) | (~m_counter_cell_v_value(c_bit1, s47)) | (~node2(c_bit1, s47))),
% 13.25/13.41 inference(modus_ponens,[status(thm)],[3028, 3027])).
% 13.25/13.41 tff(3030,plain,
% 13.25/13.41 ($false),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[3029, 93, 3026, 3025, 2988])).
% 13.25/13.41 tff(3031,plain,((~node2(c_bit1, s47)) | (~m_counter_cell_v_value(c_bit1, s47))), inference(lemma,lemma(discharge,[]))).
% 13.25/13.41 tff(3032,plain,
% 13.25/13.41 (~node2(c_bit1, s47)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[3031, 2987])).
% 13.25/13.41 tff(3033,plain,
% 13.25/13.41 (succ(s47, s48) <=> succ(s47, s48)),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(3034,axiom,(succ(s47, s48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound48')).
% 13.25/13.41 tff(3035,plain,
% 13.25/13.41 (succ(s47, s48)),
% 13.25/13.41 inference(modus_ponens,[status(thm)],[3034, 3033])).
% 13.25/13.41 tff(3036,plain,
% 13.25/13.41 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s47, s48)) | trans(s47, s48))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s47, s48)) | trans(s47, s48))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(3037,plain,
% 13.25/13.41 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s47, s48)) | trans(s47, s48))),
% 13.25/13.41 inference(quant_inst,[status(thm)],[])).
% 13.25/13.41 tff(3038,plain,
% 13.25/13.41 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s47, s48)) | trans(s47, s48)),
% 13.25/13.41 inference(modus_ponens,[status(thm)],[3037, 3036])).
% 13.25/13.41 tff(3039,plain,
% 13.25/13.41 (trans(s47, s48)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[3038, 3035, 45])).
% 13.25/13.41 tff(3040,plain,
% 13.25/13.41 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s47, s48)) | node3(c_bit1, s47, s48))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s47, s48)) | node3(c_bit1, s47, s48))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(3041,plain,
% 13.25/13.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s47, s48)) | node3(c_bit1, s47, s48))),
% 13.25/13.41 inference(quant_inst,[status(thm)],[])).
% 13.25/13.41 tff(3042,plain,
% 13.25/13.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s47, s48)) | node3(c_bit1, s47, s48)),
% 13.25/13.41 inference(modus_ponens,[status(thm)],[3041, 3040])).
% 13.25/13.41 tff(3043,plain,
% 13.25/13.41 (node3(c_bit1, s47, s48)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[3042, 59, 3039])).
% 13.25/13.41 tff(3044,plain,
% 13.25/13.41 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s48)) | node2(c_bit1, s47) | (~node3(c_bit1, s47, s48)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s48)) | node2(c_bit1, s47) | (~node3(c_bit1, s47, s48)))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(3045,plain,
% 13.25/13.41 ((node2(c_bit1, s47) | (~node3(c_bit1, s47, s48)) | (~m_counter_cell_v_value(c_bit1, s48))) <=> ((~m_counter_cell_v_value(c_bit1, s48)) | node2(c_bit1, s47) | (~node3(c_bit1, s47, s48)))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(3046,plain,
% 13.25/13.41 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s47) | (~node3(c_bit1, s47, s48)) | (~m_counter_cell_v_value(c_bit1, s48)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s48)) | node2(c_bit1, s47) | (~node3(c_bit1, s47, s48))))),
% 13.25/13.41 inference(monotonicity,[status(thm)],[3045])).
% 13.25/13.41 tff(3047,plain,
% 13.25/13.41 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s47) | (~node3(c_bit1, s47, s48)) | (~m_counter_cell_v_value(c_bit1, s48)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s48)) | node2(c_bit1, s47) | (~node3(c_bit1, s47, s48)))),
% 13.25/13.41 inference(transitivity,[status(thm)],[3046, 3044])).
% 13.25/13.41 tff(3048,plain,
% 13.25/13.41 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s47) | (~node3(c_bit1, s47, s48)) | (~m_counter_cell_v_value(c_bit1, s48)))),
% 13.25/13.41 inference(quant_inst,[status(thm)],[])).
% 13.25/13.41 tff(3049,plain,
% 13.25/13.41 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s48)) | node2(c_bit1, s47) | (~node3(c_bit1, s47, s48))),
% 13.25/13.41 inference(modus_ponens,[status(thm)],[3048, 3047])).
% 13.25/13.41 tff(3050,plain,
% 13.25/13.41 ((~m_counter_cell_v_value(c_bit1, s48)) | node2(c_bit1, s47)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[3049, 121, 3043])).
% 13.25/13.41 tff(3051,plain,
% 13.25/13.41 (~m_counter_cell_v_value(c_bit1, s48)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[3050, 3032])).
% 13.25/13.41 tff(3052,plain,
% 13.25/13.41 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s47)) | (~m_counter_cell_v_value(c_bit0, s47)) | (~node2(c_bit0, s47)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s47)) | (~m_counter_cell_v_value(c_bit0, s47)) | (~node2(c_bit0, s47)))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(3053,plain,
% 13.25/13.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s47)) | (~m_counter_cell_v_value(c_bit0, s47)) | (~node2(c_bit0, s47)))),
% 13.25/13.41 inference(quant_inst,[status(thm)],[])).
% 13.25/13.41 tff(3054,plain,
% 13.25/13.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s47)) | (~m_counter_cell_v_value(c_bit0, s47)) | (~node2(c_bit0, s47))),
% 13.25/13.41 inference(modus_ponens,[status(thm)],[3053, 3052])).
% 13.25/13.41 tff(3055,plain,
% 13.25/13.41 ((~m_counter_cell_v_value(c_bit0, s47)) | (~node2(c_bit0, s47))),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[3054, 93, 3016])).
% 13.25/13.41 tff(3056,plain,
% 13.25/13.41 (~node2(c_bit0, s47)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[3055, 3012])).
% 13.25/13.41 tff(3057,plain,
% 13.25/13.41 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s47, s48)) | node3(c_bit0, s47, s48))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s47, s48)) | node3(c_bit0, s47, s48))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(3058,plain,
% 13.25/13.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s47, s48)) | node3(c_bit0, s47, s48))),
% 13.25/13.41 inference(quant_inst,[status(thm)],[])).
% 13.25/13.41 tff(3059,plain,
% 13.25/13.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s47, s48)) | node3(c_bit0, s47, s48)),
% 13.25/13.41 inference(modus_ponens,[status(thm)],[3058, 3057])).
% 13.25/13.41 tff(3060,plain,
% 13.25/13.41 (node3(c_bit0, s47, s48)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[3059, 59, 3039])).
% 13.25/13.41 tff(3061,plain,
% 13.25/13.41 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s48)) | node2(c_bit0, s47) | (~node3(c_bit0, s47, s48)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s48)) | node2(c_bit0, s47) | (~node3(c_bit0, s47, s48)))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(3062,plain,
% 13.25/13.41 ((node2(c_bit0, s47) | (~node3(c_bit0, s47, s48)) | (~m_counter_cell_v_value(c_bit0, s48))) <=> ((~m_counter_cell_v_value(c_bit0, s48)) | node2(c_bit0, s47) | (~node3(c_bit0, s47, s48)))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(3063,plain,
% 13.25/13.41 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s47) | (~node3(c_bit0, s47, s48)) | (~m_counter_cell_v_value(c_bit0, s48)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s48)) | node2(c_bit0, s47) | (~node3(c_bit0, s47, s48))))),
% 13.25/13.41 inference(monotonicity,[status(thm)],[3062])).
% 13.25/13.41 tff(3064,plain,
% 13.25/13.41 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s47) | (~node3(c_bit0, s47, s48)) | (~m_counter_cell_v_value(c_bit0, s48)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s48)) | node2(c_bit0, s47) | (~node3(c_bit0, s47, s48)))),
% 13.25/13.41 inference(transitivity,[status(thm)],[3063, 3061])).
% 13.25/13.41 tff(3065,plain,
% 13.25/13.41 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s47) | (~node3(c_bit0, s47, s48)) | (~m_counter_cell_v_value(c_bit0, s48)))),
% 13.25/13.41 inference(quant_inst,[status(thm)],[])).
% 13.25/13.41 tff(3066,plain,
% 13.25/13.41 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s48)) | node2(c_bit0, s47) | (~node3(c_bit0, s47, s48))),
% 13.25/13.41 inference(modus_ponens,[status(thm)],[3065, 3064])).
% 13.25/13.41 tff(3067,plain,
% 13.25/13.41 ((~m_counter_cell_v_value(c_bit0, s48)) | node2(c_bit0, s47)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[3066, 121, 3060])).
% 13.25/13.41 tff(3068,plain,
% 13.25/13.41 (~m_counter_cell_v_value(c_bit0, s48)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[3067, 3056])).
% 13.25/13.41 tff(3069,plain,
% 13.25/13.41 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s48) | (~node4(c_bit0, s48)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s48) | (~node4(c_bit0, s48)))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(3070,plain,
% 13.25/13.41 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s48) | (~node4(c_bit0, s48)))),
% 13.25/13.41 inference(quant_inst,[status(thm)],[])).
% 13.25/13.41 tff(3071,plain,
% 13.25/13.41 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s48) | (~node4(c_bit0, s48))),
% 13.25/13.41 inference(modus_ponens,[status(thm)],[3070, 3069])).
% 13.25/13.41 tff(3072,plain,
% 13.25/13.41 (~node4(c_bit0, s48)),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[3071, 1344, 3068])).
% 13.25/13.41 tff(3073,assumption,(m_counter_cell_v_carry_out(c_bit0, s48)), introduced(assumption)).
% 13.25/13.41 tff(3074,plain,
% 13.25/13.41 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s48)) | node4(c_bit0, s48))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s48)) | node4(c_bit0, s48))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(3075,plain,
% 13.25/13.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s48)) | node4(c_bit0, s48))),
% 13.25/13.41 inference(quant_inst,[status(thm)],[])).
% 13.25/13.41 tff(3076,plain,
% 13.25/13.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s48)) | node4(c_bit0, s48)),
% 13.25/13.41 inference(modus_ponens,[status(thm)],[3075, 3074])).
% 13.25/13.41 tff(3077,plain,
% 13.25/13.41 ($false),
% 13.25/13.41 inference(unit_resolution,[status(thm)],[3076, 1359, 3073, 3072])).
% 13.25/13.41 tff(3078,plain,(~m_counter_cell_v_carry_out(c_bit0, s48)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.41 tff(3079,plain,
% 13.25/13.41 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s48)) | m_counter_cell_v_carry_out(c_bit0, s48))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s48)) | m_counter_cell_v_carry_out(c_bit0, s48))),
% 13.25/13.41 inference(rewrite,[status(thm)],[])).
% 13.25/13.41 tff(3080,plain,
% 13.25/13.41 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s48)) | m_counter_cell_v_carry_out(c_bit0, s48))),
% 13.25/13.41 inference(quant_inst,[status(thm)],[])).
% 13.25/13.41 tff(3081,plain,
% 13.25/13.41 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s48)) | m_counter_cell_v_carry_out(c_bit0, s48)),
% 13.25/13.42 inference(modus_ponens,[status(thm)],[3080, 3079])).
% 13.25/13.42 tff(3082,plain,
% 13.25/13.42 (~m_counter_cell_v_carry_in(c_bit1, s48)),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3081, 1374, 3078])).
% 13.25/13.42 tff(3083,assumption,(~m_counter_cell_v_value(c_bit1, s48)), introduced(assumption)).
% 13.25/13.42 tff(3084,assumption,(node2(c_bit1, s48)), introduced(assumption)).
% 13.25/13.42 tff(3085,plain,
% 13.25/13.42 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s48) | m_counter_cell_v_value(c_bit1, s48) | (~node2(c_bit1, s48)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s48) | m_counter_cell_v_value(c_bit1, s48) | (~node2(c_bit1, s48)))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3086,plain,
% 13.25/13.42 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s48) | m_counter_cell_v_value(c_bit1, s48) | (~node2(c_bit1, s48)))),
% 13.25/13.42 inference(quant_inst,[status(thm)],[])).
% 13.25/13.42 tff(3087,plain,
% 13.25/13.42 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s48) | m_counter_cell_v_value(c_bit1, s48) | (~node2(c_bit1, s48))),
% 13.25/13.42 inference(modus_ponens,[status(thm)],[3086, 3085])).
% 13.25/13.42 tff(3088,plain,
% 13.25/13.42 ($false),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3087, 1498, 3084, 3083, 3082])).
% 13.25/13.42 tff(3089,plain,(m_counter_cell_v_value(c_bit1, s48) | (~node2(c_bit1, s48))), inference(lemma,lemma(discharge,[]))).
% 13.25/13.42 tff(3090,plain,
% 13.25/13.42 (~node2(c_bit1, s48)),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3089, 3051])).
% 13.25/13.42 tff(3091,plain,
% 13.25/13.42 (succ(s48, s49) <=> succ(s48, s49)),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3092,axiom,(succ(s48, s49)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound49')).
% 13.25/13.42 tff(3093,plain,
% 13.25/13.42 (succ(s48, s49)),
% 13.25/13.42 inference(modus_ponens,[status(thm)],[3092, 3091])).
% 13.25/13.42 tff(3094,plain,
% 13.25/13.42 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s48, s49)) | trans(s48, s49))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s48, s49)) | trans(s48, s49))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3095,plain,
% 13.25/13.42 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s48, s49)) | trans(s48, s49))),
% 13.25/13.42 inference(quant_inst,[status(thm)],[])).
% 13.25/13.42 tff(3096,plain,
% 13.25/13.42 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s48, s49)) | trans(s48, s49)),
% 13.25/13.42 inference(modus_ponens,[status(thm)],[3095, 3094])).
% 13.25/13.42 tff(3097,plain,
% 13.25/13.42 (trans(s48, s49)),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3096, 3093, 45])).
% 13.25/13.42 tff(3098,plain,
% 13.25/13.42 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s48, s49)) | node3(c_bit1, s48, s49))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s48, s49)) | node3(c_bit1, s48, s49))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3099,plain,
% 13.25/13.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s48, s49)) | node3(c_bit1, s48, s49))),
% 13.25/13.42 inference(quant_inst,[status(thm)],[])).
% 13.25/13.42 tff(3100,plain,
% 13.25/13.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s48, s49)) | node3(c_bit1, s48, s49)),
% 13.25/13.42 inference(modus_ponens,[status(thm)],[3099, 3098])).
% 13.25/13.42 tff(3101,plain,
% 13.25/13.42 (node3(c_bit1, s48, s49)),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3100, 59, 3097])).
% 13.25/13.42 tff(3102,plain,
% 13.25/13.42 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s49)) | node2(c_bit1, s48) | (~node3(c_bit1, s48, s49)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s49)) | node2(c_bit1, s48) | (~node3(c_bit1, s48, s49)))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3103,plain,
% 13.25/13.42 ((node2(c_bit1, s48) | (~node3(c_bit1, s48, s49)) | (~m_counter_cell_v_value(c_bit1, s49))) <=> ((~m_counter_cell_v_value(c_bit1, s49)) | node2(c_bit1, s48) | (~node3(c_bit1, s48, s49)))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3104,plain,
% 13.25/13.42 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s48) | (~node3(c_bit1, s48, s49)) | (~m_counter_cell_v_value(c_bit1, s49)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s49)) | node2(c_bit1, s48) | (~node3(c_bit1, s48, s49))))),
% 13.25/13.42 inference(monotonicity,[status(thm)],[3103])).
% 13.25/13.42 tff(3105,plain,
% 13.25/13.42 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s48) | (~node3(c_bit1, s48, s49)) | (~m_counter_cell_v_value(c_bit1, s49)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s49)) | node2(c_bit1, s48) | (~node3(c_bit1, s48, s49)))),
% 13.25/13.42 inference(transitivity,[status(thm)],[3104, 3102])).
% 13.25/13.42 tff(3106,plain,
% 13.25/13.42 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s48) | (~node3(c_bit1, s48, s49)) | (~m_counter_cell_v_value(c_bit1, s49)))),
% 13.25/13.42 inference(quant_inst,[status(thm)],[])).
% 13.25/13.42 tff(3107,plain,
% 13.25/13.42 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s49)) | node2(c_bit1, s48) | (~node3(c_bit1, s48, s49))),
% 13.25/13.42 inference(modus_ponens,[status(thm)],[3106, 3105])).
% 13.25/13.42 tff(3108,plain,
% 13.25/13.42 ((~m_counter_cell_v_value(c_bit1, s49)) | node2(c_bit1, s48)),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3107, 121, 3101])).
% 13.25/13.42 tff(3109,plain,
% 13.25/13.42 (~m_counter_cell_v_value(c_bit1, s49)),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3108, 3090])).
% 13.25/13.42 tff(3110,assumption,(~m_counter_cell_v_carry_in(c_bit0, s48)), introduced(assumption)).
% 13.25/13.42 tff(3111,plain,
% 13.25/13.42 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s48)),
% 13.25/13.42 inference(quant_inst,[status(thm)],[])).
% 13.25/13.42 tff(3112,plain,
% 13.25/13.42 ($false),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3111, 18, 3110])).
% 13.25/13.42 tff(3113,plain,(m_counter_cell_v_carry_in(c_bit0, s48)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.42 tff(3114,plain,
% 13.25/13.42 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s48)) | m_counter_cell_v_value(c_bit0, s48) | (~node1(c_bit0, s48)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s48)) | m_counter_cell_v_value(c_bit0, s48) | (~node1(c_bit0, s48)))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3115,plain,
% 13.25/13.42 (((~node1(c_bit0, s48)) | (~m_counter_cell_v_carry_in(c_bit0, s48)) | m_counter_cell_v_value(c_bit0, s48)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s48)) | m_counter_cell_v_value(c_bit0, s48) | (~node1(c_bit0, s48)))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3116,plain,
% 13.25/13.42 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s48)) | (~m_counter_cell_v_carry_in(c_bit0, s48)) | m_counter_cell_v_value(c_bit0, s48))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s48)) | m_counter_cell_v_value(c_bit0, s48) | (~node1(c_bit0, s48))))),
% 13.25/13.42 inference(monotonicity,[status(thm)],[3115])).
% 13.25/13.42 tff(3117,plain,
% 13.25/13.42 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s48)) | (~m_counter_cell_v_carry_in(c_bit0, s48)) | m_counter_cell_v_value(c_bit0, s48))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s48)) | m_counter_cell_v_value(c_bit0, s48) | (~node1(c_bit0, s48)))),
% 13.25/13.42 inference(transitivity,[status(thm)],[3116, 3114])).
% 13.25/13.42 tff(3118,plain,
% 13.25/13.42 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s48)) | (~m_counter_cell_v_carry_in(c_bit0, s48)) | m_counter_cell_v_value(c_bit0, s48))),
% 13.25/13.42 inference(quant_inst,[status(thm)],[])).
% 13.25/13.42 tff(3119,plain,
% 13.25/13.42 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s48)) | m_counter_cell_v_value(c_bit0, s48) | (~node1(c_bit0, s48))),
% 13.25/13.42 inference(modus_ponens,[status(thm)],[3118, 3117])).
% 13.25/13.42 tff(3120,plain,
% 13.25/13.42 (m_counter_cell_v_value(c_bit0, s48) | (~node1(c_bit0, s48))),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3119, 30, 3113])).
% 13.25/13.42 tff(3121,plain,
% 13.25/13.42 (~node1(c_bit0, s48)),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3120, 3068])).
% 13.25/13.42 tff(3122,plain,
% 13.25/13.42 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s48, s49)) | node3(c_bit0, s48, s49))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s48, s49)) | node3(c_bit0, s48, s49))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3123,plain,
% 13.25/13.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s48, s49)) | node3(c_bit0, s48, s49))),
% 13.25/13.42 inference(quant_inst,[status(thm)],[])).
% 13.25/13.42 tff(3124,plain,
% 13.25/13.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s48, s49)) | node3(c_bit0, s48, s49)),
% 13.25/13.42 inference(modus_ponens,[status(thm)],[3123, 3122])).
% 13.25/13.42 tff(3125,plain,
% 13.25/13.42 (node3(c_bit0, s48, s49)),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3124, 59, 3097])).
% 13.25/13.42 tff(3126,plain,
% 13.25/13.42 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s49) | node1(c_bit0, s48) | (~node3(c_bit0, s48, s49)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s49) | node1(c_bit0, s48) | (~node3(c_bit0, s48, s49)))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3127,plain,
% 13.25/13.42 ((node1(c_bit0, s48) | (~node3(c_bit0, s48, s49)) | m_counter_cell_v_value(c_bit0, s49)) <=> (m_counter_cell_v_value(c_bit0, s49) | node1(c_bit0, s48) | (~node3(c_bit0, s48, s49)))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3128,plain,
% 13.25/13.42 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s48) | (~node3(c_bit0, s48, s49)) | m_counter_cell_v_value(c_bit0, s49))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s49) | node1(c_bit0, s48) | (~node3(c_bit0, s48, s49))))),
% 13.25/13.42 inference(monotonicity,[status(thm)],[3127])).
% 13.25/13.42 tff(3129,plain,
% 13.25/13.42 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s48) | (~node3(c_bit0, s48, s49)) | m_counter_cell_v_value(c_bit0, s49))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s49) | node1(c_bit0, s48) | (~node3(c_bit0, s48, s49)))),
% 13.25/13.42 inference(transitivity,[status(thm)],[3128, 3126])).
% 13.25/13.42 tff(3130,plain,
% 13.25/13.42 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s48) | (~node3(c_bit0, s48, s49)) | m_counter_cell_v_value(c_bit0, s49))),
% 13.25/13.42 inference(quant_inst,[status(thm)],[])).
% 13.25/13.42 tff(3131,plain,
% 13.25/13.42 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s49) | node1(c_bit0, s48) | (~node3(c_bit0, s48, s49))),
% 13.25/13.42 inference(modus_ponens,[status(thm)],[3130, 3129])).
% 13.25/13.42 tff(3132,plain,
% 13.25/13.42 (m_counter_cell_v_value(c_bit0, s49) | node1(c_bit0, s48)),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3131, 73, 3125])).
% 13.25/13.42 tff(3133,plain,
% 13.25/13.42 (m_counter_cell_v_value(c_bit0, s49)),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3132, 3121])).
% 13.25/13.42 tff(3134,assumption,(m_counter_cell_v_value(c_bit0, s49)), introduced(assumption)).
% 13.25/13.42 tff(3135,assumption,(~m_counter_cell_v_carry_in(c_bit0, s49)), introduced(assumption)).
% 13.25/13.42 tff(3136,plain,
% 13.25/13.42 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s49)),
% 13.25/13.42 inference(quant_inst,[status(thm)],[])).
% 13.25/13.42 tff(3137,plain,
% 13.25/13.42 ($false),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3136, 18, 3135])).
% 13.25/13.42 tff(3138,plain,(m_counter_cell_v_carry_in(c_bit0, s49)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.42 tff(3139,plain,
% 13.25/13.42 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s49)) | (~m_counter_cell_v_value(c_bit0, s49)) | (~node2(c_bit0, s49)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s49)) | (~m_counter_cell_v_value(c_bit0, s49)) | (~node2(c_bit0, s49)))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3140,plain,
% 13.25/13.42 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s49)) | (~m_counter_cell_v_value(c_bit0, s49)) | (~node2(c_bit0, s49)))),
% 13.25/13.42 inference(quant_inst,[status(thm)],[])).
% 13.25/13.42 tff(3141,plain,
% 13.25/13.42 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s49)) | (~m_counter_cell_v_value(c_bit0, s49)) | (~node2(c_bit0, s49))),
% 13.25/13.42 inference(modus_ponens,[status(thm)],[3140, 3139])).
% 13.25/13.42 tff(3142,plain,
% 13.25/13.42 ((~m_counter_cell_v_value(c_bit0, s49)) | (~node2(c_bit0, s49))),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3141, 93, 3138])).
% 13.25/13.42 tff(3143,plain,
% 13.25/13.42 (~node2(c_bit0, s49)),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3142, 3134])).
% 13.25/13.42 tff(3144,assumption,(~node3(c_bit0, s49, s50)), introduced(assumption)).
% 13.25/13.42 tff(3145,plain,
% 13.25/13.42 (succ(s49, s50) <=> succ(s49, s50)),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3146,axiom,(succ(s49, s50)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound50')).
% 13.25/13.42 tff(3147,plain,
% 13.25/13.42 (succ(s49, s50)),
% 13.25/13.42 inference(modus_ponens,[status(thm)],[3146, 3145])).
% 13.25/13.42 tff(3148,plain,
% 13.25/13.42 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s49, s50)) | trans(s49, s50))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s49, s50)) | trans(s49, s50))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3149,plain,
% 13.25/13.42 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s49, s50)) | trans(s49, s50))),
% 13.25/13.42 inference(quant_inst,[status(thm)],[])).
% 13.25/13.42 tff(3150,plain,
% 13.25/13.42 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s49, s50)) | trans(s49, s50)),
% 13.25/13.42 inference(modus_ponens,[status(thm)],[3149, 3148])).
% 13.25/13.42 tff(3151,plain,
% 13.25/13.42 (trans(s49, s50)),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3150, 3147, 45])).
% 13.25/13.42 tff(3152,plain,
% 13.25/13.42 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s49, s50)) | node3(c_bit0, s49, s50))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s49, s50)) | node3(c_bit0, s49, s50))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3153,plain,
% 13.25/13.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s49, s50)) | node3(c_bit0, s49, s50))),
% 13.25/13.42 inference(quant_inst,[status(thm)],[])).
% 13.25/13.42 tff(3154,plain,
% 13.25/13.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s49, s50)) | node3(c_bit0, s49, s50)),
% 13.25/13.42 inference(modus_ponens,[status(thm)],[3153, 3152])).
% 13.25/13.42 tff(3155,plain,
% 13.25/13.42 ($false),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3154, 59, 3151, 3144])).
% 13.25/13.42 tff(3156,plain,(node3(c_bit0, s49, s50)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.42 tff(3157,plain,
% 13.25/13.42 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s50)) | node2(c_bit0, s49) | (~node3(c_bit0, s49, s50)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s50)) | node2(c_bit0, s49) | (~node3(c_bit0, s49, s50)))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3158,plain,
% 13.25/13.42 ((node2(c_bit0, s49) | (~node3(c_bit0, s49, s50)) | (~m_counter_cell_v_value(c_bit0, s50))) <=> ((~m_counter_cell_v_value(c_bit0, s50)) | node2(c_bit0, s49) | (~node3(c_bit0, s49, s50)))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3159,plain,
% 13.25/13.42 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s49) | (~node3(c_bit0, s49, s50)) | (~m_counter_cell_v_value(c_bit0, s50)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s50)) | node2(c_bit0, s49) | (~node3(c_bit0, s49, s50))))),
% 13.25/13.42 inference(monotonicity,[status(thm)],[3158])).
% 13.25/13.42 tff(3160,plain,
% 13.25/13.42 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s49) | (~node3(c_bit0, s49, s50)) | (~m_counter_cell_v_value(c_bit0, s50)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s50)) | node2(c_bit0, s49) | (~node3(c_bit0, s49, s50)))),
% 13.25/13.42 inference(transitivity,[status(thm)],[3159, 3157])).
% 13.25/13.42 tff(3161,plain,
% 13.25/13.42 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s49) | (~node3(c_bit0, s49, s50)) | (~m_counter_cell_v_value(c_bit0, s50)))),
% 13.25/13.42 inference(quant_inst,[status(thm)],[])).
% 13.25/13.42 tff(3162,plain,
% 13.25/13.42 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s50)) | node2(c_bit0, s49) | (~node3(c_bit0, s49, s50))),
% 13.25/13.42 inference(modus_ponens,[status(thm)],[3161, 3160])).
% 13.25/13.42 tff(3163,plain,
% 13.25/13.42 ((~m_counter_cell_v_value(c_bit0, s50)) | node2(c_bit0, s49)),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3162, 121, 3156])).
% 13.25/13.42 tff(3164,plain,
% 13.25/13.42 (~m_counter_cell_v_value(c_bit0, s50)),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3163, 3143])).
% 13.25/13.42 tff(3165,plain,
% 13.25/13.42 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s50) | (~node4(c_bit0, s50)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s50) | (~node4(c_bit0, s50)))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3166,plain,
% 13.25/13.42 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s50) | (~node4(c_bit0, s50)))),
% 13.25/13.42 inference(quant_inst,[status(thm)],[])).
% 13.25/13.42 tff(3167,plain,
% 13.25/13.42 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s50) | (~node4(c_bit0, s50))),
% 13.25/13.42 inference(modus_ponens,[status(thm)],[3166, 3165])).
% 13.25/13.42 tff(3168,plain,
% 13.25/13.42 (~node4(c_bit0, s50)),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3167, 1344, 3164])).
% 13.25/13.42 tff(3169,assumption,(~m_counter_cell_v_value(c_bit1, s49)), introduced(assumption)).
% 13.25/13.42 tff(3170,plain,
% 13.25/13.42 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s49)) | (~m_counter_cell_v_value(c_bit0, s49)) | m_counter_cell_v_carry_out(c_bit0, s49))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s49)) | (~m_counter_cell_v_value(c_bit0, s49)) | m_counter_cell_v_carry_out(c_bit0, s49))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3171,plain,
% 13.25/13.42 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s49)) | (~m_counter_cell_v_value(c_bit0, s49)) | m_counter_cell_v_carry_out(c_bit0, s49))),
% 13.25/13.42 inference(quant_inst,[status(thm)],[])).
% 13.25/13.42 tff(3172,plain,
% 13.25/13.42 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s49)) | (~m_counter_cell_v_value(c_bit0, s49)) | m_counter_cell_v_carry_out(c_bit0, s49)),
% 13.25/13.42 inference(modus_ponens,[status(thm)],[3171, 3170])).
% 13.25/13.42 tff(3173,plain,
% 13.25/13.42 ((~m_counter_cell_v_value(c_bit0, s49)) | m_counter_cell_v_carry_out(c_bit0, s49)),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3172, 1390, 3138])).
% 13.25/13.42 tff(3174,plain,
% 13.25/13.42 (m_counter_cell_v_carry_out(c_bit0, s49)),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3173, 3134])).
% 13.25/13.42 tff(3175,plain,
% 13.25/13.42 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s49)) | m_counter_cell_v_carry_in(c_bit1, s49))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s49)) | m_counter_cell_v_carry_in(c_bit1, s49))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3176,plain,
% 13.25/13.42 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s49)) | m_counter_cell_v_carry_in(c_bit1, s49))),
% 13.25/13.42 inference(quant_inst,[status(thm)],[])).
% 13.25/13.42 tff(3177,plain,
% 13.25/13.42 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s49)) | m_counter_cell_v_carry_in(c_bit1, s49)),
% 13.25/13.42 inference(modus_ponens,[status(thm)],[3176, 3175])).
% 13.25/13.42 tff(3178,plain,
% 13.25/13.42 (m_counter_cell_v_carry_in(c_bit1, s49)),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3177, 1405, 3174])).
% 13.25/13.42 tff(3179,assumption,(m_counter_cell_v_carry_in(c_bit1, s49)), introduced(assumption)).
% 13.25/13.42 tff(3180,assumption,(node1(c_bit1, s49)), introduced(assumption)).
% 13.25/13.42 tff(3181,plain,
% 13.25/13.42 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49) | (~node1(c_bit1, s49)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49) | (~node1(c_bit1, s49)))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3182,plain,
% 13.25/13.42 (((~node1(c_bit1, s49)) | (~m_counter_cell_v_carry_in(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49) | (~node1(c_bit1, s49)))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3183,plain,
% 13.25/13.42 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s49)) | (~m_counter_cell_v_carry_in(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49) | (~node1(c_bit1, s49))))),
% 13.25/13.42 inference(monotonicity,[status(thm)],[3182])).
% 13.25/13.42 tff(3184,plain,
% 13.25/13.42 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s49)) | (~m_counter_cell_v_carry_in(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49) | (~node1(c_bit1, s49)))),
% 13.25/13.42 inference(transitivity,[status(thm)],[3183, 3181])).
% 13.25/13.42 tff(3185,plain,
% 13.25/13.42 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s49)) | (~m_counter_cell_v_carry_in(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49))),
% 13.25/13.42 inference(quant_inst,[status(thm)],[])).
% 13.25/13.42 tff(3186,plain,
% 13.25/13.42 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49) | (~node1(c_bit1, s49))),
% 13.25/13.42 inference(modus_ponens,[status(thm)],[3185, 3184])).
% 13.25/13.42 tff(3187,plain,
% 13.25/13.42 ($false),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3186, 30, 3169, 3180, 3179])).
% 13.25/13.42 tff(3188,plain,(m_counter_cell_v_value(c_bit1, s49) | (~node1(c_bit1, s49)) | (~m_counter_cell_v_carry_in(c_bit1, s49))), inference(lemma,lemma(discharge,[]))).
% 13.25/13.42 tff(3189,plain,
% 13.25/13.42 (~node1(c_bit1, s49)),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3188, 3178, 3169])).
% 13.25/13.42 tff(3190,plain,
% 13.25/13.42 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s49, s50)) | node3(c_bit1, s49, s50))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s49, s50)) | node3(c_bit1, s49, s50))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3191,plain,
% 13.25/13.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s49, s50)) | node3(c_bit1, s49, s50))),
% 13.25/13.42 inference(quant_inst,[status(thm)],[])).
% 13.25/13.42 tff(3192,plain,
% 13.25/13.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s49, s50)) | node3(c_bit1, s49, s50)),
% 13.25/13.42 inference(modus_ponens,[status(thm)],[3191, 3190])).
% 13.25/13.42 tff(3193,plain,
% 13.25/13.42 (node3(c_bit1, s49, s50)),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3192, 59, 3151])).
% 13.25/13.42 tff(3194,plain,
% 13.25/13.42 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s50) | node1(c_bit1, s49) | (~node3(c_bit1, s49, s50)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s50) | node1(c_bit1, s49) | (~node3(c_bit1, s49, s50)))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3195,plain,
% 13.25/13.42 ((node1(c_bit1, s49) | (~node3(c_bit1, s49, s50)) | m_counter_cell_v_value(c_bit1, s50)) <=> (m_counter_cell_v_value(c_bit1, s50) | node1(c_bit1, s49) | (~node3(c_bit1, s49, s50)))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3196,plain,
% 13.25/13.42 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s49) | (~node3(c_bit1, s49, s50)) | m_counter_cell_v_value(c_bit1, s50))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s50) | node1(c_bit1, s49) | (~node3(c_bit1, s49, s50))))),
% 13.25/13.42 inference(monotonicity,[status(thm)],[3195])).
% 13.25/13.42 tff(3197,plain,
% 13.25/13.42 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s49) | (~node3(c_bit1, s49, s50)) | m_counter_cell_v_value(c_bit1, s50))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s50) | node1(c_bit1, s49) | (~node3(c_bit1, s49, s50)))),
% 13.25/13.42 inference(transitivity,[status(thm)],[3196, 3194])).
% 13.25/13.42 tff(3198,plain,
% 13.25/13.42 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s49) | (~node3(c_bit1, s49, s50)) | m_counter_cell_v_value(c_bit1, s50))),
% 13.25/13.42 inference(quant_inst,[status(thm)],[])).
% 13.25/13.42 tff(3199,plain,
% 13.25/13.42 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s50) | node1(c_bit1, s49) | (~node3(c_bit1, s49, s50))),
% 13.25/13.42 inference(modus_ponens,[status(thm)],[3198, 3197])).
% 13.25/13.42 tff(3200,plain,
% 13.25/13.42 (m_counter_cell_v_value(c_bit1, s50) | node1(c_bit1, s49)),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3199, 73, 3193])).
% 13.25/13.42 tff(3201,plain,
% 13.25/13.42 (m_counter_cell_v_value(c_bit1, s50)),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3200, 3189])).
% 13.25/13.42 tff(3202,assumption,(node1(c_bit1, s50)), introduced(assumption)).
% 13.25/13.42 tff(3203,plain,
% 13.25/13.42 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50)) | (~node1(c_bit1, s50)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50)) | (~node1(c_bit1, s50)))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3204,plain,
% 13.25/13.42 (((~node1(c_bit1, s50)) | m_counter_cell_v_carry_in(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50))) <=> (m_counter_cell_v_carry_in(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50)) | (~node1(c_bit1, s50)))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3205,plain,
% 13.25/13.42 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s50)) | m_counter_cell_v_carry_in(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50)) | (~node1(c_bit1, s50))))),
% 13.25/13.42 inference(monotonicity,[status(thm)],[3204])).
% 13.25/13.42 tff(3206,plain,
% 13.25/13.42 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s50)) | m_counter_cell_v_carry_in(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50)) | (~node1(c_bit1, s50)))),
% 13.25/13.42 inference(transitivity,[status(thm)],[3205, 3203])).
% 13.25/13.42 tff(3207,plain,
% 13.25/13.42 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s50)) | m_counter_cell_v_carry_in(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50)))),
% 13.25/13.42 inference(quant_inst,[status(thm)],[])).
% 13.25/13.42 tff(3208,plain,
% 13.25/13.42 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50)) | (~node1(c_bit1, s50))),
% 13.25/13.42 inference(modus_ponens,[status(thm)],[3207, 3206])).
% 13.25/13.42 tff(3209,plain,
% 13.25/13.42 (m_counter_cell_v_carry_in(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50))),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3208, 1569, 3202])).
% 13.25/13.42 tff(3210,plain,
% 13.25/13.42 (m_counter_cell_v_carry_in(c_bit1, s50)),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3209, 3201])).
% 13.25/13.42 tff(3211,assumption,(m_counter_cell_v_carry_in(c_bit1, s50)), introduced(assumption)).
% 13.25/13.42 tff(3212,assumption,(~m_counter_cell_v_carry_out(c_bit0, s50)), introduced(assumption)).
% 13.25/13.42 tff(3213,plain,
% 13.25/13.42 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s50)) | m_counter_cell_v_carry_out(c_bit0, s50))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s50)) | m_counter_cell_v_carry_out(c_bit0, s50))),
% 13.25/13.42 inference(rewrite,[status(thm)],[])).
% 13.25/13.42 tff(3214,plain,
% 13.25/13.42 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s50)) | m_counter_cell_v_carry_out(c_bit0, s50))),
% 13.25/13.42 inference(quant_inst,[status(thm)],[])).
% 13.25/13.42 tff(3215,plain,
% 13.25/13.42 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s50)) | m_counter_cell_v_carry_out(c_bit0, s50)),
% 13.25/13.42 inference(modus_ponens,[status(thm)],[3214, 3213])).
% 13.25/13.42 tff(3216,plain,
% 13.25/13.42 ($false),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3215, 1374, 3212, 3211])).
% 13.25/13.42 tff(3217,plain,((~m_counter_cell_v_carry_in(c_bit1, s50)) | m_counter_cell_v_carry_out(c_bit0, s50)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.42 tff(3218,plain,
% 13.25/13.42 (m_counter_cell_v_carry_out(c_bit0, s50)),
% 13.25/13.42 inference(unit_resolution,[status(thm)],[3217, 3210])).
% 13.25/13.42 tff(3219,plain,
% 13.25/13.42 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s50)) | node4(c_bit0, s50))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s50)) | node4(c_bit0, s50))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3220,plain,
% 13.25/13.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s50)) | node4(c_bit0, s50))),
% 13.25/13.43 inference(quant_inst,[status(thm)],[])).
% 13.25/13.43 tff(3221,plain,
% 13.25/13.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s50)) | node4(c_bit0, s50)),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3220, 3219])).
% 13.25/13.43 tff(3222,plain,
% 13.25/13.43 ($false),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3221, 1359, 3218, 3168])).
% 13.25/13.43 tff(3223,plain,((~m_counter_cell_v_value(c_bit0, s49)) | (~node1(c_bit1, s50)) | m_counter_cell_v_value(c_bit1, s49)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.43 tff(3224,plain,
% 13.25/13.43 ((~node1(c_bit1, s50)) | m_counter_cell_v_value(c_bit1, s49)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3223, 3133])).
% 13.25/13.43 tff(3225,plain,
% 13.25/13.43 (~node1(c_bit1, s50)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3224, 3109])).
% 13.25/13.43 tff(3226,plain,
% 13.25/13.43 (succ(s50, s51) <=> succ(s50, s51)),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3227,axiom,(succ(s50, s51)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound51')).
% 13.25/13.43 tff(3228,plain,
% 13.25/13.43 (succ(s50, s51)),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3227, 3226])).
% 13.25/13.43 tff(3229,plain,
% 13.25/13.43 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s50, s51)) | trans(s50, s51))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s50, s51)) | trans(s50, s51))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3230,plain,
% 13.25/13.43 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s50, s51)) | trans(s50, s51))),
% 13.25/13.43 inference(quant_inst,[status(thm)],[])).
% 13.25/13.43 tff(3231,plain,
% 13.25/13.43 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s50, s51)) | trans(s50, s51)),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3230, 3229])).
% 13.25/13.43 tff(3232,plain,
% 13.25/13.43 (trans(s50, s51)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3231, 3228, 45])).
% 13.25/13.43 tff(3233,plain,
% 13.25/13.43 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s50, s51)) | node3(c_bit1, s50, s51))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s50, s51)) | node3(c_bit1, s50, s51))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3234,plain,
% 13.25/13.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s50, s51)) | node3(c_bit1, s50, s51))),
% 13.25/13.43 inference(quant_inst,[status(thm)],[])).
% 13.25/13.43 tff(3235,plain,
% 13.25/13.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s50, s51)) | node3(c_bit1, s50, s51)),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3234, 3233])).
% 13.25/13.43 tff(3236,plain,
% 13.25/13.43 (node3(c_bit1, s50, s51)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3235, 59, 3232])).
% 13.25/13.43 tff(3237,plain,
% 13.25/13.43 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s51) | node1(c_bit1, s50) | (~node3(c_bit1, s50, s51)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s51) | node1(c_bit1, s50) | (~node3(c_bit1, s50, s51)))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3238,plain,
% 13.25/13.43 ((node1(c_bit1, s50) | (~node3(c_bit1, s50, s51)) | m_counter_cell_v_value(c_bit1, s51)) <=> (m_counter_cell_v_value(c_bit1, s51) | node1(c_bit1, s50) | (~node3(c_bit1, s50, s51)))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3239,plain,
% 13.25/13.43 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s50) | (~node3(c_bit1, s50, s51)) | m_counter_cell_v_value(c_bit1, s51))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s51) | node1(c_bit1, s50) | (~node3(c_bit1, s50, s51))))),
% 13.25/13.43 inference(monotonicity,[status(thm)],[3238])).
% 13.25/13.43 tff(3240,plain,
% 13.25/13.43 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s50) | (~node3(c_bit1, s50, s51)) | m_counter_cell_v_value(c_bit1, s51))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s51) | node1(c_bit1, s50) | (~node3(c_bit1, s50, s51)))),
% 13.25/13.43 inference(transitivity,[status(thm)],[3239, 3237])).
% 13.25/13.43 tff(3241,plain,
% 13.25/13.43 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s50) | (~node3(c_bit1, s50, s51)) | m_counter_cell_v_value(c_bit1, s51))),
% 13.25/13.43 inference(quant_inst,[status(thm)],[])).
% 13.25/13.43 tff(3242,plain,
% 13.25/13.43 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s51) | node1(c_bit1, s50) | (~node3(c_bit1, s50, s51))),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3241, 3240])).
% 13.25/13.43 tff(3243,plain,
% 13.25/13.43 (m_counter_cell_v_value(c_bit1, s51) | node1(c_bit1, s50)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3242, 73, 3236])).
% 13.25/13.43 tff(3244,plain,
% 13.25/13.43 (m_counter_cell_v_value(c_bit1, s51)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3243, 3225])).
% 13.25/13.43 tff(3245,plain,
% 13.25/13.43 (~node2(c_bit0, s49)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3142, 3133])).
% 13.25/13.43 tff(3246,plain,
% 13.25/13.43 (~m_counter_cell_v_value(c_bit0, s50)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3163, 3245])).
% 13.25/13.43 tff(3247,assumption,(~m_counter_cell_v_carry_in(c_bit0, s50)), introduced(assumption)).
% 13.25/13.43 tff(3248,plain,
% 13.25/13.43 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s50)),
% 13.25/13.43 inference(quant_inst,[status(thm)],[])).
% 13.25/13.43 tff(3249,plain,
% 13.25/13.43 ($false),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3248, 18, 3247])).
% 13.25/13.43 tff(3250,plain,(m_counter_cell_v_carry_in(c_bit0, s50)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.43 tff(3251,plain,
% 13.25/13.43 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s50)) | m_counter_cell_v_value(c_bit0, s50) | (~node1(c_bit0, s50)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s50)) | m_counter_cell_v_value(c_bit0, s50) | (~node1(c_bit0, s50)))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3252,plain,
% 13.25/13.43 (((~node1(c_bit0, s50)) | (~m_counter_cell_v_carry_in(c_bit0, s50)) | m_counter_cell_v_value(c_bit0, s50)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s50)) | m_counter_cell_v_value(c_bit0, s50) | (~node1(c_bit0, s50)))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3253,plain,
% 13.25/13.43 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s50)) | (~m_counter_cell_v_carry_in(c_bit0, s50)) | m_counter_cell_v_value(c_bit0, s50))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s50)) | m_counter_cell_v_value(c_bit0, s50) | (~node1(c_bit0, s50))))),
% 13.25/13.43 inference(monotonicity,[status(thm)],[3252])).
% 13.25/13.43 tff(3254,plain,
% 13.25/13.43 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s50)) | (~m_counter_cell_v_carry_in(c_bit0, s50)) | m_counter_cell_v_value(c_bit0, s50))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s50)) | m_counter_cell_v_value(c_bit0, s50) | (~node1(c_bit0, s50)))),
% 13.25/13.43 inference(transitivity,[status(thm)],[3253, 3251])).
% 13.25/13.43 tff(3255,plain,
% 13.25/13.43 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s50)) | (~m_counter_cell_v_carry_in(c_bit0, s50)) | m_counter_cell_v_value(c_bit0, s50))),
% 13.25/13.43 inference(quant_inst,[status(thm)],[])).
% 13.25/13.43 tff(3256,plain,
% 13.25/13.43 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s50)) | m_counter_cell_v_value(c_bit0, s50) | (~node1(c_bit0, s50))),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3255, 3254])).
% 13.25/13.43 tff(3257,plain,
% 13.25/13.43 (m_counter_cell_v_value(c_bit0, s50) | (~node1(c_bit0, s50))),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3256, 30, 3250])).
% 13.25/13.43 tff(3258,plain,
% 13.25/13.43 (~node1(c_bit0, s50)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3257, 3246])).
% 13.25/13.43 tff(3259,plain,
% 13.25/13.43 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s50, s51)) | node3(c_bit0, s50, s51))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s50, s51)) | node3(c_bit0, s50, s51))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3260,plain,
% 13.25/13.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s50, s51)) | node3(c_bit0, s50, s51))),
% 13.25/13.43 inference(quant_inst,[status(thm)],[])).
% 13.25/13.43 tff(3261,plain,
% 13.25/13.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s50, s51)) | node3(c_bit0, s50, s51)),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3260, 3259])).
% 13.25/13.43 tff(3262,plain,
% 13.25/13.43 (node3(c_bit0, s50, s51)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3261, 59, 3232])).
% 13.25/13.43 tff(3263,plain,
% 13.25/13.43 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s51) | node1(c_bit0, s50) | (~node3(c_bit0, s50, s51)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s51) | node1(c_bit0, s50) | (~node3(c_bit0, s50, s51)))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3264,plain,
% 13.25/13.43 ((node1(c_bit0, s50) | (~node3(c_bit0, s50, s51)) | m_counter_cell_v_value(c_bit0, s51)) <=> (m_counter_cell_v_value(c_bit0, s51) | node1(c_bit0, s50) | (~node3(c_bit0, s50, s51)))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3265,plain,
% 13.25/13.43 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s50) | (~node3(c_bit0, s50, s51)) | m_counter_cell_v_value(c_bit0, s51))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s51) | node1(c_bit0, s50) | (~node3(c_bit0, s50, s51))))),
% 13.25/13.43 inference(monotonicity,[status(thm)],[3264])).
% 13.25/13.43 tff(3266,plain,
% 13.25/13.43 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s50) | (~node3(c_bit0, s50, s51)) | m_counter_cell_v_value(c_bit0, s51))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s51) | node1(c_bit0, s50) | (~node3(c_bit0, s50, s51)))),
% 13.25/13.43 inference(transitivity,[status(thm)],[3265, 3263])).
% 13.25/13.43 tff(3267,plain,
% 13.25/13.43 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s50) | (~node3(c_bit0, s50, s51)) | m_counter_cell_v_value(c_bit0, s51))),
% 13.25/13.43 inference(quant_inst,[status(thm)],[])).
% 13.25/13.43 tff(3268,plain,
% 13.25/13.43 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s51) | node1(c_bit0, s50) | (~node3(c_bit0, s50, s51))),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3267, 3266])).
% 13.25/13.43 tff(3269,plain,
% 13.25/13.43 (m_counter_cell_v_value(c_bit0, s51) | node1(c_bit0, s50)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3268, 73, 3262])).
% 13.25/13.43 tff(3270,plain,
% 13.25/13.43 (m_counter_cell_v_value(c_bit0, s51)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3269, 3258])).
% 13.25/13.43 tff(3271,assumption,(~m_counter_cell_v_carry_in(c_bit0, s51)), introduced(assumption)).
% 13.25/13.43 tff(3272,plain,
% 13.25/13.43 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s51)),
% 13.25/13.43 inference(quant_inst,[status(thm)],[])).
% 13.25/13.43 tff(3273,plain,
% 13.25/13.43 ($false),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3272, 18, 3271])).
% 13.25/13.43 tff(3274,plain,(m_counter_cell_v_carry_in(c_bit0, s51)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.43 tff(3275,plain,
% 13.25/13.43 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s51)) | (~m_counter_cell_v_value(c_bit0, s51)) | m_counter_cell_v_carry_out(c_bit0, s51))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s51)) | (~m_counter_cell_v_value(c_bit0, s51)) | m_counter_cell_v_carry_out(c_bit0, s51))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3276,plain,
% 13.25/13.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s51)) | (~m_counter_cell_v_value(c_bit0, s51)) | m_counter_cell_v_carry_out(c_bit0, s51))),
% 13.25/13.43 inference(quant_inst,[status(thm)],[])).
% 13.25/13.43 tff(3277,plain,
% 13.25/13.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s51)) | (~m_counter_cell_v_value(c_bit0, s51)) | m_counter_cell_v_carry_out(c_bit0, s51)),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3276, 3275])).
% 13.25/13.43 tff(3278,plain,
% 13.25/13.43 ((~m_counter_cell_v_value(c_bit0, s51)) | m_counter_cell_v_carry_out(c_bit0, s51)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3277, 1390, 3274])).
% 13.25/13.43 tff(3279,plain,
% 13.25/13.43 (m_counter_cell_v_carry_out(c_bit0, s51)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3278, 3270])).
% 13.25/13.43 tff(3280,plain,
% 13.25/13.43 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s51)) | m_counter_cell_v_carry_in(c_bit1, s51))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s51)) | m_counter_cell_v_carry_in(c_bit1, s51))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3281,plain,
% 13.25/13.43 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s51)) | m_counter_cell_v_carry_in(c_bit1, s51))),
% 13.25/13.43 inference(quant_inst,[status(thm)],[])).
% 13.25/13.43 tff(3282,plain,
% 13.25/13.43 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s51)) | m_counter_cell_v_carry_in(c_bit1, s51)),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3281, 3280])).
% 13.25/13.43 tff(3283,plain,
% 13.25/13.43 (m_counter_cell_v_carry_in(c_bit1, s51)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3282, 1405, 3279])).
% 13.25/13.43 tff(3284,assumption,(~m_counter_cell_v_carry_out(c_bit1, s51)), introduced(assumption)).
% 13.25/13.43 tff(3285,assumption,(m_counter_cell_v_carry_in(c_bit1, s51)), introduced(assumption)).
% 13.25/13.43 tff(3286,assumption,(m_counter_cell_v_value(c_bit1, s51)), introduced(assumption)).
% 13.25/13.43 tff(3287,plain,
% 13.25/13.43 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s51)) | (~m_counter_cell_v_value(c_bit1, s51)) | m_counter_cell_v_carry_out(c_bit1, s51))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s51)) | (~m_counter_cell_v_value(c_bit1, s51)) | m_counter_cell_v_carry_out(c_bit1, s51))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3288,plain,
% 13.25/13.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s51)) | (~m_counter_cell_v_value(c_bit1, s51)) | m_counter_cell_v_carry_out(c_bit1, s51))),
% 13.25/13.43 inference(quant_inst,[status(thm)],[])).
% 13.25/13.43 tff(3289,plain,
% 13.25/13.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s51)) | (~m_counter_cell_v_value(c_bit1, s51)) | m_counter_cell_v_carry_out(c_bit1, s51)),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3288, 3287])).
% 13.25/13.43 tff(3290,plain,
% 13.25/13.43 ($false),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3289, 1390, 3286, 3285, 3284])).
% 13.25/13.43 tff(3291,plain,(m_counter_cell_v_carry_out(c_bit1, s51) | (~m_counter_cell_v_value(c_bit1, s51)) | (~m_counter_cell_v_carry_in(c_bit1, s51))), inference(lemma,lemma(discharge,[]))).
% 13.25/13.43 tff(3292,plain,
% 13.25/13.43 (m_counter_cell_v_carry_out(c_bit1, s51) | (~m_counter_cell_v_value(c_bit1, s51))),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3291, 3283])).
% 13.25/13.43 tff(3293,plain,
% 13.25/13.43 (m_counter_cell_v_carry_out(c_bit1, s51)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3292, 3244])).
% 13.25/13.43 tff(3294,assumption,(~m_counter_cell_v_carry_in(c_bit2, s51)), introduced(assumption)).
% 13.25/13.43 tff(3295,assumption,(m_counter_cell_v_carry_out(c_bit1, s51)), introduced(assumption)).
% 13.25/13.43 tff(3296,plain,
% 13.25/13.43 (^[X: $i] : refl(((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X)) <=> ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X)))),
% 13.25/13.43 inference(bind,[status(th)],[])).
% 13.25/13.43 tff(3297,plain,
% 13.25/13.43 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X)) <=> ![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))),
% 13.25/13.43 inference(quant_intro,[status(thm)],[3296])).
% 13.25/13.43 tff(3298,plain,
% 13.25/13.43 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X)) <=> ![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3299,plain,
% 13.25/13.43 (^[X: $i] : rewrite((m_counter_cell_v_carry_in(c_bit2, X) | (~m_counter_cell_v_carry_out(c_bit1, X))) <=> ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X)))),
% 13.25/13.43 inference(bind,[status(th)],[])).
% 13.25/13.43 tff(3300,plain,
% 13.25/13.43 (![X: $i] : (m_counter_cell_v_carry_in(c_bit2, X) | (~m_counter_cell_v_carry_out(c_bit1, X))) <=> ![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))),
% 13.25/13.43 inference(quant_intro,[status(thm)],[3299])).
% 13.25/13.43 tff(3301,axiom,(![X: $i] : (m_counter_cell_v_carry_in(c_bit2, X) | (~m_counter_cell_v_carry_out(c_bit1, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_4')).
% 13.25/13.43 tff(3302,plain,
% 13.25/13.43 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3301, 3300])).
% 13.25/13.43 tff(3303,plain,
% 13.25/13.43 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3302, 3298])).
% 13.25/13.43 tff(3304,plain,(
% 13.25/13.43 ![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))),
% 13.25/13.43 inference(skolemize,[status(sab)],[3303])).
% 13.25/13.43 tff(3305,plain,
% 13.25/13.43 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3304, 3297])).
% 13.25/13.43 tff(3306,plain,
% 13.25/13.43 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s51)) | m_counter_cell_v_carry_in(c_bit2, s51))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s51)) | m_counter_cell_v_carry_in(c_bit2, s51))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3307,plain,
% 13.25/13.43 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s51)) | m_counter_cell_v_carry_in(c_bit2, s51))),
% 13.25/13.43 inference(quant_inst,[status(thm)],[])).
% 13.25/13.43 tff(3308,plain,
% 13.25/13.43 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s51)) | m_counter_cell_v_carry_in(c_bit2, s51)),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3307, 3306])).
% 13.25/13.43 tff(3309,plain,
% 13.25/13.43 ($false),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3308, 3305, 3295, 3294])).
% 13.25/13.43 tff(3310,plain,(m_counter_cell_v_carry_in(c_bit2, s51) | (~m_counter_cell_v_carry_out(c_bit1, s51))), inference(lemma,lemma(discharge,[]))).
% 13.25/13.43 tff(3311,plain,
% 13.25/13.43 (m_counter_cell_v_carry_in(c_bit2, s51)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3310, 3293])).
% 13.25/13.43 tff(3312,assumption,(node2(c_bit1, s51)), introduced(assumption)).
% 13.25/13.43 tff(3313,plain,
% 13.25/13.43 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s51)) | (~m_counter_cell_v_value(c_bit1, s51)) | (~node2(c_bit1, s51)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s51)) | (~m_counter_cell_v_value(c_bit1, s51)) | (~node2(c_bit1, s51)))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3314,plain,
% 13.25/13.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s51)) | (~m_counter_cell_v_value(c_bit1, s51)) | (~node2(c_bit1, s51)))),
% 13.25/13.43 inference(quant_inst,[status(thm)],[])).
% 13.25/13.43 tff(3315,plain,
% 13.25/13.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s51)) | (~m_counter_cell_v_value(c_bit1, s51)) | (~node2(c_bit1, s51))),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3314, 3313])).
% 13.25/13.43 tff(3316,plain,
% 13.25/13.43 ($false),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3315, 93, 3286, 3283, 3312])).
% 13.25/13.43 tff(3317,plain,((~node2(c_bit1, s51)) | (~m_counter_cell_v_value(c_bit1, s51))), inference(lemma,lemma(discharge,[]))).
% 13.25/13.43 tff(3318,plain,
% 13.25/13.43 (~node2(c_bit1, s51)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3317, 3244])).
% 13.25/13.43 tff(3319,plain,
% 13.25/13.43 (succ(s51, s52) <=> succ(s51, s52)),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3320,axiom,(succ(s51, s52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound52')).
% 13.25/13.43 tff(3321,plain,
% 13.25/13.43 (succ(s51, s52)),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3320, 3319])).
% 13.25/13.43 tff(3322,plain,
% 13.25/13.43 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s51, s52)) | trans(s51, s52))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s51, s52)) | trans(s51, s52))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3323,plain,
% 13.25/13.43 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s51, s52)) | trans(s51, s52))),
% 13.25/13.43 inference(quant_inst,[status(thm)],[])).
% 13.25/13.43 tff(3324,plain,
% 13.25/13.43 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s51, s52)) | trans(s51, s52)),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3323, 3322])).
% 13.25/13.43 tff(3325,plain,
% 13.25/13.43 (trans(s51, s52)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3324, 3321, 45])).
% 13.25/13.43 tff(3326,plain,
% 13.25/13.43 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s51, s52)) | node3(c_bit1, s51, s52))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s51, s52)) | node3(c_bit1, s51, s52))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3327,plain,
% 13.25/13.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s51, s52)) | node3(c_bit1, s51, s52))),
% 13.25/13.43 inference(quant_inst,[status(thm)],[])).
% 13.25/13.43 tff(3328,plain,
% 13.25/13.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s51, s52)) | node3(c_bit1, s51, s52)),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3327, 3326])).
% 13.25/13.43 tff(3329,plain,
% 13.25/13.43 (node3(c_bit1, s51, s52)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3328, 59, 3325])).
% 13.25/13.43 tff(3330,plain,
% 13.25/13.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s52)) | node2(c_bit1, s51) | (~node3(c_bit1, s51, s52)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s52)) | node2(c_bit1, s51) | (~node3(c_bit1, s51, s52)))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3331,plain,
% 13.25/13.43 ((node2(c_bit1, s51) | (~node3(c_bit1, s51, s52)) | (~m_counter_cell_v_value(c_bit1, s52))) <=> ((~m_counter_cell_v_value(c_bit1, s52)) | node2(c_bit1, s51) | (~node3(c_bit1, s51, s52)))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3332,plain,
% 13.25/13.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s51) | (~node3(c_bit1, s51, s52)) | (~m_counter_cell_v_value(c_bit1, s52)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s52)) | node2(c_bit1, s51) | (~node3(c_bit1, s51, s52))))),
% 13.25/13.43 inference(monotonicity,[status(thm)],[3331])).
% 13.25/13.43 tff(3333,plain,
% 13.25/13.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s51) | (~node3(c_bit1, s51, s52)) | (~m_counter_cell_v_value(c_bit1, s52)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s52)) | node2(c_bit1, s51) | (~node3(c_bit1, s51, s52)))),
% 13.25/13.43 inference(transitivity,[status(thm)],[3332, 3330])).
% 13.25/13.43 tff(3334,plain,
% 13.25/13.43 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s51) | (~node3(c_bit1, s51, s52)) | (~m_counter_cell_v_value(c_bit1, s52)))),
% 13.25/13.43 inference(quant_inst,[status(thm)],[])).
% 13.25/13.43 tff(3335,plain,
% 13.25/13.43 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s52)) | node2(c_bit1, s51) | (~node3(c_bit1, s51, s52))),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3334, 3333])).
% 13.25/13.43 tff(3336,plain,
% 13.25/13.43 ((~m_counter_cell_v_value(c_bit1, s52)) | node2(c_bit1, s51)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3335, 121, 3329])).
% 13.25/13.43 tff(3337,plain,
% 13.25/13.43 (~m_counter_cell_v_value(c_bit1, s52)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3336, 3318])).
% 13.25/13.43 tff(3338,plain,
% 13.25/13.43 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s51)) | (~m_counter_cell_v_value(c_bit0, s51)) | (~node2(c_bit0, s51)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s51)) | (~m_counter_cell_v_value(c_bit0, s51)) | (~node2(c_bit0, s51)))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3339,plain,
% 13.25/13.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s51)) | (~m_counter_cell_v_value(c_bit0, s51)) | (~node2(c_bit0, s51)))),
% 13.25/13.43 inference(quant_inst,[status(thm)],[])).
% 13.25/13.43 tff(3340,plain,
% 13.25/13.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s51)) | (~m_counter_cell_v_value(c_bit0, s51)) | (~node2(c_bit0, s51))),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3339, 3338])).
% 13.25/13.43 tff(3341,plain,
% 13.25/13.43 ((~m_counter_cell_v_value(c_bit0, s51)) | (~node2(c_bit0, s51))),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3340, 93, 3274])).
% 13.25/13.43 tff(3342,plain,
% 13.25/13.43 (~node2(c_bit0, s51)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3341, 3270])).
% 13.25/13.43 tff(3343,plain,
% 13.25/13.43 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s51, s52)) | node3(c_bit0, s51, s52))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s51, s52)) | node3(c_bit0, s51, s52))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3344,plain,
% 13.25/13.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s51, s52)) | node3(c_bit0, s51, s52))),
% 13.25/13.43 inference(quant_inst,[status(thm)],[])).
% 13.25/13.43 tff(3345,plain,
% 13.25/13.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s51, s52)) | node3(c_bit0, s51, s52)),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3344, 3343])).
% 13.25/13.43 tff(3346,plain,
% 13.25/13.43 (node3(c_bit0, s51, s52)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3345, 59, 3325])).
% 13.25/13.43 tff(3347,plain,
% 13.25/13.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s52)) | node2(c_bit0, s51) | (~node3(c_bit0, s51, s52)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s52)) | node2(c_bit0, s51) | (~node3(c_bit0, s51, s52)))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3348,plain,
% 13.25/13.43 ((node2(c_bit0, s51) | (~node3(c_bit0, s51, s52)) | (~m_counter_cell_v_value(c_bit0, s52))) <=> ((~m_counter_cell_v_value(c_bit0, s52)) | node2(c_bit0, s51) | (~node3(c_bit0, s51, s52)))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3349,plain,
% 13.25/13.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s51) | (~node3(c_bit0, s51, s52)) | (~m_counter_cell_v_value(c_bit0, s52)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s52)) | node2(c_bit0, s51) | (~node3(c_bit0, s51, s52))))),
% 13.25/13.43 inference(monotonicity,[status(thm)],[3348])).
% 13.25/13.43 tff(3350,plain,
% 13.25/13.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s51) | (~node3(c_bit0, s51, s52)) | (~m_counter_cell_v_value(c_bit0, s52)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s52)) | node2(c_bit0, s51) | (~node3(c_bit0, s51, s52)))),
% 13.25/13.43 inference(transitivity,[status(thm)],[3349, 3347])).
% 13.25/13.43 tff(3351,plain,
% 13.25/13.43 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s51) | (~node3(c_bit0, s51, s52)) | (~m_counter_cell_v_value(c_bit0, s52)))),
% 13.25/13.43 inference(quant_inst,[status(thm)],[])).
% 13.25/13.43 tff(3352,plain,
% 13.25/13.43 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s52)) | node2(c_bit0, s51) | (~node3(c_bit0, s51, s52))),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3351, 3350])).
% 13.25/13.43 tff(3353,plain,
% 13.25/13.43 ((~m_counter_cell_v_value(c_bit0, s52)) | node2(c_bit0, s51)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3352, 121, 3346])).
% 13.25/13.43 tff(3354,plain,
% 13.25/13.43 (~m_counter_cell_v_value(c_bit0, s52)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3353, 3342])).
% 13.25/13.43 tff(3355,plain,
% 13.25/13.43 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s52) | (~node4(c_bit0, s52)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s52) | (~node4(c_bit0, s52)))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3356,plain,
% 13.25/13.43 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s52) | (~node4(c_bit0, s52)))),
% 13.25/13.43 inference(quant_inst,[status(thm)],[])).
% 13.25/13.43 tff(3357,plain,
% 13.25/13.43 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s52) | (~node4(c_bit0, s52))),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3356, 3355])).
% 13.25/13.43 tff(3358,plain,
% 13.25/13.43 (~node4(c_bit0, s52)),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3357, 1344, 3354])).
% 13.25/13.43 tff(3359,assumption,(m_counter_cell_v_carry_out(c_bit0, s52)), introduced(assumption)).
% 13.25/13.43 tff(3360,plain,
% 13.25/13.43 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s52)) | node4(c_bit0, s52))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s52)) | node4(c_bit0, s52))),
% 13.25/13.43 inference(rewrite,[status(thm)],[])).
% 13.25/13.43 tff(3361,plain,
% 13.25/13.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s52)) | node4(c_bit0, s52))),
% 13.25/13.43 inference(quant_inst,[status(thm)],[])).
% 13.25/13.43 tff(3362,plain,
% 13.25/13.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s52)) | node4(c_bit0, s52)),
% 13.25/13.43 inference(modus_ponens,[status(thm)],[3361, 3360])).
% 13.25/13.43 tff(3363,plain,
% 13.25/13.43 ($false),
% 13.25/13.43 inference(unit_resolution,[status(thm)],[3362, 1359, 3359, 3358])).
% 13.25/13.43 tff(3364,plain,(~m_counter_cell_v_carry_out(c_bit0, s52)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.44 tff(3365,plain,
% 13.25/13.44 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s52)) | m_counter_cell_v_carry_out(c_bit0, s52))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s52)) | m_counter_cell_v_carry_out(c_bit0, s52))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3366,plain,
% 13.25/13.44 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s52)) | m_counter_cell_v_carry_out(c_bit0, s52))),
% 13.25/13.44 inference(quant_inst,[status(thm)],[])).
% 13.25/13.44 tff(3367,plain,
% 13.25/13.44 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s52)) | m_counter_cell_v_carry_out(c_bit0, s52)),
% 13.25/13.44 inference(modus_ponens,[status(thm)],[3366, 3365])).
% 13.25/13.44 tff(3368,plain,
% 13.25/13.44 (~m_counter_cell_v_carry_in(c_bit1, s52)),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3367, 1374, 3364])).
% 13.25/13.44 tff(3369,assumption,(~m_counter_cell_v_value(c_bit1, s52)), introduced(assumption)).
% 13.25/13.44 tff(3370,assumption,(node2(c_bit1, s52)), introduced(assumption)).
% 13.25/13.44 tff(3371,plain,
% 13.25/13.44 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s52) | m_counter_cell_v_value(c_bit1, s52) | (~node2(c_bit1, s52)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s52) | m_counter_cell_v_value(c_bit1, s52) | (~node2(c_bit1, s52)))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3372,plain,
% 13.25/13.44 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s52) | m_counter_cell_v_value(c_bit1, s52) | (~node2(c_bit1, s52)))),
% 13.25/13.44 inference(quant_inst,[status(thm)],[])).
% 13.25/13.44 tff(3373,plain,
% 13.25/13.44 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s52) | m_counter_cell_v_value(c_bit1, s52) | (~node2(c_bit1, s52))),
% 13.25/13.44 inference(modus_ponens,[status(thm)],[3372, 3371])).
% 13.25/13.44 tff(3374,plain,
% 13.25/13.44 ($false),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3373, 1498, 3370, 3369, 3368])).
% 13.25/13.44 tff(3375,plain,(m_counter_cell_v_value(c_bit1, s52) | (~node2(c_bit1, s52))), inference(lemma,lemma(discharge,[]))).
% 13.25/13.44 tff(3376,plain,
% 13.25/13.44 (~node2(c_bit1, s52)),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3375, 3337])).
% 13.25/13.44 tff(3377,plain,
% 13.25/13.44 (succ(s52, s53) <=> succ(s52, s53)),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3378,axiom,(succ(s52, s53)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound53')).
% 13.25/13.44 tff(3379,plain,
% 13.25/13.44 (succ(s52, s53)),
% 13.25/13.44 inference(modus_ponens,[status(thm)],[3378, 3377])).
% 13.25/13.44 tff(3380,plain,
% 13.25/13.44 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s52, s53)) | trans(s52, s53))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s52, s53)) | trans(s52, s53))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3381,plain,
% 13.25/13.44 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s52, s53)) | trans(s52, s53))),
% 13.25/13.44 inference(quant_inst,[status(thm)],[])).
% 13.25/13.44 tff(3382,plain,
% 13.25/13.44 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s52, s53)) | trans(s52, s53)),
% 13.25/13.44 inference(modus_ponens,[status(thm)],[3381, 3380])).
% 13.25/13.44 tff(3383,plain,
% 13.25/13.44 (trans(s52, s53)),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3382, 3379, 45])).
% 13.25/13.44 tff(3384,plain,
% 13.25/13.44 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s52, s53)) | node3(c_bit1, s52, s53))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s52, s53)) | node3(c_bit1, s52, s53))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3385,plain,
% 13.25/13.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s52, s53)) | node3(c_bit1, s52, s53))),
% 13.25/13.44 inference(quant_inst,[status(thm)],[])).
% 13.25/13.44 tff(3386,plain,
% 13.25/13.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s52, s53)) | node3(c_bit1, s52, s53)),
% 13.25/13.44 inference(modus_ponens,[status(thm)],[3385, 3384])).
% 13.25/13.44 tff(3387,plain,
% 13.25/13.44 (node3(c_bit1, s52, s53)),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3386, 59, 3383])).
% 13.25/13.44 tff(3388,plain,
% 13.25/13.44 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s53)) | node2(c_bit1, s52) | (~node3(c_bit1, s52, s53)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s53)) | node2(c_bit1, s52) | (~node3(c_bit1, s52, s53)))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3389,plain,
% 13.25/13.44 ((node2(c_bit1, s52) | (~node3(c_bit1, s52, s53)) | (~m_counter_cell_v_value(c_bit1, s53))) <=> ((~m_counter_cell_v_value(c_bit1, s53)) | node2(c_bit1, s52) | (~node3(c_bit1, s52, s53)))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3390,plain,
% 13.25/13.44 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s52) | (~node3(c_bit1, s52, s53)) | (~m_counter_cell_v_value(c_bit1, s53)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s53)) | node2(c_bit1, s52) | (~node3(c_bit1, s52, s53))))),
% 13.25/13.44 inference(monotonicity,[status(thm)],[3389])).
% 13.25/13.44 tff(3391,plain,
% 13.25/13.44 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s52) | (~node3(c_bit1, s52, s53)) | (~m_counter_cell_v_value(c_bit1, s53)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s53)) | node2(c_bit1, s52) | (~node3(c_bit1, s52, s53)))),
% 13.25/13.44 inference(transitivity,[status(thm)],[3390, 3388])).
% 13.25/13.44 tff(3392,plain,
% 13.25/13.44 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s52) | (~node3(c_bit1, s52, s53)) | (~m_counter_cell_v_value(c_bit1, s53)))),
% 13.25/13.44 inference(quant_inst,[status(thm)],[])).
% 13.25/13.44 tff(3393,plain,
% 13.25/13.44 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s53)) | node2(c_bit1, s52) | (~node3(c_bit1, s52, s53))),
% 13.25/13.44 inference(modus_ponens,[status(thm)],[3392, 3391])).
% 13.25/13.44 tff(3394,plain,
% 13.25/13.44 ((~m_counter_cell_v_value(c_bit1, s53)) | node2(c_bit1, s52)),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3393, 121, 3387])).
% 13.25/13.44 tff(3395,plain,
% 13.25/13.44 (~m_counter_cell_v_value(c_bit1, s53)),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3394, 3376])).
% 13.25/13.44 tff(3396,assumption,(node1(c_bit1, s53)), introduced(assumption)).
% 13.25/13.44 tff(3397,assumption,(~m_counter_cell_v_carry_in(c_bit0, s52)), introduced(assumption)).
% 13.25/13.44 tff(3398,plain,
% 13.25/13.44 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s52)),
% 13.25/13.44 inference(quant_inst,[status(thm)],[])).
% 13.25/13.44 tff(3399,plain,
% 13.25/13.44 ($false),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3398, 18, 3397])).
% 13.25/13.44 tff(3400,plain,(m_counter_cell_v_carry_in(c_bit0, s52)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.44 tff(3401,plain,
% 13.25/13.44 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s52)) | m_counter_cell_v_value(c_bit0, s52) | (~node1(c_bit0, s52)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s52)) | m_counter_cell_v_value(c_bit0, s52) | (~node1(c_bit0, s52)))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3402,plain,
% 13.25/13.44 (((~node1(c_bit0, s52)) | (~m_counter_cell_v_carry_in(c_bit0, s52)) | m_counter_cell_v_value(c_bit0, s52)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s52)) | m_counter_cell_v_value(c_bit0, s52) | (~node1(c_bit0, s52)))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3403,plain,
% 13.25/13.44 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s52)) | (~m_counter_cell_v_carry_in(c_bit0, s52)) | m_counter_cell_v_value(c_bit0, s52))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s52)) | m_counter_cell_v_value(c_bit0, s52) | (~node1(c_bit0, s52))))),
% 13.25/13.44 inference(monotonicity,[status(thm)],[3402])).
% 13.25/13.44 tff(3404,plain,
% 13.25/13.44 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s52)) | (~m_counter_cell_v_carry_in(c_bit0, s52)) | m_counter_cell_v_value(c_bit0, s52))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s52)) | m_counter_cell_v_value(c_bit0, s52) | (~node1(c_bit0, s52)))),
% 13.25/13.44 inference(transitivity,[status(thm)],[3403, 3401])).
% 13.25/13.44 tff(3405,plain,
% 13.25/13.44 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s52)) | (~m_counter_cell_v_carry_in(c_bit0, s52)) | m_counter_cell_v_value(c_bit0, s52))),
% 13.25/13.44 inference(quant_inst,[status(thm)],[])).
% 13.25/13.44 tff(3406,plain,
% 13.25/13.44 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s52)) | m_counter_cell_v_value(c_bit0, s52) | (~node1(c_bit0, s52))),
% 13.25/13.44 inference(modus_ponens,[status(thm)],[3405, 3404])).
% 13.25/13.44 tff(3407,plain,
% 13.25/13.44 (m_counter_cell_v_value(c_bit0, s52) | (~node1(c_bit0, s52))),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3406, 30, 3400])).
% 13.25/13.44 tff(3408,plain,
% 13.25/13.44 (~node1(c_bit0, s52)),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3407, 3354])).
% 13.25/13.44 tff(3409,plain,
% 13.25/13.44 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s52, s53)) | node3(c_bit0, s52, s53))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s52, s53)) | node3(c_bit0, s52, s53))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3410,plain,
% 13.25/13.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s52, s53)) | node3(c_bit0, s52, s53))),
% 13.25/13.44 inference(quant_inst,[status(thm)],[])).
% 13.25/13.44 tff(3411,plain,
% 13.25/13.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s52, s53)) | node3(c_bit0, s52, s53)),
% 13.25/13.44 inference(modus_ponens,[status(thm)],[3410, 3409])).
% 13.25/13.44 tff(3412,plain,
% 13.25/13.44 (node3(c_bit0, s52, s53)),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3411, 59, 3383])).
% 13.25/13.44 tff(3413,plain,
% 13.25/13.44 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s53) | node1(c_bit0, s52) | (~node3(c_bit0, s52, s53)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s53) | node1(c_bit0, s52) | (~node3(c_bit0, s52, s53)))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3414,plain,
% 13.25/13.44 ((node1(c_bit0, s52) | (~node3(c_bit0, s52, s53)) | m_counter_cell_v_value(c_bit0, s53)) <=> (m_counter_cell_v_value(c_bit0, s53) | node1(c_bit0, s52) | (~node3(c_bit0, s52, s53)))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3415,plain,
% 13.25/13.44 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s52) | (~node3(c_bit0, s52, s53)) | m_counter_cell_v_value(c_bit0, s53))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s53) | node1(c_bit0, s52) | (~node3(c_bit0, s52, s53))))),
% 13.25/13.44 inference(monotonicity,[status(thm)],[3414])).
% 13.25/13.44 tff(3416,plain,
% 13.25/13.44 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s52) | (~node3(c_bit0, s52, s53)) | m_counter_cell_v_value(c_bit0, s53))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s53) | node1(c_bit0, s52) | (~node3(c_bit0, s52, s53)))),
% 13.25/13.44 inference(transitivity,[status(thm)],[3415, 3413])).
% 13.25/13.44 tff(3417,plain,
% 13.25/13.44 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s52) | (~node3(c_bit0, s52, s53)) | m_counter_cell_v_value(c_bit0, s53))),
% 13.25/13.44 inference(quant_inst,[status(thm)],[])).
% 13.25/13.44 tff(3418,plain,
% 13.25/13.44 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s53) | node1(c_bit0, s52) | (~node3(c_bit0, s52, s53))),
% 13.25/13.44 inference(modus_ponens,[status(thm)],[3417, 3416])).
% 13.25/13.44 tff(3419,plain,
% 13.25/13.44 (m_counter_cell_v_value(c_bit0, s53) | node1(c_bit0, s52)),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3418, 73, 3412])).
% 13.25/13.44 tff(3420,plain,
% 13.25/13.44 (m_counter_cell_v_value(c_bit0, s53)),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3419, 3408])).
% 13.25/13.44 tff(3421,assumption,(~m_counter_cell_v_carry_in(c_bit0, s53)), introduced(assumption)).
% 13.25/13.44 tff(3422,plain,
% 13.25/13.44 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s53)),
% 13.25/13.44 inference(quant_inst,[status(thm)],[])).
% 13.25/13.44 tff(3423,plain,
% 13.25/13.44 ($false),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3422, 18, 3421])).
% 13.25/13.44 tff(3424,plain,(m_counter_cell_v_carry_in(c_bit0, s53)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.44 tff(3425,plain,
% 13.25/13.44 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s53)) | (~m_counter_cell_v_value(c_bit0, s53)) | m_counter_cell_v_carry_out(c_bit0, s53))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s53)) | (~m_counter_cell_v_value(c_bit0, s53)) | m_counter_cell_v_carry_out(c_bit0, s53))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3426,plain,
% 13.25/13.44 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s53)) | (~m_counter_cell_v_value(c_bit0, s53)) | m_counter_cell_v_carry_out(c_bit0, s53))),
% 13.25/13.44 inference(quant_inst,[status(thm)],[])).
% 13.25/13.44 tff(3427,plain,
% 13.25/13.44 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s53)) | (~m_counter_cell_v_value(c_bit0, s53)) | m_counter_cell_v_carry_out(c_bit0, s53)),
% 13.25/13.44 inference(modus_ponens,[status(thm)],[3426, 3425])).
% 13.25/13.44 tff(3428,plain,
% 13.25/13.44 ((~m_counter_cell_v_value(c_bit0, s53)) | m_counter_cell_v_carry_out(c_bit0, s53)),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3427, 1390, 3424])).
% 13.25/13.44 tff(3429,plain,
% 13.25/13.44 (m_counter_cell_v_carry_out(c_bit0, s53)),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3428, 3420])).
% 13.25/13.44 tff(3430,plain,
% 13.25/13.44 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s53)) | m_counter_cell_v_carry_in(c_bit1, s53))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s53)) | m_counter_cell_v_carry_in(c_bit1, s53))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3431,plain,
% 13.25/13.44 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s53)) | m_counter_cell_v_carry_in(c_bit1, s53))),
% 13.25/13.44 inference(quant_inst,[status(thm)],[])).
% 13.25/13.44 tff(3432,plain,
% 13.25/13.44 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s53)) | m_counter_cell_v_carry_in(c_bit1, s53)),
% 13.25/13.44 inference(modus_ponens,[status(thm)],[3431, 3430])).
% 13.25/13.44 tff(3433,plain,
% 13.25/13.44 (m_counter_cell_v_carry_in(c_bit1, s53)),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3432, 1405, 3429])).
% 13.25/13.44 tff(3434,assumption,(~m_counter_cell_v_value(c_bit1, s53)), introduced(assumption)).
% 13.25/13.44 tff(3435,plain,
% 13.25/13.44 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s53)) | m_counter_cell_v_value(c_bit1, s53) | (~node1(c_bit1, s53)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s53)) | m_counter_cell_v_value(c_bit1, s53) | (~node1(c_bit1, s53)))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3436,plain,
% 13.25/13.44 (((~node1(c_bit1, s53)) | (~m_counter_cell_v_carry_in(c_bit1, s53)) | m_counter_cell_v_value(c_bit1, s53)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s53)) | m_counter_cell_v_value(c_bit1, s53) | (~node1(c_bit1, s53)))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3437,plain,
% 13.25/13.44 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s53)) | (~m_counter_cell_v_carry_in(c_bit1, s53)) | m_counter_cell_v_value(c_bit1, s53))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s53)) | m_counter_cell_v_value(c_bit1, s53) | (~node1(c_bit1, s53))))),
% 13.25/13.44 inference(monotonicity,[status(thm)],[3436])).
% 13.25/13.44 tff(3438,plain,
% 13.25/13.44 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s53)) | (~m_counter_cell_v_carry_in(c_bit1, s53)) | m_counter_cell_v_value(c_bit1, s53))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s53)) | m_counter_cell_v_value(c_bit1, s53) | (~node1(c_bit1, s53)))),
% 13.25/13.44 inference(transitivity,[status(thm)],[3437, 3435])).
% 13.25/13.44 tff(3439,plain,
% 13.25/13.44 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s53)) | (~m_counter_cell_v_carry_in(c_bit1, s53)) | m_counter_cell_v_value(c_bit1, s53))),
% 13.25/13.44 inference(quant_inst,[status(thm)],[])).
% 13.25/13.44 tff(3440,plain,
% 13.25/13.44 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s53)) | m_counter_cell_v_value(c_bit1, s53) | (~node1(c_bit1, s53))),
% 13.25/13.44 inference(modus_ponens,[status(thm)],[3439, 3438])).
% 13.25/13.44 tff(3441,plain,
% 13.25/13.44 ($false),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3440, 30, 3434, 3433, 3396])).
% 13.25/13.44 tff(3442,plain,(m_counter_cell_v_value(c_bit1, s53) | (~node1(c_bit1, s53))), inference(lemma,lemma(discharge,[]))).
% 13.25/13.44 tff(3443,plain,
% 13.25/13.44 (~node1(c_bit1, s53)),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3442, 3395])).
% 13.25/13.44 tff(3444,plain,
% 13.25/13.44 (succ(s53, s54) <=> succ(s53, s54)),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3445,axiom,(succ(s53, s54)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound54')).
% 13.25/13.44 tff(3446,plain,
% 13.25/13.44 (succ(s53, s54)),
% 13.25/13.44 inference(modus_ponens,[status(thm)],[3445, 3444])).
% 13.25/13.44 tff(3447,plain,
% 13.25/13.44 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s53, s54)) | trans(s53, s54))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s53, s54)) | trans(s53, s54))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3448,plain,
% 13.25/13.44 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s53, s54)) | trans(s53, s54))),
% 13.25/13.44 inference(quant_inst,[status(thm)],[])).
% 13.25/13.44 tff(3449,plain,
% 13.25/13.44 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s53, s54)) | trans(s53, s54)),
% 13.25/13.44 inference(modus_ponens,[status(thm)],[3448, 3447])).
% 13.25/13.44 tff(3450,plain,
% 13.25/13.44 (trans(s53, s54)),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3449, 3446, 45])).
% 13.25/13.44 tff(3451,plain,
% 13.25/13.44 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s53, s54)) | node3(c_bit1, s53, s54))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s53, s54)) | node3(c_bit1, s53, s54))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3452,plain,
% 13.25/13.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s53, s54)) | node3(c_bit1, s53, s54))),
% 13.25/13.44 inference(quant_inst,[status(thm)],[])).
% 13.25/13.44 tff(3453,plain,
% 13.25/13.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s53, s54)) | node3(c_bit1, s53, s54)),
% 13.25/13.44 inference(modus_ponens,[status(thm)],[3452, 3451])).
% 13.25/13.44 tff(3454,plain,
% 13.25/13.44 (node3(c_bit1, s53, s54)),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3453, 59, 3450])).
% 13.25/13.44 tff(3455,plain,
% 13.25/13.44 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s54) | node1(c_bit1, s53) | (~node3(c_bit1, s53, s54)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s54) | node1(c_bit1, s53) | (~node3(c_bit1, s53, s54)))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3456,plain,
% 13.25/13.44 ((node1(c_bit1, s53) | (~node3(c_bit1, s53, s54)) | m_counter_cell_v_value(c_bit1, s54)) <=> (m_counter_cell_v_value(c_bit1, s54) | node1(c_bit1, s53) | (~node3(c_bit1, s53, s54)))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3457,plain,
% 13.25/13.44 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s53) | (~node3(c_bit1, s53, s54)) | m_counter_cell_v_value(c_bit1, s54))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s54) | node1(c_bit1, s53) | (~node3(c_bit1, s53, s54))))),
% 13.25/13.44 inference(monotonicity,[status(thm)],[3456])).
% 13.25/13.44 tff(3458,plain,
% 13.25/13.44 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s53) | (~node3(c_bit1, s53, s54)) | m_counter_cell_v_value(c_bit1, s54))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s54) | node1(c_bit1, s53) | (~node3(c_bit1, s53, s54)))),
% 13.25/13.44 inference(transitivity,[status(thm)],[3457, 3455])).
% 13.25/13.44 tff(3459,plain,
% 13.25/13.44 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s53) | (~node3(c_bit1, s53, s54)) | m_counter_cell_v_value(c_bit1, s54))),
% 13.25/13.44 inference(quant_inst,[status(thm)],[])).
% 13.25/13.44 tff(3460,plain,
% 13.25/13.44 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s54) | node1(c_bit1, s53) | (~node3(c_bit1, s53, s54))),
% 13.25/13.44 inference(modus_ponens,[status(thm)],[3459, 3458])).
% 13.25/13.44 tff(3461,plain,
% 13.25/13.44 (m_counter_cell_v_value(c_bit1, s54) | node1(c_bit1, s53)),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3460, 73, 3454])).
% 13.25/13.44 tff(3462,plain,
% 13.25/13.44 (m_counter_cell_v_value(c_bit1, s54)),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3461, 3443])).
% 13.25/13.44 tff(3463,plain,
% 13.25/13.44 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s53)) | (~m_counter_cell_v_value(c_bit0, s53)) | (~node2(c_bit0, s53)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s53)) | (~m_counter_cell_v_value(c_bit0, s53)) | (~node2(c_bit0, s53)))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3464,plain,
% 13.25/13.44 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s53)) | (~m_counter_cell_v_value(c_bit0, s53)) | (~node2(c_bit0, s53)))),
% 13.25/13.44 inference(quant_inst,[status(thm)],[])).
% 13.25/13.44 tff(3465,plain,
% 13.25/13.44 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s53)) | (~m_counter_cell_v_value(c_bit0, s53)) | (~node2(c_bit0, s53))),
% 13.25/13.44 inference(modus_ponens,[status(thm)],[3464, 3463])).
% 13.25/13.44 tff(3466,plain,
% 13.25/13.44 ((~m_counter_cell_v_value(c_bit0, s53)) | (~node2(c_bit0, s53))),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3465, 93, 3424])).
% 13.25/13.44 tff(3467,plain,
% 13.25/13.44 (~node2(c_bit0, s53)),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3466, 3420])).
% 13.25/13.44 tff(3468,plain,
% 13.25/13.44 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s53, s54)) | node3(c_bit0, s53, s54))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s53, s54)) | node3(c_bit0, s53, s54))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3469,plain,
% 13.25/13.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s53, s54)) | node3(c_bit0, s53, s54))),
% 13.25/13.44 inference(quant_inst,[status(thm)],[])).
% 13.25/13.44 tff(3470,plain,
% 13.25/13.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s53, s54)) | node3(c_bit0, s53, s54)),
% 13.25/13.44 inference(modus_ponens,[status(thm)],[3469, 3468])).
% 13.25/13.44 tff(3471,plain,
% 13.25/13.44 (node3(c_bit0, s53, s54)),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3470, 59, 3450])).
% 13.25/13.44 tff(3472,plain,
% 13.25/13.44 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s54)) | node2(c_bit0, s53) | (~node3(c_bit0, s53, s54)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s54)) | node2(c_bit0, s53) | (~node3(c_bit0, s53, s54)))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3473,plain,
% 13.25/13.44 ((node2(c_bit0, s53) | (~node3(c_bit0, s53, s54)) | (~m_counter_cell_v_value(c_bit0, s54))) <=> ((~m_counter_cell_v_value(c_bit0, s54)) | node2(c_bit0, s53) | (~node3(c_bit0, s53, s54)))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3474,plain,
% 13.25/13.44 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s53) | (~node3(c_bit0, s53, s54)) | (~m_counter_cell_v_value(c_bit0, s54)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s54)) | node2(c_bit0, s53) | (~node3(c_bit0, s53, s54))))),
% 13.25/13.44 inference(monotonicity,[status(thm)],[3473])).
% 13.25/13.44 tff(3475,plain,
% 13.25/13.44 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s53) | (~node3(c_bit0, s53, s54)) | (~m_counter_cell_v_value(c_bit0, s54)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s54)) | node2(c_bit0, s53) | (~node3(c_bit0, s53, s54)))),
% 13.25/13.44 inference(transitivity,[status(thm)],[3474, 3472])).
% 13.25/13.44 tff(3476,plain,
% 13.25/13.44 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s53) | (~node3(c_bit0, s53, s54)) | (~m_counter_cell_v_value(c_bit0, s54)))),
% 13.25/13.44 inference(quant_inst,[status(thm)],[])).
% 13.25/13.44 tff(3477,plain,
% 13.25/13.44 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s54)) | node2(c_bit0, s53) | (~node3(c_bit0, s53, s54))),
% 13.25/13.44 inference(modus_ponens,[status(thm)],[3476, 3475])).
% 13.25/13.44 tff(3478,plain,
% 13.25/13.44 ((~m_counter_cell_v_value(c_bit0, s54)) | node2(c_bit0, s53)),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3477, 121, 3471])).
% 13.25/13.44 tff(3479,plain,
% 13.25/13.44 (~m_counter_cell_v_value(c_bit0, s54)),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3478, 3467])).
% 13.25/13.44 tff(3480,plain,
% 13.25/13.44 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s54) | (~node4(c_bit0, s54)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s54) | (~node4(c_bit0, s54)))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3481,plain,
% 13.25/13.44 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s54) | (~node4(c_bit0, s54)))),
% 13.25/13.44 inference(quant_inst,[status(thm)],[])).
% 13.25/13.44 tff(3482,plain,
% 13.25/13.44 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s54) | (~node4(c_bit0, s54))),
% 13.25/13.44 inference(modus_ponens,[status(thm)],[3481, 3480])).
% 13.25/13.44 tff(3483,plain,
% 13.25/13.44 (~node4(c_bit0, s54)),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3482, 1344, 3479])).
% 13.25/13.44 tff(3484,assumption,(m_counter_cell_v_carry_out(c_bit0, s54)), introduced(assumption)).
% 13.25/13.44 tff(3485,plain,
% 13.25/13.44 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s54)) | node4(c_bit0, s54))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s54)) | node4(c_bit0, s54))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3486,plain,
% 13.25/13.44 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s54)) | node4(c_bit0, s54))),
% 13.25/13.44 inference(quant_inst,[status(thm)],[])).
% 13.25/13.44 tff(3487,plain,
% 13.25/13.44 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s54)) | node4(c_bit0, s54)),
% 13.25/13.44 inference(modus_ponens,[status(thm)],[3486, 3485])).
% 13.25/13.44 tff(3488,plain,
% 13.25/13.44 ($false),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3487, 1359, 3484, 3483])).
% 13.25/13.44 tff(3489,plain,(~m_counter_cell_v_carry_out(c_bit0, s54)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.44 tff(3490,assumption,(m_counter_cell_v_carry_in(c_bit1, s54)), introduced(assumption)).
% 13.25/13.44 tff(3491,assumption,(~m_counter_cell_v_carry_out(c_bit0, s54)), introduced(assumption)).
% 13.25/13.44 tff(3492,plain,
% 13.25/13.44 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s54)) | m_counter_cell_v_carry_out(c_bit0, s54))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s54)) | m_counter_cell_v_carry_out(c_bit0, s54))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3493,plain,
% 13.25/13.44 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s54)) | m_counter_cell_v_carry_out(c_bit0, s54))),
% 13.25/13.44 inference(quant_inst,[status(thm)],[])).
% 13.25/13.44 tff(3494,plain,
% 13.25/13.44 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s54)) | m_counter_cell_v_carry_out(c_bit0, s54)),
% 13.25/13.44 inference(modus_ponens,[status(thm)],[3493, 3492])).
% 13.25/13.44 tff(3495,plain,
% 13.25/13.44 ($false),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3494, 1374, 3491, 3490])).
% 13.25/13.44 tff(3496,plain,((~m_counter_cell_v_carry_in(c_bit1, s54)) | m_counter_cell_v_carry_out(c_bit0, s54)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.44 tff(3497,plain,
% 13.25/13.44 (~m_counter_cell_v_carry_in(c_bit1, s54)),
% 13.25/13.44 inference(unit_resolution,[status(thm)],[3496, 3489])).
% 13.25/13.44 tff(3498,plain,
% 13.25/13.44 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s54) | (~m_counter_cell_v_value(c_bit1, s54)) | (~node1(c_bit1, s54)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s54) | (~m_counter_cell_v_value(c_bit1, s54)) | (~node1(c_bit1, s54)))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3499,plain,
% 13.25/13.44 (((~node1(c_bit1, s54)) | m_counter_cell_v_carry_in(c_bit1, s54) | (~m_counter_cell_v_value(c_bit1, s54))) <=> (m_counter_cell_v_carry_in(c_bit1, s54) | (~m_counter_cell_v_value(c_bit1, s54)) | (~node1(c_bit1, s54)))),
% 13.25/13.44 inference(rewrite,[status(thm)],[])).
% 13.25/13.44 tff(3500,plain,
% 13.25/13.44 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s54)) | m_counter_cell_v_carry_in(c_bit1, s54) | (~m_counter_cell_v_value(c_bit1, s54)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s54) | (~m_counter_cell_v_value(c_bit1, s54)) | (~node1(c_bit1, s54))))),
% 13.25/13.44 inference(monotonicity,[status(thm)],[3499])).
% 13.25/13.44 tff(3501,plain,
% 13.25/13.44 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s54)) | m_counter_cell_v_carry_in(c_bit1, s54) | (~m_counter_cell_v_value(c_bit1, s54)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s54) | (~m_counter_cell_v_value(c_bit1, s54)) | (~node1(c_bit1, s54)))),
% 13.25/13.45 inference(transitivity,[status(thm)],[3500, 3498])).
% 13.25/13.45 tff(3502,plain,
% 13.25/13.45 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s54)) | m_counter_cell_v_carry_in(c_bit1, s54) | (~m_counter_cell_v_value(c_bit1, s54)))),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3503,plain,
% 13.25/13.45 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s54) | (~m_counter_cell_v_value(c_bit1, s54)) | (~node1(c_bit1, s54))),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3502, 3501])).
% 13.25/13.45 tff(3504,plain,
% 13.25/13.45 ((~m_counter_cell_v_value(c_bit1, s54)) | (~node1(c_bit1, s54))),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3503, 1569, 3497])).
% 13.25/13.45 tff(3505,plain,
% 13.25/13.45 (~node1(c_bit1, s54)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3504, 3462])).
% 13.25/13.45 tff(3506,plain,
% 13.25/13.45 (succ(s54, s55) <=> succ(s54, s55)),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3507,axiom,(succ(s54, s55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound55')).
% 13.25/13.45 tff(3508,plain,
% 13.25/13.45 (succ(s54, s55)),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3507, 3506])).
% 13.25/13.45 tff(3509,plain,
% 13.25/13.45 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s54, s55)) | trans(s54, s55))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s54, s55)) | trans(s54, s55))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3510,plain,
% 13.25/13.45 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s54, s55)) | trans(s54, s55))),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3511,plain,
% 13.25/13.45 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s54, s55)) | trans(s54, s55)),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3510, 3509])).
% 13.25/13.45 tff(3512,plain,
% 13.25/13.45 (trans(s54, s55)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3511, 3508, 45])).
% 13.25/13.45 tff(3513,plain,
% 13.25/13.45 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s54, s55)) | node3(c_bit1, s54, s55))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s54, s55)) | node3(c_bit1, s54, s55))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3514,plain,
% 13.25/13.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s54, s55)) | node3(c_bit1, s54, s55))),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3515,plain,
% 13.25/13.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s54, s55)) | node3(c_bit1, s54, s55)),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3514, 3513])).
% 13.25/13.45 tff(3516,plain,
% 13.25/13.45 (node3(c_bit1, s54, s55)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3515, 59, 3512])).
% 13.25/13.45 tff(3517,plain,
% 13.25/13.45 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s55) | node1(c_bit1, s54) | (~node3(c_bit1, s54, s55)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s55) | node1(c_bit1, s54) | (~node3(c_bit1, s54, s55)))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3518,plain,
% 13.25/13.45 ((node1(c_bit1, s54) | (~node3(c_bit1, s54, s55)) | m_counter_cell_v_value(c_bit1, s55)) <=> (m_counter_cell_v_value(c_bit1, s55) | node1(c_bit1, s54) | (~node3(c_bit1, s54, s55)))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3519,plain,
% 13.25/13.45 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s54) | (~node3(c_bit1, s54, s55)) | m_counter_cell_v_value(c_bit1, s55))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s55) | node1(c_bit1, s54) | (~node3(c_bit1, s54, s55))))),
% 13.25/13.45 inference(monotonicity,[status(thm)],[3518])).
% 13.25/13.45 tff(3520,plain,
% 13.25/13.45 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s54) | (~node3(c_bit1, s54, s55)) | m_counter_cell_v_value(c_bit1, s55))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s55) | node1(c_bit1, s54) | (~node3(c_bit1, s54, s55)))),
% 13.25/13.45 inference(transitivity,[status(thm)],[3519, 3517])).
% 13.25/13.45 tff(3521,plain,
% 13.25/13.45 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s54) | (~node3(c_bit1, s54, s55)) | m_counter_cell_v_value(c_bit1, s55))),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3522,plain,
% 13.25/13.45 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s55) | node1(c_bit1, s54) | (~node3(c_bit1, s54, s55))),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3521, 3520])).
% 13.25/13.45 tff(3523,plain,
% 13.25/13.45 (m_counter_cell_v_value(c_bit1, s55) | node1(c_bit1, s54)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3522, 73, 3516])).
% 13.25/13.45 tff(3524,plain,
% 13.25/13.45 (m_counter_cell_v_value(c_bit1, s55)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3523, 3505])).
% 13.25/13.45 tff(3525,assumption,(m_counter_cell_v_value(c_bit1, s55)), introduced(assumption)).
% 13.25/13.45 tff(3526,assumption,(~m_counter_cell_v_carry_in(c_bit0, s54)), introduced(assumption)).
% 13.25/13.45 tff(3527,plain,
% 13.25/13.45 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s54)),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3528,plain,
% 13.25/13.45 ($false),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3527, 18, 3526])).
% 13.25/13.45 tff(3529,plain,(m_counter_cell_v_carry_in(c_bit0, s54)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.45 tff(3530,plain,
% 13.25/13.45 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s54)) | m_counter_cell_v_value(c_bit0, s54) | (~node1(c_bit0, s54)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s54)) | m_counter_cell_v_value(c_bit0, s54) | (~node1(c_bit0, s54)))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3531,plain,
% 13.25/13.45 (((~node1(c_bit0, s54)) | (~m_counter_cell_v_carry_in(c_bit0, s54)) | m_counter_cell_v_value(c_bit0, s54)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s54)) | m_counter_cell_v_value(c_bit0, s54) | (~node1(c_bit0, s54)))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3532,plain,
% 13.25/13.45 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s54)) | (~m_counter_cell_v_carry_in(c_bit0, s54)) | m_counter_cell_v_value(c_bit0, s54))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s54)) | m_counter_cell_v_value(c_bit0, s54) | (~node1(c_bit0, s54))))),
% 13.25/13.45 inference(monotonicity,[status(thm)],[3531])).
% 13.25/13.45 tff(3533,plain,
% 13.25/13.45 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s54)) | (~m_counter_cell_v_carry_in(c_bit0, s54)) | m_counter_cell_v_value(c_bit0, s54))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s54)) | m_counter_cell_v_value(c_bit0, s54) | (~node1(c_bit0, s54)))),
% 13.25/13.45 inference(transitivity,[status(thm)],[3532, 3530])).
% 13.25/13.45 tff(3534,plain,
% 13.25/13.45 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s54)) | (~m_counter_cell_v_carry_in(c_bit0, s54)) | m_counter_cell_v_value(c_bit0, s54))),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3535,plain,
% 13.25/13.45 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s54)) | m_counter_cell_v_value(c_bit0, s54) | (~node1(c_bit0, s54))),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3534, 3533])).
% 13.25/13.45 tff(3536,plain,
% 13.25/13.45 (m_counter_cell_v_value(c_bit0, s54) | (~node1(c_bit0, s54))),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3535, 30, 3529])).
% 13.25/13.45 tff(3537,plain,
% 13.25/13.45 (~node1(c_bit0, s54)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3536, 3479])).
% 13.25/13.45 tff(3538,plain,
% 13.25/13.45 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s54, s55)) | node3(c_bit0, s54, s55))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s54, s55)) | node3(c_bit0, s54, s55))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3539,plain,
% 13.25/13.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s54, s55)) | node3(c_bit0, s54, s55))),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3540,plain,
% 13.25/13.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s54, s55)) | node3(c_bit0, s54, s55)),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3539, 3538])).
% 13.25/13.45 tff(3541,plain,
% 13.25/13.45 (node3(c_bit0, s54, s55)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3540, 59, 3512])).
% 13.25/13.45 tff(3542,plain,
% 13.25/13.45 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s55) | node1(c_bit0, s54) | (~node3(c_bit0, s54, s55)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s55) | node1(c_bit0, s54) | (~node3(c_bit0, s54, s55)))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3543,plain,
% 13.25/13.45 ((node1(c_bit0, s54) | (~node3(c_bit0, s54, s55)) | m_counter_cell_v_value(c_bit0, s55)) <=> (m_counter_cell_v_value(c_bit0, s55) | node1(c_bit0, s54) | (~node3(c_bit0, s54, s55)))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3544,plain,
% 13.25/13.45 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s54) | (~node3(c_bit0, s54, s55)) | m_counter_cell_v_value(c_bit0, s55))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s55) | node1(c_bit0, s54) | (~node3(c_bit0, s54, s55))))),
% 13.25/13.45 inference(monotonicity,[status(thm)],[3543])).
% 13.25/13.45 tff(3545,plain,
% 13.25/13.45 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s54) | (~node3(c_bit0, s54, s55)) | m_counter_cell_v_value(c_bit0, s55))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s55) | node1(c_bit0, s54) | (~node3(c_bit0, s54, s55)))),
% 13.25/13.45 inference(transitivity,[status(thm)],[3544, 3542])).
% 13.25/13.45 tff(3546,plain,
% 13.25/13.45 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s54) | (~node3(c_bit0, s54, s55)) | m_counter_cell_v_value(c_bit0, s55))),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3547,plain,
% 13.25/13.45 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s55) | node1(c_bit0, s54) | (~node3(c_bit0, s54, s55))),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3546, 3545])).
% 13.25/13.45 tff(3548,plain,
% 13.25/13.45 (m_counter_cell_v_value(c_bit0, s55) | node1(c_bit0, s54)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3547, 73, 3541])).
% 13.25/13.45 tff(3549,plain,
% 13.25/13.45 (m_counter_cell_v_value(c_bit0, s55)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3548, 3537])).
% 13.25/13.45 tff(3550,assumption,(~m_counter_cell_v_carry_in(c_bit0, s55)), introduced(assumption)).
% 13.25/13.45 tff(3551,plain,
% 13.25/13.45 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s55)),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3552,plain,
% 13.25/13.45 ($false),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3551, 18, 3550])).
% 13.25/13.45 tff(3553,plain,(m_counter_cell_v_carry_in(c_bit0, s55)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.45 tff(3554,plain,
% 13.25/13.45 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s55)) | (~m_counter_cell_v_value(c_bit0, s55)) | m_counter_cell_v_carry_out(c_bit0, s55))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s55)) | (~m_counter_cell_v_value(c_bit0, s55)) | m_counter_cell_v_carry_out(c_bit0, s55))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3555,plain,
% 13.25/13.45 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s55)) | (~m_counter_cell_v_value(c_bit0, s55)) | m_counter_cell_v_carry_out(c_bit0, s55))),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3556,plain,
% 13.25/13.45 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s55)) | (~m_counter_cell_v_value(c_bit0, s55)) | m_counter_cell_v_carry_out(c_bit0, s55)),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3555, 3554])).
% 13.25/13.45 tff(3557,plain,
% 13.25/13.45 ((~m_counter_cell_v_value(c_bit0, s55)) | m_counter_cell_v_carry_out(c_bit0, s55)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3556, 1390, 3553])).
% 13.25/13.45 tff(3558,plain,
% 13.25/13.45 (m_counter_cell_v_carry_out(c_bit0, s55)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3557, 3549])).
% 13.25/13.45 tff(3559,plain,
% 13.25/13.45 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s55)) | m_counter_cell_v_carry_in(c_bit1, s55))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s55)) | m_counter_cell_v_carry_in(c_bit1, s55))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3560,plain,
% 13.25/13.45 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s55)) | m_counter_cell_v_carry_in(c_bit1, s55))),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3561,plain,
% 13.25/13.45 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s55)) | m_counter_cell_v_carry_in(c_bit1, s55)),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3560, 3559])).
% 13.25/13.45 tff(3562,plain,
% 13.25/13.45 (m_counter_cell_v_carry_in(c_bit1, s55)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3561, 1405, 3558])).
% 13.25/13.45 tff(3563,assumption,(node2(c_bit1, s55)), introduced(assumption)).
% 13.25/13.45 tff(3564,plain,
% 13.25/13.45 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s55)) | (~m_counter_cell_v_value(c_bit1, s55)) | (~node2(c_bit1, s55)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s55)) | (~m_counter_cell_v_value(c_bit1, s55)) | (~node2(c_bit1, s55)))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3565,plain,
% 13.25/13.45 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s55)) | (~m_counter_cell_v_value(c_bit1, s55)) | (~node2(c_bit1, s55)))),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3566,plain,
% 13.25/13.45 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s55)) | (~m_counter_cell_v_value(c_bit1, s55)) | (~node2(c_bit1, s55))),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3565, 3564])).
% 13.25/13.45 tff(3567,plain,
% 13.25/13.45 ($false),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3566, 93, 3563, 3562, 3525])).
% 13.25/13.45 tff(3568,plain,((~node2(c_bit1, s55)) | (~m_counter_cell_v_value(c_bit1, s55))), inference(lemma,lemma(discharge,[]))).
% 13.25/13.45 tff(3569,plain,
% 13.25/13.45 (~node2(c_bit1, s55)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3568, 3524])).
% 13.25/13.45 tff(3570,plain,
% 13.25/13.45 (succ(s55, s56) <=> succ(s55, s56)),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3571,axiom,(succ(s55, s56)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound56')).
% 13.25/13.45 tff(3572,plain,
% 13.25/13.45 (succ(s55, s56)),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3571, 3570])).
% 13.25/13.45 tff(3573,plain,
% 13.25/13.45 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s55, s56)) | trans(s55, s56))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s55, s56)) | trans(s55, s56))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3574,plain,
% 13.25/13.45 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s55, s56)) | trans(s55, s56))),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3575,plain,
% 13.25/13.45 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s55, s56)) | trans(s55, s56)),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3574, 3573])).
% 13.25/13.45 tff(3576,plain,
% 13.25/13.45 (trans(s55, s56)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3575, 3572, 45])).
% 13.25/13.45 tff(3577,plain,
% 13.25/13.45 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s55, s56)) | node3(c_bit1, s55, s56))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s55, s56)) | node3(c_bit1, s55, s56))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3578,plain,
% 13.25/13.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s55, s56)) | node3(c_bit1, s55, s56))),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3579,plain,
% 13.25/13.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s55, s56)) | node3(c_bit1, s55, s56)),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3578, 3577])).
% 13.25/13.45 tff(3580,plain,
% 13.25/13.45 (node3(c_bit1, s55, s56)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3579, 59, 3576])).
% 13.25/13.45 tff(3581,plain,
% 13.25/13.45 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s56)) | node2(c_bit1, s55) | (~node3(c_bit1, s55, s56)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s56)) | node2(c_bit1, s55) | (~node3(c_bit1, s55, s56)))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3582,plain,
% 13.25/13.45 ((node2(c_bit1, s55) | (~node3(c_bit1, s55, s56)) | (~m_counter_cell_v_value(c_bit1, s56))) <=> ((~m_counter_cell_v_value(c_bit1, s56)) | node2(c_bit1, s55) | (~node3(c_bit1, s55, s56)))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3583,plain,
% 13.25/13.45 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s55) | (~node3(c_bit1, s55, s56)) | (~m_counter_cell_v_value(c_bit1, s56)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s56)) | node2(c_bit1, s55) | (~node3(c_bit1, s55, s56))))),
% 13.25/13.45 inference(monotonicity,[status(thm)],[3582])).
% 13.25/13.45 tff(3584,plain,
% 13.25/13.45 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s55) | (~node3(c_bit1, s55, s56)) | (~m_counter_cell_v_value(c_bit1, s56)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s56)) | node2(c_bit1, s55) | (~node3(c_bit1, s55, s56)))),
% 13.25/13.45 inference(transitivity,[status(thm)],[3583, 3581])).
% 13.25/13.45 tff(3585,plain,
% 13.25/13.45 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s55) | (~node3(c_bit1, s55, s56)) | (~m_counter_cell_v_value(c_bit1, s56)))),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3586,plain,
% 13.25/13.45 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s56)) | node2(c_bit1, s55) | (~node3(c_bit1, s55, s56))),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3585, 3584])).
% 13.25/13.45 tff(3587,plain,
% 13.25/13.45 ((~m_counter_cell_v_value(c_bit1, s56)) | node2(c_bit1, s55)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3586, 121, 3580])).
% 13.25/13.45 tff(3588,plain,
% 13.25/13.45 (~m_counter_cell_v_value(c_bit1, s56)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3587, 3569])).
% 13.25/13.45 tff(3589,assumption,(~m_counter_cell_v_value(c_bit1, s56)), introduced(assumption)).
% 13.25/13.45 tff(3590,plain,
% 13.25/13.45 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s56) | (~node4(c_bit1, s56)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s56) | (~node4(c_bit1, s56)))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3591,plain,
% 13.25/13.45 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s56) | (~node4(c_bit1, s56)))),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3592,plain,
% 13.25/13.45 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s56) | (~node4(c_bit1, s56))),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3591, 3590])).
% 13.25/13.45 tff(3593,plain,
% 13.25/13.45 (~node4(c_bit1, s56)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3592, 1344, 3589])).
% 13.25/13.45 tff(3594,plain,
% 13.25/13.45 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s56)) | node4(c_bit1, s56))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s56)) | node4(c_bit1, s56))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3595,plain,
% 13.25/13.45 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s56)) | node4(c_bit1, s56))),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3596,plain,
% 13.25/13.45 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s56)) | node4(c_bit1, s56)),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3595, 3594])).
% 13.25/13.45 tff(3597,plain,
% 13.25/13.45 (~m_counter_cell_v_carry_out(c_bit1, s56)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3596, 1359, 3593])).
% 13.25/13.45 tff(3598,plain,
% 13.25/13.45 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s55)) | (~m_counter_cell_v_value(c_bit0, s55)) | (~node2(c_bit0, s55)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s55)) | (~m_counter_cell_v_value(c_bit0, s55)) | (~node2(c_bit0, s55)))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3599,plain,
% 13.25/13.45 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s55)) | (~m_counter_cell_v_value(c_bit0, s55)) | (~node2(c_bit0, s55)))),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3600,plain,
% 13.25/13.45 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s55)) | (~m_counter_cell_v_value(c_bit0, s55)) | (~node2(c_bit0, s55))),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3599, 3598])).
% 13.25/13.45 tff(3601,plain,
% 13.25/13.45 ((~m_counter_cell_v_value(c_bit0, s55)) | (~node2(c_bit0, s55))),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3600, 93, 3553])).
% 13.25/13.45 tff(3602,plain,
% 13.25/13.45 (~node2(c_bit0, s55)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3601, 3549])).
% 13.25/13.45 tff(3603,plain,
% 13.25/13.45 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s55, s56)) | node3(c_bit0, s55, s56))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s55, s56)) | node3(c_bit0, s55, s56))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3604,plain,
% 13.25/13.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s55, s56)) | node3(c_bit0, s55, s56))),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3605,plain,
% 13.25/13.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s55, s56)) | node3(c_bit0, s55, s56)),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3604, 3603])).
% 13.25/13.45 tff(3606,plain,
% 13.25/13.45 (node3(c_bit0, s55, s56)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3605, 59, 3576])).
% 13.25/13.45 tff(3607,plain,
% 13.25/13.45 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s56)) | node2(c_bit0, s55) | (~node3(c_bit0, s55, s56)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s56)) | node2(c_bit0, s55) | (~node3(c_bit0, s55, s56)))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3608,plain,
% 13.25/13.45 ((node2(c_bit0, s55) | (~node3(c_bit0, s55, s56)) | (~m_counter_cell_v_value(c_bit0, s56))) <=> ((~m_counter_cell_v_value(c_bit0, s56)) | node2(c_bit0, s55) | (~node3(c_bit0, s55, s56)))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3609,plain,
% 13.25/13.45 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s55) | (~node3(c_bit0, s55, s56)) | (~m_counter_cell_v_value(c_bit0, s56)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s56)) | node2(c_bit0, s55) | (~node3(c_bit0, s55, s56))))),
% 13.25/13.45 inference(monotonicity,[status(thm)],[3608])).
% 13.25/13.45 tff(3610,plain,
% 13.25/13.45 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s55) | (~node3(c_bit0, s55, s56)) | (~m_counter_cell_v_value(c_bit0, s56)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s56)) | node2(c_bit0, s55) | (~node3(c_bit0, s55, s56)))),
% 13.25/13.45 inference(transitivity,[status(thm)],[3609, 3607])).
% 13.25/13.45 tff(3611,plain,
% 13.25/13.45 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s55) | (~node3(c_bit0, s55, s56)) | (~m_counter_cell_v_value(c_bit0, s56)))),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3612,plain,
% 13.25/13.45 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s56)) | node2(c_bit0, s55) | (~node3(c_bit0, s55, s56))),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3611, 3610])).
% 13.25/13.45 tff(3613,plain,
% 13.25/13.45 ((~m_counter_cell_v_value(c_bit0, s56)) | node2(c_bit0, s55)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3612, 121, 3606])).
% 13.25/13.45 tff(3614,plain,
% 13.25/13.45 (~m_counter_cell_v_value(c_bit0, s56)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3613, 3602])).
% 13.25/13.45 tff(3615,plain,
% 13.25/13.45 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s56) | (~node4(c_bit0, s56)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s56) | (~node4(c_bit0, s56)))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3616,plain,
% 13.25/13.45 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s56) | (~node4(c_bit0, s56)))),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3617,plain,
% 13.25/13.45 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s56) | (~node4(c_bit0, s56))),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3616, 3615])).
% 13.25/13.45 tff(3618,plain,
% 13.25/13.45 (~node4(c_bit0, s56)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3617, 1344, 3614])).
% 13.25/13.45 tff(3619,assumption,(m_counter_cell_v_carry_out(c_bit0, s56)), introduced(assumption)).
% 13.25/13.45 tff(3620,plain,
% 13.25/13.45 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s56)) | node4(c_bit0, s56))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s56)) | node4(c_bit0, s56))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3621,plain,
% 13.25/13.45 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s56)) | node4(c_bit0, s56))),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3622,plain,
% 13.25/13.45 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s56)) | node4(c_bit0, s56)),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3621, 3620])).
% 13.25/13.45 tff(3623,plain,
% 13.25/13.45 ($false),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3622, 1359, 3619, 3618])).
% 13.25/13.45 tff(3624,plain,(~m_counter_cell_v_carry_out(c_bit0, s56)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.45 tff(3625,plain,
% 13.25/13.45 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s56)) | m_counter_cell_v_carry_out(c_bit0, s56))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s56)) | m_counter_cell_v_carry_out(c_bit0, s56))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3626,plain,
% 13.25/13.45 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s56)) | m_counter_cell_v_carry_out(c_bit0, s56))),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3627,plain,
% 13.25/13.45 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s56)) | m_counter_cell_v_carry_out(c_bit0, s56)),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3626, 3625])).
% 13.25/13.45 tff(3628,plain,
% 13.25/13.45 (~m_counter_cell_v_carry_in(c_bit1, s56)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3627, 1374, 3624])).
% 13.25/13.45 tff(3629,assumption,(node2(c_bit1, s56)), introduced(assumption)).
% 13.25/13.45 tff(3630,plain,
% 13.25/13.45 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s56) | m_counter_cell_v_value(c_bit1, s56) | (~node2(c_bit1, s56)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s56) | m_counter_cell_v_value(c_bit1, s56) | (~node2(c_bit1, s56)))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3631,plain,
% 13.25/13.45 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s56) | m_counter_cell_v_value(c_bit1, s56) | (~node2(c_bit1, s56)))),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3632,plain,
% 13.25/13.45 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s56) | m_counter_cell_v_value(c_bit1, s56) | (~node2(c_bit1, s56))),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3631, 3630])).
% 13.25/13.45 tff(3633,plain,
% 13.25/13.45 ($false),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3632, 1498, 3589, 3629, 3628])).
% 13.25/13.45 tff(3634,plain,((~node2(c_bit1, s56)) | m_counter_cell_v_value(c_bit1, s56)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.45 tff(3635,plain,
% 13.25/13.45 (~node2(c_bit1, s56)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3634, 3589])).
% 13.25/13.45 tff(3636,plain,
% 13.25/13.45 (succ(s56, s57) <=> succ(s56, s57)),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3637,axiom,(succ(s56, s57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound57')).
% 13.25/13.45 tff(3638,plain,
% 13.25/13.45 (succ(s56, s57)),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3637, 3636])).
% 13.25/13.45 tff(3639,plain,
% 13.25/13.45 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s56, s57)) | trans(s56, s57))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s56, s57)) | trans(s56, s57))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3640,plain,
% 13.25/13.45 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s56, s57)) | trans(s56, s57))),
% 13.25/13.45 inference(quant_inst,[status(thm)],[])).
% 13.25/13.45 tff(3641,plain,
% 13.25/13.45 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s56, s57)) | trans(s56, s57)),
% 13.25/13.45 inference(modus_ponens,[status(thm)],[3640, 3639])).
% 13.25/13.45 tff(3642,plain,
% 13.25/13.45 (trans(s56, s57)),
% 13.25/13.45 inference(unit_resolution,[status(thm)],[3641, 3638, 45])).
% 13.25/13.45 tff(3643,plain,
% 13.25/13.45 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s56, s57)) | node3(c_bit1, s56, s57))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s56, s57)) | node3(c_bit1, s56, s57))),
% 13.25/13.45 inference(rewrite,[status(thm)],[])).
% 13.25/13.45 tff(3644,plain,
% 13.25/13.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s56, s57)) | node3(c_bit1, s56, s57))),
% 13.25/13.46 inference(quant_inst,[status(thm)],[])).
% 13.25/13.46 tff(3645,plain,
% 13.25/13.46 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s56, s57)) | node3(c_bit1, s56, s57)),
% 13.25/13.46 inference(modus_ponens,[status(thm)],[3644, 3643])).
% 13.25/13.46 tff(3646,plain,
% 13.25/13.46 (node3(c_bit1, s56, s57)),
% 13.25/13.46 inference(unit_resolution,[status(thm)],[3645, 59, 3642])).
% 13.25/13.46 tff(3647,plain,
% 13.25/13.46 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s57)) | node2(c_bit1, s56) | (~node3(c_bit1, s56, s57)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s57)) | node2(c_bit1, s56) | (~node3(c_bit1, s56, s57)))),
% 13.25/13.46 inference(rewrite,[status(thm)],[])).
% 13.25/13.46 tff(3648,plain,
% 13.25/13.46 ((node2(c_bit1, s56) | (~node3(c_bit1, s56, s57)) | (~m_counter_cell_v_value(c_bit1, s57))) <=> ((~m_counter_cell_v_value(c_bit1, s57)) | node2(c_bit1, s56) | (~node3(c_bit1, s56, s57)))),
% 13.25/13.46 inference(rewrite,[status(thm)],[])).
% 13.25/13.46 tff(3649,plain,
% 13.25/13.46 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s56) | (~node3(c_bit1, s56, s57)) | (~m_counter_cell_v_value(c_bit1, s57)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s57)) | node2(c_bit1, s56) | (~node3(c_bit1, s56, s57))))),
% 13.25/13.46 inference(monotonicity,[status(thm)],[3648])).
% 13.25/13.46 tff(3650,plain,
% 13.25/13.46 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s56) | (~node3(c_bit1, s56, s57)) | (~m_counter_cell_v_value(c_bit1, s57)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s57)) | node2(c_bit1, s56) | (~node3(c_bit1, s56, s57)))),
% 13.25/13.46 inference(transitivity,[status(thm)],[3649, 3647])).
% 13.25/13.46 tff(3651,plain,
% 13.25/13.46 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s56) | (~node3(c_bit1, s56, s57)) | (~m_counter_cell_v_value(c_bit1, s57)))),
% 13.25/13.46 inference(quant_inst,[status(thm)],[])).
% 13.25/13.46 tff(3652,plain,
% 13.25/13.46 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s57)) | node2(c_bit1, s56) | (~node3(c_bit1, s56, s57))),
% 13.25/13.46 inference(modus_ponens,[status(thm)],[3651, 3650])).
% 13.25/13.46 tff(3653,plain,
% 13.25/13.46 ((~m_counter_cell_v_value(c_bit1, s57)) | node2(c_bit1, s56)),
% 13.25/13.46 inference(unit_resolution,[status(thm)],[3652, 121, 3646])).
% 13.25/13.46 tff(3654,plain,
% 13.25/13.46 (~m_counter_cell_v_value(c_bit1, s57)),
% 13.25/13.46 inference(unit_resolution,[status(thm)],[3653, 3635])).
% 13.25/13.46 tff(3655,plain,
% 13.25/13.46 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s57) | (~node4(c_bit1, s57)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s57) | (~node4(c_bit1, s57)))),
% 13.25/13.46 inference(rewrite,[status(thm)],[])).
% 13.25/13.46 tff(3656,plain,
% 13.25/13.46 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s57) | (~node4(c_bit1, s57)))),
% 13.25/13.46 inference(quant_inst,[status(thm)],[])).
% 13.25/13.46 tff(3657,plain,
% 13.25/13.46 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s57) | (~node4(c_bit1, s57))),
% 13.25/13.46 inference(modus_ponens,[status(thm)],[3656, 3655])).
% 13.25/13.46 tff(3658,plain,
% 13.25/13.46 (~node4(c_bit1, s57)),
% 13.25/13.46 inference(unit_resolution,[status(thm)],[3657, 1344, 3654])).
% 13.25/13.46 tff(3659,assumption,(m_counter_cell_v_carry_out(c_bit1, s57)), introduced(assumption)).
% 13.25/13.46 tff(3660,assumption,(~node4(c_bit1, s57)), introduced(assumption)).
% 13.25/13.46 tff(3661,plain,
% 13.25/13.46 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s57)) | node4(c_bit1, s57))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s57)) | node4(c_bit1, s57))),
% 13.25/13.46 inference(rewrite,[status(thm)],[])).
% 13.25/13.46 tff(3662,plain,
% 13.25/13.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s57)) | node4(c_bit1, s57))),
% 13.25/13.46 inference(quant_inst,[status(thm)],[])).
% 13.25/13.46 tff(3663,plain,
% 13.25/13.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s57)) | node4(c_bit1, s57)),
% 13.25/13.46 inference(modus_ponens,[status(thm)],[3662, 3661])).
% 13.25/13.46 tff(3664,plain,
% 13.25/13.46 ($false),
% 13.25/13.46 inference(unit_resolution,[status(thm)],[3663, 1359, 3660, 3659])).
% 13.25/13.46 tff(3665,plain,((~m_counter_cell_v_carry_out(c_bit1, s57)) | node4(c_bit1, s57)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.46 tff(3666,plain,
% 13.25/13.46 (~m_counter_cell_v_carry_out(c_bit1, s57)),
% 13.25/13.46 inference(unit_resolution,[status(thm)],[3665, 3658])).
% 13.25/13.46 tff(3667,assumption,(m_counter_cell_v_carry_in(c_bit2, s57)), introduced(assumption)).
% 13.25/13.46 tff(3668,assumption,(~m_counter_cell_v_carry_out(c_bit1, s57)), introduced(assumption)).
% 13.25/13.46 tff(3669,plain,
% 13.25/13.46 (^[X: $i] : refl(((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X)) <=> ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X)))),
% 13.25/13.46 inference(bind,[status(th)],[])).
% 13.25/13.46 tff(3670,plain,
% 13.25/13.46 (![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X)) <=> ![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))),
% 13.25/13.46 inference(quant_intro,[status(thm)],[3669])).
% 13.25/13.46 tff(3671,plain,
% 13.25/13.46 (![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X)) <=> ![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))),
% 13.25/13.46 inference(rewrite,[status(thm)],[])).
% 13.25/13.46 tff(3672,axiom,(![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_5')).
% 13.25/13.46 tff(3673,plain,
% 13.25/13.46 (![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))),
% 13.25/13.46 inference(modus_ponens,[status(thm)],[3672, 3671])).
% 13.25/13.46 tff(3674,plain,(
% 13.25/13.46 ![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))),
% 13.25/13.46 inference(skolemize,[status(sab)],[3673])).
% 13.25/13.46 tff(3675,plain,
% 13.25/13.46 (![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))),
% 13.25/13.46 inference(modus_ponens,[status(thm)],[3674, 3670])).
% 13.25/13.46 tff(3676,plain,
% 13.25/13.46 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s57)) | m_counter_cell_v_carry_out(c_bit1, s57))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s57)) | m_counter_cell_v_carry_out(c_bit1, s57))),
% 13.25/13.46 inference(rewrite,[status(thm)],[])).
% 13.25/13.46 tff(3677,plain,
% 13.25/13.46 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s57)) | m_counter_cell_v_carry_out(c_bit1, s57))),
% 13.25/13.46 inference(quant_inst,[status(thm)],[])).
% 13.25/13.46 tff(3678,plain,
% 13.25/13.46 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s57)) | m_counter_cell_v_carry_out(c_bit1, s57)),
% 13.25/13.46 inference(modus_ponens,[status(thm)],[3677, 3676])).
% 13.25/13.46 tff(3679,plain,
% 13.25/13.46 ($false),
% 13.25/13.46 inference(unit_resolution,[status(thm)],[3678, 3675, 3668, 3667])).
% 13.25/13.46 tff(3680,plain,((~m_counter_cell_v_carry_in(c_bit2, s57)) | m_counter_cell_v_carry_out(c_bit1, s57)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.46 tff(3681,plain,
% 13.25/13.46 (~m_counter_cell_v_carry_in(c_bit2, s57)),
% 13.25/13.46 inference(unit_resolution,[status(thm)],[3680, 3666])).
% 13.25/13.46 tff(3682,assumption,(~m_counter_cell_v_carry_in(c_bit0, s56)), introduced(assumption)).
% 13.25/13.46 tff(3683,plain,
% 13.25/13.46 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s56)),
% 13.25/13.46 inference(quant_inst,[status(thm)],[])).
% 13.25/13.46 tff(3684,plain,
% 13.25/13.46 ($false),
% 13.25/13.46 inference(unit_resolution,[status(thm)],[3683, 18, 3682])).
% 13.25/13.46 tff(3685,plain,(m_counter_cell_v_carry_in(c_bit0, s56)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.46 tff(3686,plain,
% 13.25/13.46 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s56)) | m_counter_cell_v_value(c_bit0, s56) | (~node1(c_bit0, s56)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s56)) | m_counter_cell_v_value(c_bit0, s56) | (~node1(c_bit0, s56)))),
% 13.25/13.46 inference(rewrite,[status(thm)],[])).
% 13.25/13.46 tff(3687,plain,
% 13.25/13.46 (((~node1(c_bit0, s56)) | (~m_counter_cell_v_carry_in(c_bit0, s56)) | m_counter_cell_v_value(c_bit0, s56)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s56)) | m_counter_cell_v_value(c_bit0, s56) | (~node1(c_bit0, s56)))),
% 13.25/13.46 inference(rewrite,[status(thm)],[])).
% 13.25/13.46 tff(3688,plain,
% 13.25/13.46 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s56)) | (~m_counter_cell_v_carry_in(c_bit0, s56)) | m_counter_cell_v_value(c_bit0, s56))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s56)) | m_counter_cell_v_value(c_bit0, s56) | (~node1(c_bit0, s56))))),
% 13.25/13.46 inference(monotonicity,[status(thm)],[3687])).
% 13.25/13.46 tff(3689,plain,
% 13.25/13.46 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s56)) | (~m_counter_cell_v_carry_in(c_bit0, s56)) | m_counter_cell_v_value(c_bit0, s56))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s56)) | m_counter_cell_v_value(c_bit0, s56) | (~node1(c_bit0, s56)))),
% 13.25/13.46 inference(transitivity,[status(thm)],[3688, 3686])).
% 13.25/13.46 tff(3690,plain,
% 13.25/13.46 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s56)) | (~m_counter_cell_v_carry_in(c_bit0, s56)) | m_counter_cell_v_value(c_bit0, s56))),
% 13.25/13.46 inference(quant_inst,[status(thm)],[])).
% 13.25/13.46 tff(3691,plain,
% 13.25/13.46 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s56)) | m_counter_cell_v_value(c_bit0, s56) | (~node1(c_bit0, s56))),
% 13.25/13.46 inference(modus_ponens,[status(thm)],[3690, 3689])).
% 13.25/13.46 tff(3692,plain,
% 13.25/13.46 (m_counter_cell_v_value(c_bit0, s56) | (~node1(c_bit0, s56))),
% 13.25/13.46 inference(unit_resolution,[status(thm)],[3691, 30, 3685])).
% 13.25/13.46 tff(3693,plain,
% 13.25/13.46 (~node1(c_bit0, s56)),
% 13.25/13.46 inference(unit_resolution,[status(thm)],[3692, 3614])).
% 13.25/13.46 tff(3694,plain,
% 13.25/13.46 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s56, s57)) | node3(c_bit0, s56, s57))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s56, s57)) | node3(c_bit0, s56, s57))),
% 13.25/13.46 inference(rewrite,[status(thm)],[])).
% 13.25/13.46 tff(3695,plain,
% 13.25/13.46 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s56, s57)) | node3(c_bit0, s56, s57))),
% 13.25/13.46 inference(quant_inst,[status(thm)],[])).
% 13.25/13.46 tff(3696,plain,
% 13.25/13.46 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s56, s57)) | node3(c_bit0, s56, s57)),
% 13.25/13.46 inference(modus_ponens,[status(thm)],[3695, 3694])).
% 13.25/13.46 tff(3697,plain,
% 13.25/13.46 (node3(c_bit0, s56, s57)),
% 13.25/13.46 inference(unit_resolution,[status(thm)],[3696, 59, 3642])).
% 13.25/13.46 tff(3698,plain,
% 13.25/13.46 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s57) | node1(c_bit0, s56) | (~node3(c_bit0, s56, s57)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s57) | node1(c_bit0, s56) | (~node3(c_bit0, s56, s57)))),
% 13.25/13.46 inference(rewrite,[status(thm)],[])).
% 13.25/13.46 tff(3699,plain,
% 13.25/13.46 ((node1(c_bit0, s56) | (~node3(c_bit0, s56, s57)) | m_counter_cell_v_value(c_bit0, s57)) <=> (m_counter_cell_v_value(c_bit0, s57) | node1(c_bit0, s56) | (~node3(c_bit0, s56, s57)))),
% 13.25/13.46 inference(rewrite,[status(thm)],[])).
% 13.25/13.46 tff(3700,plain,
% 13.25/13.46 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s56) | (~node3(c_bit0, s56, s57)) | m_counter_cell_v_value(c_bit0, s57))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s57) | node1(c_bit0, s56) | (~node3(c_bit0, s56, s57))))),
% 13.25/13.46 inference(monotonicity,[status(thm)],[3699])).
% 13.25/13.46 tff(3701,plain,
% 13.25/13.46 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s56) | (~node3(c_bit0, s56, s57)) | m_counter_cell_v_value(c_bit0, s57))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s57) | node1(c_bit0, s56) | (~node3(c_bit0, s56, s57)))),
% 13.25/13.46 inference(transitivity,[status(thm)],[3700, 3698])).
% 13.25/13.46 tff(3702,plain,
% 13.25/13.46 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s56) | (~node3(c_bit0, s56, s57)) | m_counter_cell_v_value(c_bit0, s57))),
% 13.25/13.46 inference(quant_inst,[status(thm)],[])).
% 13.25/13.46 tff(3703,plain,
% 13.25/13.46 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s57) | node1(c_bit0, s56) | (~node3(c_bit0, s56, s57))),
% 13.25/13.46 inference(modus_ponens,[status(thm)],[3702, 3701])).
% 13.25/13.46 tff(3704,plain,
% 13.25/13.46 (m_counter_cell_v_value(c_bit0, s57) | node1(c_bit0, s56)),
% 13.25/13.46 inference(unit_resolution,[status(thm)],[3703, 73, 3697])).
% 13.25/13.46 tff(3705,plain,
% 13.25/13.46 (m_counter_cell_v_value(c_bit0, s57)),
% 13.25/13.46 inference(unit_resolution,[status(thm)],[3704, 3693])).
% 13.25/13.46 tff(3706,assumption,(~m_counter_cell_v_carry_in(c_bit0, s57)), introduced(assumption)).
% 13.25/13.46 tff(3707,plain,
% 13.25/13.46 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s57)),
% 13.25/13.46 inference(quant_inst,[status(thm)],[])).
% 13.25/13.46 tff(3708,plain,
% 13.25/13.46 ($false),
% 13.25/13.46 inference(unit_resolution,[status(thm)],[3707, 18, 3706])).
% 13.25/13.46 tff(3709,plain,(m_counter_cell_v_carry_in(c_bit0, s57)), inference(lemma,lemma(discharge,[]))).
% 13.25/13.46 tff(3710,plain,
% 13.25/13.46 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s57)) | (~m_counter_cell_v_value(c_bit0, s57)) | m_counter_cell_v_carry_out(c_bit0, s57))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s57)) | (~m_counter_cell_v_value(c_bit0, s57)) | m_counter_cell_v_carry_out(c_bit0, s57))),
% 13.25/13.46 inference(rewrite,[status(thm)],[])).
% 13.25/13.46 tff(3711,plain,
% 13.25/13.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s57)) | (~m_counter_cell_v_value(c_bit0, s57)) | m_counter_cell_v_carry_out(c_bit0, s57))),
% 13.25/13.46 inference(quant_inst,[status(thm)],[])).
% 13.25/13.46 tff(3712,plain,
% 13.25/13.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s57)) | (~m_counter_cell_v_value(c_bit0, s57)) | m_counter_cell_v_carry_out(c_bit0, s57)),
% 13.25/13.46 inference(modus_ponens,[status(thm)],[3711, 3710])).
% 13.25/13.46 tff(3713,plain,
% 13.25/13.46 ((~m_counter_cell_v_value(c_bit0, s57)) | m_counter_cell_v_carry_out(c_bit0, s57)),
% 13.25/13.46 inference(unit_resolution,[status(thm)],[3712, 1390, 3709])).
% 13.25/13.46 tff(3714,plain,
% 13.25/13.46 (m_counter_cell_v_carry_out(c_bit0, s57)),
% 13.25/13.46 inference(unit_resolution,[status(thm)],[3713, 3705])).
% 13.25/13.46 tff(3715,plain,
% 13.25/13.46 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s57)) | m_counter_cell_v_carry_in(c_bit1, s57))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s57)) | m_counter_cell_v_carry_in(c_bit1, s57))),
% 13.25/13.46 inference(rewrite,[status(thm)],[])).
% 13.25/13.46 tff(3716,plain,
% 13.25/13.46 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s57)) | m_counter_cell_v_carry_in(c_bit1, s57))),
% 13.25/13.46 inference(quant_inst,[status(thm)],[])).
% 13.25/13.46 tff(3717,plain,
% 13.25/13.46 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s57)) | m_counter_cell_v_carry_in(c_bit1, s57)),
% 13.25/13.46 inference(modus_ponens,[status(thm)],[3716, 3715])).
% 13.25/13.46 tff(3718,plain,
% 13.25/13.46 (m_counter_cell_v_carry_in(c_bit1, s57)),
% 13.25/13.46 inference(unit_resolution,[status(thm)],[3717, 1405, 3714])).
% 13.25/13.46 tff(3719,plain,
% 13.25/13.46 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s57)) | m_counter_cell_v_value(c_bit1, s57) | (~node1(c_bit1, s57)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s57)) | m_counter_cell_v_value(c_bit1, s57) | (~node1(c_bit1, s57)))),
% 13.25/13.46 inference(rewrite,[status(thm)],[])).
% 13.25/13.46 tff(3720,plain,
% 13.25/13.46 (((~node1(c_bit1, s57)) | (~m_counter_cell_v_carry_in(c_bit1, s57)) | m_counter_cell_v_value(c_bit1, s57)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s57)) | m_counter_cell_v_value(c_bit1, s57) | (~node1(c_bit1, s57)))),
% 13.25/13.46 inference(rewrite,[status(thm)],[])).
% 13.25/13.46 tff(3721,plain,
% 13.25/13.46 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s57)) | (~m_counter_cell_v_carry_in(c_bit1, s57)) | m_counter_cell_v_value(c_bit1, s57))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s57)) | m_counter_cell_v_value(c_bit1, s57) | (~node1(c_bit1, s57))))),
% 13.25/13.46 inference(monotonicity,[status(thm)],[3720])).
% 13.25/13.46 tff(3722,plain,
% 13.25/13.46 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s57)) | (~m_counter_cell_v_carry_in(c_bit1, s57)) | m_counter_cell_v_value(c_bit1, s57))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s57)) | m_counter_cell_v_value(c_bit1, s57) | (~node1(c_bit1, s57)))),
% 13.25/13.46 inference(transitivity,[status(thm)],[3721, 3719])).
% 13.25/13.46 tff(3723,plain,
% 13.25/13.46 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s57)) | (~m_counter_cell_v_carry_in(c_bit1, s57)) | m_counter_cell_v_value(c_bit1, s57))),
% 13.25/13.46 inference(quant_inst,[status(thm)],[])).
% 13.25/13.46 tff(3724,plain,
% 13.25/13.46 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s57)) | m_counter_cell_v_value(c_bit1, s57) | (~node1(c_bit1, s57))),
% 13.25/13.46 inference(modus_ponens,[status(thm)],[3723, 3722])).
% 13.25/13.46 tff(3725,plain,
% 13.25/13.46 (m_counter_cell_v_value(c_bit1, s57) | (~node1(c_bit1, s57))),
% 13.25/13.46 inference(unit_resolution,[status(thm)],[3724, 30, 3718])).
% 13.25/13.46 tff(3726,plain,
% 13.25/13.46 (~node1(c_bit1, s57)),
% 13.25/13.46 inference(unit_resolution,[status(thm)],[3725, 3654])).
% 13.25/13.46 tff(3727,plain,
% 13.25/13.46 (succ(s57, s58) <=> succ(s57, s58)),
% 13.25/13.46 inference(rewrite,[status(thm)],[])).
% 13.25/13.46 tff(3728,axiom,(succ(s57, s58)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound58')).
% 13.25/13.46 tff(3729,plain,
% 13.25/13.46 (succ(s57, s58)),
% 13.25/13.46 inference(modus_ponens,[status(thm)],[3728, 3727])).
% 13.25/13.46 tff(3730,plain,
% 13.25/13.46 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s57, s58)) | trans(s57, s58))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s57, s58)) | trans(s57, s58))),
% 13.25/13.46 inference(rewrite,[status(thm)],[])).
% 13.25/13.46 tff(3731,plain,
% 13.25/13.46 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s57, s58)) | trans(s57, s58))),
% 13.25/13.46 inference(quant_inst,[status(thm)],[])).
% 13.25/13.46 tff(3732,plain,
% 13.25/13.46 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s57, s58)) | trans(s57, s58)),
% 13.25/13.46 inference(modus_ponens,[status(thm)],[3731, 3730])).
% 13.25/13.46 tff(3733,plain,
% 13.25/13.46 (trans(s57, s58)),
% 13.25/13.46 inference(unit_resolution,[status(thm)],[3732, 3729, 45])).
% 13.25/13.46 tff(3734,plain,
% 13.25/13.46 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s57, s58)) | node3(c_bit1, s57, s58))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s57, s58)) | node3(c_bit1, s57, s58))),
% 13.25/13.46 inference(rewrite,[status(thm)],[])).
% 13.25/13.46 tff(3735,plain,
% 13.25/13.46 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s57, s58)) | node3(c_bit1, s57, s58))),
% 13.25/13.46 inference(quant_inst,[status(thm)],[])).
% 13.25/13.46 tff(3736,plain,
% 13.25/13.46 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s57, s58)) | node3(c_bit1, s57, s58)),
% 13.25/13.46 inference(modus_ponens,[status(thm)],[3735, 3734])).
% 13.25/13.46 tff(3737,plain,
% 13.25/13.46 (node3(c_bit1, s57, s58)),
% 13.25/13.46 inference(unit_resolution,[status(thm)],[3736, 59, 3733])).
% 13.25/13.46 tff(3738,plain,
% 13.25/13.46 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s57) | (~node3(c_bit1, s57, s58)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s57) | (~node3(c_bit1, s57, s58)))),
% 13.25/13.46 inference(rewrite,[status(thm)],[])).
% 13.25/13.46 tff(3739,plain,
% 13.25/13.46 ((node1(c_bit1, s57) | (~node3(c_bit1, s57, s58)) | m_counter_cell_v_value(c_bit1, s58)) <=> (m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s57) | (~node3(c_bit1, s57, s58)))),
% 13.25/13.46 inference(rewrite,[status(thm)],[])).
% 13.25/13.46 tff(3740,plain,
% 13.25/13.46 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s57) | (~node3(c_bit1, s57, s58)) | m_counter_cell_v_value(c_bit1, s58))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s57) | (~node3(c_bit1, s57, s58))))),
% 13.25/13.46 inference(monotonicity,[status(thm)],[3739])).
% 13.25/13.46 tff(3741,plain,
% 13.25/13.46 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s57) | (~node3(c_bit1, s57, s58)) | m_counter_cell_v_value(c_bit1, s58))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s57) | (~node3(c_bit1, s57, s58)))),
% 13.25/13.46 inference(transitivity,[status(thm)],[3740, 3738])).
% 13.25/13.46 tff(3742,plain,
% 13.25/13.46 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s57) | (~node3(c_bit1, s57, s58)) | m_counter_cell_v_value(c_bit1, s58))),
% 13.25/13.46 inference(quant_inst,[status(thm)],[])).
% 13.25/13.46 tff(3743,plain,
% 13.25/13.46 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s57) | (~node3(c_bit1, s57, s58))),
% 13.25/13.46 inference(modus_ponens,[status(thm)],[3742, 3741])).
% 13.25/13.46 tff(3744,plain,
% 13.25/13.46 (m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s57)),
% 13.25/13.46 inference(unit_resolution,[status(thm)],[3743, 73, 3737])).
% 13.25/13.46 tff(3745,plain,
% 13.25/13.46 (m_counter_cell_v_value(c_bit1, s58)),
% 13.25/13.46 inference(unit_resolution,[status(thm)],[3744, 3726])).
% 13.25/13.46 tff(3746,assumption,(node4(c_bit1, s58)), introduced(assumption)).
% 13.25/13.46 tff(3747,plain,
% 13.25/13.46 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s57)) | (~m_counter_cell_v_value(c_bit0, s57)) | (~node2(c_bit0, s57)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s57)) | (~m_counter_cell_v_value(c_bit0, s57)) | (~node2(c_bit0, s57)))),
% 13.32/13.46 inference(rewrite,[status(thm)],[])).
% 13.32/13.46 tff(3748,plain,
% 13.32/13.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s57)) | (~m_counter_cell_v_value(c_bit0, s57)) | (~node2(c_bit0, s57)))),
% 13.32/13.46 inference(quant_inst,[status(thm)],[])).
% 13.32/13.46 tff(3749,plain,
% 13.32/13.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s57)) | (~m_counter_cell_v_value(c_bit0, s57)) | (~node2(c_bit0, s57))),
% 13.32/13.46 inference(modus_ponens,[status(thm)],[3748, 3747])).
% 13.32/13.46 tff(3750,plain,
% 13.32/13.46 ((~m_counter_cell_v_value(c_bit0, s57)) | (~node2(c_bit0, s57))),
% 13.32/13.46 inference(unit_resolution,[status(thm)],[3749, 93, 3709])).
% 13.32/13.46 tff(3751,plain,
% 13.32/13.46 (~node2(c_bit0, s57)),
% 13.32/13.46 inference(unit_resolution,[status(thm)],[3750, 3705])).
% 13.32/13.46 tff(3752,plain,
% 13.32/13.46 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s57, s58)) | node3(c_bit0, s57, s58))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s57, s58)) | node3(c_bit0, s57, s58))),
% 13.32/13.46 inference(rewrite,[status(thm)],[])).
% 13.32/13.46 tff(3753,plain,
% 13.32/13.46 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s57, s58)) | node3(c_bit0, s57, s58))),
% 13.32/13.46 inference(quant_inst,[status(thm)],[])).
% 13.32/13.46 tff(3754,plain,
% 13.32/13.46 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s57, s58)) | node3(c_bit0, s57, s58)),
% 13.32/13.46 inference(modus_ponens,[status(thm)],[3753, 3752])).
% 13.32/13.46 tff(3755,plain,
% 13.32/13.46 (node3(c_bit0, s57, s58)),
% 13.32/13.46 inference(unit_resolution,[status(thm)],[3754, 59, 3733])).
% 13.32/13.46 tff(3756,plain,
% 13.32/13.46 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s58)) | node2(c_bit0, s57) | (~node3(c_bit0, s57, s58)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s58)) | node2(c_bit0, s57) | (~node3(c_bit0, s57, s58)))),
% 13.32/13.46 inference(rewrite,[status(thm)],[])).
% 13.32/13.46 tff(3757,plain,
% 13.32/13.46 ((node2(c_bit0, s57) | (~node3(c_bit0, s57, s58)) | (~m_counter_cell_v_value(c_bit0, s58))) <=> ((~m_counter_cell_v_value(c_bit0, s58)) | node2(c_bit0, s57) | (~node3(c_bit0, s57, s58)))),
% 13.32/13.46 inference(rewrite,[status(thm)],[])).
% 13.32/13.46 tff(3758,plain,
% 13.32/13.46 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s57) | (~node3(c_bit0, s57, s58)) | (~m_counter_cell_v_value(c_bit0, s58)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s58)) | node2(c_bit0, s57) | (~node3(c_bit0, s57, s58))))),
% 13.32/13.46 inference(monotonicity,[status(thm)],[3757])).
% 13.32/13.46 tff(3759,plain,
% 13.32/13.46 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s57) | (~node3(c_bit0, s57, s58)) | (~m_counter_cell_v_value(c_bit0, s58)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s58)) | node2(c_bit0, s57) | (~node3(c_bit0, s57, s58)))),
% 13.32/13.46 inference(transitivity,[status(thm)],[3758, 3756])).
% 13.32/13.46 tff(3760,plain,
% 13.32/13.46 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s57) | (~node3(c_bit0, s57, s58)) | (~m_counter_cell_v_value(c_bit0, s58)))),
% 13.32/13.46 inference(quant_inst,[status(thm)],[])).
% 13.32/13.46 tff(3761,plain,
% 13.32/13.46 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s58)) | node2(c_bit0, s57) | (~node3(c_bit0, s57, s58))),
% 13.32/13.46 inference(modus_ponens,[status(thm)],[3760, 3759])).
% 13.32/13.46 tff(3762,plain,
% 13.32/13.46 ((~m_counter_cell_v_value(c_bit0, s58)) | node2(c_bit0, s57)),
% 13.32/13.46 inference(unit_resolution,[status(thm)],[3761, 121, 3755])).
% 13.32/13.46 tff(3763,plain,
% 13.32/13.46 (~m_counter_cell_v_value(c_bit0, s58)),
% 13.32/13.46 inference(unit_resolution,[status(thm)],[3762, 3751])).
% 13.32/13.46 tff(3764,plain,
% 13.32/13.46 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s58) | (~node4(c_bit0, s58)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s58) | (~node4(c_bit0, s58)))),
% 13.32/13.46 inference(rewrite,[status(thm)],[])).
% 13.32/13.46 tff(3765,plain,
% 13.32/13.46 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s58) | (~node4(c_bit0, s58)))),
% 13.32/13.46 inference(quant_inst,[status(thm)],[])).
% 13.32/13.46 tff(3766,plain,
% 13.32/13.46 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s58) | (~node4(c_bit0, s58))),
% 13.32/13.46 inference(modus_ponens,[status(thm)],[3765, 3764])).
% 13.32/13.46 tff(3767,plain,
% 13.32/13.46 (~node4(c_bit0, s58)),
% 13.32/13.46 inference(unit_resolution,[status(thm)],[3766, 1344, 3763])).
% 13.32/13.46 tff(3768,assumption,(m_counter_cell_v_carry_out(c_bit0, s58)), introduced(assumption)).
% 13.32/13.46 tff(3769,plain,
% 13.32/13.46 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s58)) | node4(c_bit0, s58))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s58)) | node4(c_bit0, s58))),
% 13.32/13.46 inference(rewrite,[status(thm)],[])).
% 13.32/13.46 tff(3770,plain,
% 13.32/13.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s58)) | node4(c_bit0, s58))),
% 13.32/13.46 inference(quant_inst,[status(thm)],[])).
% 13.32/13.46 tff(3771,plain,
% 13.32/13.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s58)) | node4(c_bit0, s58)),
% 13.32/13.46 inference(modus_ponens,[status(thm)],[3770, 3769])).
% 13.32/13.46 tff(3772,plain,
% 13.32/13.46 ($false),
% 13.32/13.46 inference(unit_resolution,[status(thm)],[3771, 1359, 3768, 3767])).
% 13.32/13.46 tff(3773,plain,(~m_counter_cell_v_carry_out(c_bit0, s58)), inference(lemma,lemma(discharge,[]))).
% 13.32/13.46 tff(3774,assumption,(m_counter_cell_v_carry_in(c_bit1, s58)), introduced(assumption)).
% 13.32/13.46 tff(3775,assumption,(~m_counter_cell_v_carry_out(c_bit0, s58)), introduced(assumption)).
% 13.32/13.46 tff(3776,plain,
% 13.32/13.46 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s58)) | m_counter_cell_v_carry_out(c_bit0, s58))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s58)) | m_counter_cell_v_carry_out(c_bit0, s58))),
% 13.32/13.46 inference(rewrite,[status(thm)],[])).
% 13.32/13.46 tff(3777,plain,
% 13.32/13.46 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s58)) | m_counter_cell_v_carry_out(c_bit0, s58))),
% 13.32/13.46 inference(quant_inst,[status(thm)],[])).
% 13.32/13.46 tff(3778,plain,
% 13.32/13.46 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s58)) | m_counter_cell_v_carry_out(c_bit0, s58)),
% 13.32/13.46 inference(modus_ponens,[status(thm)],[3777, 3776])).
% 13.32/13.46 tff(3779,plain,
% 13.32/13.46 ($false),
% 13.32/13.46 inference(unit_resolution,[status(thm)],[3778, 1374, 3775, 3774])).
% 13.32/13.46 tff(3780,plain,(m_counter_cell_v_carry_out(c_bit0, s58) | (~m_counter_cell_v_carry_in(c_bit1, s58))), inference(lemma,lemma(discharge,[]))).
% 13.32/13.46 tff(3781,plain,
% 13.32/13.46 (~m_counter_cell_v_carry_in(c_bit1, s58)),
% 13.32/13.46 inference(unit_resolution,[status(thm)],[3780, 3773])).
% 13.32/13.46 tff(3782,plain,
% 13.32/13.46 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s58) | (~node4(c_bit1, s58)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s58) | (~node4(c_bit1, s58)))),
% 13.32/13.46 inference(rewrite,[status(thm)],[])).
% 13.32/13.46 tff(3783,plain,
% 13.32/13.46 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s58) | (~node4(c_bit1, s58)))),
% 13.32/13.47 inference(quant_inst,[status(thm)],[])).
% 13.32/13.47 tff(3784,plain,
% 13.32/13.47 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s58) | (~node4(c_bit1, s58))),
% 13.32/13.47 inference(modus_ponens,[status(thm)],[3783, 3782])).
% 13.32/13.47 tff(3785,plain,
% 13.32/13.47 ($false),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3784, 2941, 3781, 3746])).
% 13.32/13.47 tff(3786,plain,(~node4(c_bit1, s58)), inference(lemma,lemma(discharge,[]))).
% 13.32/13.47 tff(3787,plain,
% 13.32/13.47 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s58)) | node4(c_bit1, s58))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s58)) | node4(c_bit1, s58))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3788,plain,
% 13.32/13.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s58)) | node4(c_bit1, s58))),
% 13.32/13.47 inference(quant_inst,[status(thm)],[])).
% 13.32/13.47 tff(3789,plain,
% 13.32/13.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s58)) | node4(c_bit1, s58)),
% 13.32/13.47 inference(modus_ponens,[status(thm)],[3788, 3787])).
% 13.32/13.47 tff(3790,plain,
% 13.32/13.47 (~m_counter_cell_v_carry_out(c_bit1, s58)),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3789, 1359, 3786])).
% 13.32/13.47 tff(3791,assumption,(m_counter_cell_v_value(c_bit1, s58)), introduced(assumption)).
% 13.32/13.47 tff(3792,assumption,(~m_counter_cell_v_carry_out(c_bit1, s58)), introduced(assumption)).
% 13.32/13.47 tff(3793,plain,
% 13.32/13.47 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s58)) | (~m_counter_cell_v_value(c_bit1, s58)) | m_counter_cell_v_carry_out(c_bit1, s58))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s58)) | (~m_counter_cell_v_value(c_bit1, s58)) | m_counter_cell_v_carry_out(c_bit1, s58))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3794,plain,
% 13.32/13.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s58)) | (~m_counter_cell_v_value(c_bit1, s58)) | m_counter_cell_v_carry_out(c_bit1, s58))),
% 13.32/13.47 inference(quant_inst,[status(thm)],[])).
% 13.32/13.47 tff(3795,plain,
% 13.32/13.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s58)) | (~m_counter_cell_v_value(c_bit1, s58)) | m_counter_cell_v_carry_out(c_bit1, s58)),
% 13.32/13.47 inference(modus_ponens,[status(thm)],[3794, 3793])).
% 13.32/13.47 tff(3796,plain,
% 13.32/13.47 ($false),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3795, 1390, 3774, 3791, 3792])).
% 13.32/13.47 tff(3797,plain,(m_counter_cell_v_carry_out(c_bit1, s58) | (~m_counter_cell_v_carry_in(c_bit1, s58)) | (~m_counter_cell_v_value(c_bit1, s58))), inference(lemma,lemma(discharge,[]))).
% 13.32/13.47 tff(3798,plain,
% 13.32/13.47 (~m_counter_cell_v_carry_in(c_bit1, s58)),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3797, 3791, 3792])).
% 13.32/13.47 tff(3799,assumption,(node1(c_bit1, s58)), introduced(assumption)).
% 13.32/13.47 tff(3800,plain,
% 13.32/13.47 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s58) | (~m_counter_cell_v_value(c_bit1, s58)) | (~node1(c_bit1, s58)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s58) | (~m_counter_cell_v_value(c_bit1, s58)) | (~node1(c_bit1, s58)))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3801,plain,
% 13.32/13.47 (((~node1(c_bit1, s58)) | m_counter_cell_v_carry_in(c_bit1, s58) | (~m_counter_cell_v_value(c_bit1, s58))) <=> (m_counter_cell_v_carry_in(c_bit1, s58) | (~m_counter_cell_v_value(c_bit1, s58)) | (~node1(c_bit1, s58)))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3802,plain,
% 13.32/13.47 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s58)) | m_counter_cell_v_carry_in(c_bit1, s58) | (~m_counter_cell_v_value(c_bit1, s58)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s58) | (~m_counter_cell_v_value(c_bit1, s58)) | (~node1(c_bit1, s58))))),
% 13.32/13.47 inference(monotonicity,[status(thm)],[3801])).
% 13.32/13.47 tff(3803,plain,
% 13.32/13.47 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s58)) | m_counter_cell_v_carry_in(c_bit1, s58) | (~m_counter_cell_v_value(c_bit1, s58)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s58) | (~m_counter_cell_v_value(c_bit1, s58)) | (~node1(c_bit1, s58)))),
% 13.32/13.47 inference(transitivity,[status(thm)],[3802, 3800])).
% 13.32/13.47 tff(3804,plain,
% 13.32/13.47 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s58)) | m_counter_cell_v_carry_in(c_bit1, s58) | (~m_counter_cell_v_value(c_bit1, s58)))),
% 13.32/13.47 inference(quant_inst,[status(thm)],[])).
% 13.32/13.47 tff(3805,plain,
% 13.32/13.47 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s58) | (~m_counter_cell_v_value(c_bit1, s58)) | (~node1(c_bit1, s58))),
% 13.32/13.47 inference(modus_ponens,[status(thm)],[3804, 3803])).
% 13.32/13.47 tff(3806,plain,
% 13.32/13.47 (m_counter_cell_v_carry_in(c_bit1, s58) | (~m_counter_cell_v_value(c_bit1, s58))),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3805, 1569, 3799])).
% 13.32/13.47 tff(3807,plain,
% 13.32/13.47 ($false),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3806, 3798, 3791])).
% 13.32/13.47 tff(3808,plain,((~m_counter_cell_v_value(c_bit1, s58)) | (~node1(c_bit1, s58)) | m_counter_cell_v_carry_out(c_bit1, s58)), inference(lemma,lemma(discharge,[]))).
% 13.32/13.47 tff(3809,plain,
% 13.32/13.47 ((~m_counter_cell_v_value(c_bit1, s58)) | (~node1(c_bit1, s58))),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3808, 3790])).
% 13.32/13.47 tff(3810,plain,
% 13.32/13.47 (~node1(c_bit1, s58)),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3809, 3745])).
% 13.32/13.47 tff(3811,plain,
% 13.32/13.47 (succ(s58, s59) <=> succ(s58, s59)),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3812,axiom,(succ(s58, s59)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound59')).
% 13.32/13.47 tff(3813,plain,
% 13.32/13.47 (succ(s58, s59)),
% 13.32/13.47 inference(modus_ponens,[status(thm)],[3812, 3811])).
% 13.32/13.47 tff(3814,plain,
% 13.32/13.47 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s58, s59)) | trans(s58, s59))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s58, s59)) | trans(s58, s59))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3815,plain,
% 13.32/13.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s58, s59)) | trans(s58, s59))),
% 13.32/13.47 inference(quant_inst,[status(thm)],[])).
% 13.32/13.47 tff(3816,plain,
% 13.32/13.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s58, s59)) | trans(s58, s59)),
% 13.32/13.47 inference(modus_ponens,[status(thm)],[3815, 3814])).
% 13.32/13.47 tff(3817,plain,
% 13.32/13.47 (trans(s58, s59)),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3816, 3813, 45])).
% 13.32/13.47 tff(3818,plain,
% 13.32/13.47 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s58, s59)) | node3(c_bit1, s58, s59))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s58, s59)) | node3(c_bit1, s58, s59))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3819,plain,
% 13.32/13.47 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s58, s59)) | node3(c_bit1, s58, s59))),
% 13.32/13.47 inference(quant_inst,[status(thm)],[])).
% 13.32/13.47 tff(3820,plain,
% 13.32/13.47 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s58, s59)) | node3(c_bit1, s58, s59)),
% 13.32/13.47 inference(modus_ponens,[status(thm)],[3819, 3818])).
% 13.32/13.47 tff(3821,plain,
% 13.32/13.47 (node3(c_bit1, s58, s59)),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3820, 59, 3817])).
% 13.32/13.47 tff(3822,plain,
% 13.32/13.47 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s59) | node1(c_bit1, s58) | (~node3(c_bit1, s58, s59)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s59) | node1(c_bit1, s58) | (~node3(c_bit1, s58, s59)))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3823,plain,
% 13.32/13.47 ((node1(c_bit1, s58) | (~node3(c_bit1, s58, s59)) | m_counter_cell_v_value(c_bit1, s59)) <=> (m_counter_cell_v_value(c_bit1, s59) | node1(c_bit1, s58) | (~node3(c_bit1, s58, s59)))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3824,plain,
% 13.32/13.47 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s58) | (~node3(c_bit1, s58, s59)) | m_counter_cell_v_value(c_bit1, s59))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s59) | node1(c_bit1, s58) | (~node3(c_bit1, s58, s59))))),
% 13.32/13.47 inference(monotonicity,[status(thm)],[3823])).
% 13.32/13.47 tff(3825,plain,
% 13.32/13.47 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s58) | (~node3(c_bit1, s58, s59)) | m_counter_cell_v_value(c_bit1, s59))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s59) | node1(c_bit1, s58) | (~node3(c_bit1, s58, s59)))),
% 13.32/13.47 inference(transitivity,[status(thm)],[3824, 3822])).
% 13.32/13.47 tff(3826,plain,
% 13.32/13.47 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s58) | (~node3(c_bit1, s58, s59)) | m_counter_cell_v_value(c_bit1, s59))),
% 13.32/13.47 inference(quant_inst,[status(thm)],[])).
% 13.32/13.47 tff(3827,plain,
% 13.32/13.47 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s59) | node1(c_bit1, s58) | (~node3(c_bit1, s58, s59))),
% 13.32/13.47 inference(modus_ponens,[status(thm)],[3826, 3825])).
% 13.32/13.47 tff(3828,plain,
% 13.32/13.47 (m_counter_cell_v_value(c_bit1, s59) | node1(c_bit1, s58)),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3827, 73, 3821])).
% 13.32/13.47 tff(3829,plain,
% 13.32/13.47 (m_counter_cell_v_value(c_bit1, s59)),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3828, 3810])).
% 13.32/13.47 tff(3830,assumption,(~m_counter_cell_v_carry_in(c_bit0, s58)), introduced(assumption)).
% 13.32/13.47 tff(3831,plain,
% 13.32/13.47 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s58)),
% 13.32/13.47 inference(quant_inst,[status(thm)],[])).
% 13.32/13.47 tff(3832,plain,
% 13.32/13.47 ($false),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3831, 18, 3830])).
% 13.32/13.47 tff(3833,plain,(m_counter_cell_v_carry_in(c_bit0, s58)), inference(lemma,lemma(discharge,[]))).
% 13.32/13.47 tff(3834,plain,
% 13.32/13.47 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s58)) | m_counter_cell_v_value(c_bit0, s58) | (~node1(c_bit0, s58)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s58)) | m_counter_cell_v_value(c_bit0, s58) | (~node1(c_bit0, s58)))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3835,plain,
% 13.32/13.47 (((~node1(c_bit0, s58)) | (~m_counter_cell_v_carry_in(c_bit0, s58)) | m_counter_cell_v_value(c_bit0, s58)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s58)) | m_counter_cell_v_value(c_bit0, s58) | (~node1(c_bit0, s58)))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3836,plain,
% 13.32/13.47 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s58)) | (~m_counter_cell_v_carry_in(c_bit0, s58)) | m_counter_cell_v_value(c_bit0, s58))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s58)) | m_counter_cell_v_value(c_bit0, s58) | (~node1(c_bit0, s58))))),
% 13.32/13.47 inference(monotonicity,[status(thm)],[3835])).
% 13.32/13.47 tff(3837,plain,
% 13.32/13.47 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s58)) | (~m_counter_cell_v_carry_in(c_bit0, s58)) | m_counter_cell_v_value(c_bit0, s58))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s58)) | m_counter_cell_v_value(c_bit0, s58) | (~node1(c_bit0, s58)))),
% 13.32/13.47 inference(transitivity,[status(thm)],[3836, 3834])).
% 13.32/13.47 tff(3838,plain,
% 13.32/13.47 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s58)) | (~m_counter_cell_v_carry_in(c_bit0, s58)) | m_counter_cell_v_value(c_bit0, s58))),
% 13.32/13.47 inference(quant_inst,[status(thm)],[])).
% 13.32/13.47 tff(3839,plain,
% 13.32/13.47 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s58)) | m_counter_cell_v_value(c_bit0, s58) | (~node1(c_bit0, s58))),
% 13.32/13.47 inference(modus_ponens,[status(thm)],[3838, 3837])).
% 13.32/13.47 tff(3840,plain,
% 13.32/13.47 (m_counter_cell_v_value(c_bit0, s58) | (~node1(c_bit0, s58))),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3839, 30, 3833])).
% 13.32/13.47 tff(3841,plain,
% 13.32/13.47 (~node1(c_bit0, s58)),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3840, 3763])).
% 13.32/13.47 tff(3842,plain,
% 13.32/13.47 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s58, s59)) | node3(c_bit0, s58, s59))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s58, s59)) | node3(c_bit0, s58, s59))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3843,plain,
% 13.32/13.47 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s58, s59)) | node3(c_bit0, s58, s59))),
% 13.32/13.47 inference(quant_inst,[status(thm)],[])).
% 13.32/13.47 tff(3844,plain,
% 13.32/13.47 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s58, s59)) | node3(c_bit0, s58, s59)),
% 13.32/13.47 inference(modus_ponens,[status(thm)],[3843, 3842])).
% 13.32/13.47 tff(3845,plain,
% 13.32/13.47 (node3(c_bit0, s58, s59)),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3844, 59, 3817])).
% 13.32/13.47 tff(3846,plain,
% 13.32/13.47 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s59) | node1(c_bit0, s58) | (~node3(c_bit0, s58, s59)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s59) | node1(c_bit0, s58) | (~node3(c_bit0, s58, s59)))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3847,plain,
% 13.32/13.47 ((node1(c_bit0, s58) | (~node3(c_bit0, s58, s59)) | m_counter_cell_v_value(c_bit0, s59)) <=> (m_counter_cell_v_value(c_bit0, s59) | node1(c_bit0, s58) | (~node3(c_bit0, s58, s59)))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3848,plain,
% 13.32/13.47 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s58) | (~node3(c_bit0, s58, s59)) | m_counter_cell_v_value(c_bit0, s59))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s59) | node1(c_bit0, s58) | (~node3(c_bit0, s58, s59))))),
% 13.32/13.47 inference(monotonicity,[status(thm)],[3847])).
% 13.32/13.47 tff(3849,plain,
% 13.32/13.47 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s58) | (~node3(c_bit0, s58, s59)) | m_counter_cell_v_value(c_bit0, s59))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s59) | node1(c_bit0, s58) | (~node3(c_bit0, s58, s59)))),
% 13.32/13.47 inference(transitivity,[status(thm)],[3848, 3846])).
% 13.32/13.47 tff(3850,plain,
% 13.32/13.47 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s58) | (~node3(c_bit0, s58, s59)) | m_counter_cell_v_value(c_bit0, s59))),
% 13.32/13.47 inference(quant_inst,[status(thm)],[])).
% 13.32/13.47 tff(3851,plain,
% 13.32/13.47 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s59) | node1(c_bit0, s58) | (~node3(c_bit0, s58, s59))),
% 13.32/13.47 inference(modus_ponens,[status(thm)],[3850, 3849])).
% 13.32/13.47 tff(3852,plain,
% 13.32/13.47 (m_counter_cell_v_value(c_bit0, s59) | node1(c_bit0, s58)),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3851, 73, 3845])).
% 13.32/13.47 tff(3853,plain,
% 13.32/13.47 (m_counter_cell_v_value(c_bit0, s59)),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3852, 3841])).
% 13.32/13.47 tff(3854,assumption,(~m_counter_cell_v_carry_in(c_bit0, s59)), introduced(assumption)).
% 13.32/13.47 tff(3855,plain,
% 13.32/13.47 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s59)),
% 13.32/13.47 inference(quant_inst,[status(thm)],[])).
% 13.32/13.47 tff(3856,plain,
% 13.32/13.47 ($false),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3855, 18, 3854])).
% 13.32/13.47 tff(3857,plain,(m_counter_cell_v_carry_in(c_bit0, s59)), inference(lemma,lemma(discharge,[]))).
% 13.32/13.47 tff(3858,plain,
% 13.32/13.47 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s59)) | (~m_counter_cell_v_value(c_bit0, s59)) | m_counter_cell_v_carry_out(c_bit0, s59))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s59)) | (~m_counter_cell_v_value(c_bit0, s59)) | m_counter_cell_v_carry_out(c_bit0, s59))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3859,plain,
% 13.32/13.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s59)) | (~m_counter_cell_v_value(c_bit0, s59)) | m_counter_cell_v_carry_out(c_bit0, s59))),
% 13.32/13.47 inference(quant_inst,[status(thm)],[])).
% 13.32/13.47 tff(3860,plain,
% 13.32/13.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s59)) | (~m_counter_cell_v_value(c_bit0, s59)) | m_counter_cell_v_carry_out(c_bit0, s59)),
% 13.32/13.47 inference(modus_ponens,[status(thm)],[3859, 3858])).
% 13.32/13.47 tff(3861,plain,
% 13.32/13.47 ((~m_counter_cell_v_value(c_bit0, s59)) | m_counter_cell_v_carry_out(c_bit0, s59)),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3860, 1390, 3857])).
% 13.32/13.47 tff(3862,plain,
% 13.32/13.47 (m_counter_cell_v_carry_out(c_bit0, s59)),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3861, 3853])).
% 13.32/13.47 tff(3863,plain,
% 13.32/13.47 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s59)) | m_counter_cell_v_carry_in(c_bit1, s59))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s59)) | m_counter_cell_v_carry_in(c_bit1, s59))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3864,plain,
% 13.32/13.47 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s59)) | m_counter_cell_v_carry_in(c_bit1, s59))),
% 13.32/13.47 inference(quant_inst,[status(thm)],[])).
% 13.32/13.47 tff(3865,plain,
% 13.32/13.47 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s59)) | m_counter_cell_v_carry_in(c_bit1, s59)),
% 13.32/13.47 inference(modus_ponens,[status(thm)],[3864, 3863])).
% 13.32/13.47 tff(3866,plain,
% 13.32/13.47 (m_counter_cell_v_carry_in(c_bit1, s59)),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3865, 1405, 3862])).
% 13.32/13.47 tff(3867,plain,
% 13.32/13.47 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s59)) | (~m_counter_cell_v_value(c_bit1, s59)) | m_counter_cell_v_carry_out(c_bit1, s59))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s59)) | (~m_counter_cell_v_value(c_bit1, s59)) | m_counter_cell_v_carry_out(c_bit1, s59))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3868,plain,
% 13.32/13.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s59)) | (~m_counter_cell_v_value(c_bit1, s59)) | m_counter_cell_v_carry_out(c_bit1, s59))),
% 13.32/13.47 inference(quant_inst,[status(thm)],[])).
% 13.32/13.47 tff(3869,plain,
% 13.32/13.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s59)) | (~m_counter_cell_v_value(c_bit1, s59)) | m_counter_cell_v_carry_out(c_bit1, s59)),
% 13.32/13.47 inference(modus_ponens,[status(thm)],[3868, 3867])).
% 13.32/13.47 tff(3870,plain,
% 13.32/13.47 ((~m_counter_cell_v_value(c_bit1, s59)) | m_counter_cell_v_carry_out(c_bit1, s59)),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3869, 1390, 3866])).
% 13.32/13.47 tff(3871,plain,
% 13.32/13.47 (m_counter_cell_v_carry_out(c_bit1, s59)),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3870, 3829])).
% 13.32/13.47 tff(3872,assumption,(m_counter_cell_v_carry_out(c_bit1, s59)), introduced(assumption)).
% 13.32/13.47 tff(3873,assumption,(~m_counter_cell_v_carry_in(c_bit2, s59)), introduced(assumption)).
% 13.32/13.47 tff(3874,plain,
% 13.32/13.47 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s59)) | m_counter_cell_v_carry_in(c_bit2, s59))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s59)) | m_counter_cell_v_carry_in(c_bit2, s59))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3875,plain,
% 13.32/13.47 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s59)) | m_counter_cell_v_carry_in(c_bit2, s59))),
% 13.32/13.47 inference(quant_inst,[status(thm)],[])).
% 13.32/13.47 tff(3876,plain,
% 13.32/13.47 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s59)) | m_counter_cell_v_carry_in(c_bit2, s59)),
% 13.32/13.47 inference(modus_ponens,[status(thm)],[3875, 3874])).
% 13.32/13.47 tff(3877,plain,
% 13.32/13.47 ($false),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3876, 3305, 3873, 3872])).
% 13.32/13.47 tff(3878,plain,(m_counter_cell_v_carry_in(c_bit2, s59) | (~m_counter_cell_v_carry_out(c_bit1, s59))), inference(lemma,lemma(discharge,[]))).
% 13.32/13.47 tff(3879,plain,
% 13.32/13.47 (m_counter_cell_v_carry_in(c_bit2, s59)),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3878, 3871])).
% 13.32/13.47 tff(3880,assumption,(~always5(s59)), introduced(assumption)).
% 13.32/13.47 tff(3881,plain,
% 13.32/13.47 (^[Y: $i, X: $i] : refl(((~always5(X)) | (~trans(X, Y)) | always5(Y)) <=> ((~always5(X)) | (~trans(X, Y)) | always5(Y)))),
% 13.32/13.47 inference(bind,[status(th)],[])).
% 13.32/13.47 tff(3882,plain,
% 13.32/13.47 (![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y)) <=> ![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 13.32/13.47 inference(quant_intro,[status(thm)],[3881])).
% 13.32/13.47 tff(3883,plain,
% 13.32/13.47 (![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y)) <=> ![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3884,plain,
% 13.32/13.47 (^[Y: $i, X: $i] : rewrite(((always5(Y) | (~trans(X, Y))) | (~always5(X))) <=> ((~always5(X)) | (~trans(X, Y)) | always5(Y)))),
% 13.32/13.47 inference(bind,[status(th)],[])).
% 13.32/13.47 tff(3885,plain,
% 13.32/13.47 (![Y: $i, X: $i] : ((always5(Y) | (~trans(X, Y))) | (~always5(X))) <=> ![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 13.32/13.47 inference(quant_intro,[status(thm)],[3884])).
% 13.32/13.47 tff(3886,axiom,(![Y: $i, X: $i] : ((always5(Y) | (~trans(X, Y))) | (~always5(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty2')).
% 13.32/13.47 tff(3887,plain,
% 13.32/13.47 (![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 13.32/13.47 inference(modus_ponens,[status(thm)],[3886, 3885])).
% 13.32/13.47 tff(3888,plain,
% 13.32/13.47 (![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 13.32/13.47 inference(modus_ponens,[status(thm)],[3887, 3883])).
% 13.32/13.47 tff(3889,plain,(
% 13.32/13.47 ![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 13.32/13.47 inference(skolemize,[status(sab)],[3888])).
% 13.32/13.47 tff(3890,plain,
% 13.32/13.47 (![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 13.32/13.47 inference(modus_ponens,[status(thm)],[3889, 3882])).
% 13.32/13.47 tff(3891,plain,
% 13.32/13.47 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (always5(s59) | (~trans(s58, s59)) | (~always5(s58)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | always5(s59) | (~trans(s58, s59)) | (~always5(s58)))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3892,plain,
% 13.32/13.47 (((~always5(s58)) | (~trans(s58, s59)) | always5(s59)) <=> (always5(s59) | (~trans(s58, s59)) | (~always5(s58)))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3893,plain,
% 13.32/13.47 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s58)) | (~trans(s58, s59)) | always5(s59))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (always5(s59) | (~trans(s58, s59)) | (~always5(s58))))),
% 13.32/13.47 inference(monotonicity,[status(thm)],[3892])).
% 13.32/13.47 tff(3894,plain,
% 13.32/13.47 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s58)) | (~trans(s58, s59)) | always5(s59))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | always5(s59) | (~trans(s58, s59)) | (~always5(s58)))),
% 13.32/13.47 inference(transitivity,[status(thm)],[3893, 3891])).
% 13.32/13.47 tff(3895,plain,
% 13.32/13.47 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s58)) | (~trans(s58, s59)) | always5(s59))),
% 13.32/13.47 inference(quant_inst,[status(thm)],[])).
% 13.32/13.47 tff(3896,plain,
% 13.32/13.47 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | always5(s59) | (~trans(s58, s59)) | (~always5(s58))),
% 13.32/13.47 inference(modus_ponens,[status(thm)],[3895, 3894])).
% 13.32/13.47 tff(3897,plain,
% 13.32/13.47 (always5(s59) | (~always5(s58))),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3896, 3890, 3817])).
% 13.32/13.47 tff(3898,plain,
% 13.32/13.47 (~always5(s58)),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3897, 3880])).
% 13.32/13.47 tff(3899,plain,
% 13.32/13.47 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s57, s58)) | (~always5(s57)) | always5(s58))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s57, s58)) | (~always5(s57)) | always5(s58))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3900,plain,
% 13.32/13.47 (((~always5(s57)) | (~trans(s57, s58)) | always5(s58)) <=> ((~trans(s57, s58)) | (~always5(s57)) | always5(s58))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3901,plain,
% 13.32/13.47 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s57)) | (~trans(s57, s58)) | always5(s58))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s57, s58)) | (~always5(s57)) | always5(s58)))),
% 13.32/13.47 inference(monotonicity,[status(thm)],[3900])).
% 13.32/13.47 tff(3902,plain,
% 13.32/13.47 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s57)) | (~trans(s57, s58)) | always5(s58))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s57, s58)) | (~always5(s57)) | always5(s58))),
% 13.32/13.47 inference(transitivity,[status(thm)],[3901, 3899])).
% 13.32/13.47 tff(3903,plain,
% 13.32/13.47 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s57)) | (~trans(s57, s58)) | always5(s58))),
% 13.32/13.47 inference(quant_inst,[status(thm)],[])).
% 13.32/13.47 tff(3904,plain,
% 13.32/13.47 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s57, s58)) | (~always5(s57)) | always5(s58)),
% 13.32/13.47 inference(modus_ponens,[status(thm)],[3903, 3902])).
% 13.32/13.47 tff(3905,plain,
% 13.32/13.47 ((~always5(s57)) | always5(s58)),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3904, 3890, 3733])).
% 13.32/13.47 tff(3906,plain,
% 13.32/13.47 (~always5(s57)),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3905, 3898])).
% 13.32/13.47 tff(3907,plain,
% 13.32/13.47 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s56, s57)) | (~always5(s56)) | always5(s57))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s56, s57)) | (~always5(s56)) | always5(s57))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3908,plain,
% 13.32/13.47 (((~always5(s56)) | (~trans(s56, s57)) | always5(s57)) <=> ((~trans(s56, s57)) | (~always5(s56)) | always5(s57))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3909,plain,
% 13.32/13.47 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s56)) | (~trans(s56, s57)) | always5(s57))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s56, s57)) | (~always5(s56)) | always5(s57)))),
% 13.32/13.47 inference(monotonicity,[status(thm)],[3908])).
% 13.32/13.47 tff(3910,plain,
% 13.32/13.47 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s56)) | (~trans(s56, s57)) | always5(s57))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s56, s57)) | (~always5(s56)) | always5(s57))),
% 13.32/13.47 inference(transitivity,[status(thm)],[3909, 3907])).
% 13.32/13.47 tff(3911,plain,
% 13.32/13.47 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s56)) | (~trans(s56, s57)) | always5(s57))),
% 13.32/13.47 inference(quant_inst,[status(thm)],[])).
% 13.32/13.47 tff(3912,plain,
% 13.32/13.47 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s56, s57)) | (~always5(s56)) | always5(s57)),
% 13.32/13.47 inference(modus_ponens,[status(thm)],[3911, 3910])).
% 13.32/13.47 tff(3913,plain,
% 13.32/13.47 ((~always5(s56)) | always5(s57)),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3912, 3890, 3642])).
% 13.32/13.47 tff(3914,plain,
% 13.32/13.47 (~always5(s56)),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3913, 3906])).
% 13.32/13.47 tff(3915,plain,
% 13.32/13.47 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s55, s56)) | (~always5(s55)) | always5(s56))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s55, s56)) | (~always5(s55)) | always5(s56))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3916,plain,
% 13.32/13.47 (((~always5(s55)) | (~trans(s55, s56)) | always5(s56)) <=> ((~trans(s55, s56)) | (~always5(s55)) | always5(s56))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3917,plain,
% 13.32/13.47 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s55)) | (~trans(s55, s56)) | always5(s56))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s55, s56)) | (~always5(s55)) | always5(s56)))),
% 13.32/13.47 inference(monotonicity,[status(thm)],[3916])).
% 13.32/13.47 tff(3918,plain,
% 13.32/13.47 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s55)) | (~trans(s55, s56)) | always5(s56))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s55, s56)) | (~always5(s55)) | always5(s56))),
% 13.32/13.47 inference(transitivity,[status(thm)],[3917, 3915])).
% 13.32/13.47 tff(3919,plain,
% 13.32/13.47 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s55)) | (~trans(s55, s56)) | always5(s56))),
% 13.32/13.47 inference(quant_inst,[status(thm)],[])).
% 13.32/13.47 tff(3920,plain,
% 13.32/13.47 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s55, s56)) | (~always5(s55)) | always5(s56)),
% 13.32/13.47 inference(modus_ponens,[status(thm)],[3919, 3918])).
% 13.32/13.47 tff(3921,plain,
% 13.32/13.47 ((~always5(s55)) | always5(s56)),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3920, 3890, 3576])).
% 13.32/13.47 tff(3922,plain,
% 13.32/13.47 (~always5(s55)),
% 13.32/13.47 inference(unit_resolution,[status(thm)],[3921, 3914])).
% 13.32/13.47 tff(3923,plain,
% 13.32/13.47 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s54, s55)) | (~always5(s54)) | always5(s55))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s54, s55)) | (~always5(s54)) | always5(s55))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3924,plain,
% 13.32/13.47 (((~always5(s54)) | (~trans(s54, s55)) | always5(s55)) <=> ((~trans(s54, s55)) | (~always5(s54)) | always5(s55))),
% 13.32/13.47 inference(rewrite,[status(thm)],[])).
% 13.32/13.47 tff(3925,plain,
% 13.32/13.47 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s54)) | (~trans(s54, s55)) | always5(s55))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s54, s55)) | (~always5(s54)) | always5(s55)))),
% 13.32/13.47 inference(monotonicity,[status(thm)],[3924])).
% 13.32/13.47 tff(3926,plain,
% 13.32/13.47 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s54)) | (~trans(s54, s55)) | always5(s55))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s54, s55)) | (~always5(s54)) | always5(s55))),
% 13.32/13.48 inference(transitivity,[status(thm)],[3925, 3923])).
% 13.32/13.48 tff(3927,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s54)) | (~trans(s54, s55)) | always5(s55))),
% 13.32/13.48 inference(quant_inst,[status(thm)],[])).
% 13.32/13.48 tff(3928,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s54, s55)) | (~always5(s54)) | always5(s55)),
% 13.32/13.48 inference(modus_ponens,[status(thm)],[3927, 3926])).
% 13.32/13.48 tff(3929,plain,
% 13.32/13.48 ((~always5(s54)) | always5(s55)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[3928, 3890, 3512])).
% 13.32/13.48 tff(3930,plain,
% 13.32/13.48 (~always5(s54)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[3929, 3922])).
% 13.32/13.48 tff(3931,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s53, s54)) | (~always5(s53)) | always5(s54))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s53, s54)) | (~always5(s53)) | always5(s54))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(3932,plain,
% 13.32/13.48 (((~always5(s53)) | (~trans(s53, s54)) | always5(s54)) <=> ((~trans(s53, s54)) | (~always5(s53)) | always5(s54))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(3933,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s53)) | (~trans(s53, s54)) | always5(s54))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s53, s54)) | (~always5(s53)) | always5(s54)))),
% 13.32/13.48 inference(monotonicity,[status(thm)],[3932])).
% 13.32/13.48 tff(3934,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s53)) | (~trans(s53, s54)) | always5(s54))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s53, s54)) | (~always5(s53)) | always5(s54))),
% 13.32/13.48 inference(transitivity,[status(thm)],[3933, 3931])).
% 13.32/13.48 tff(3935,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s53)) | (~trans(s53, s54)) | always5(s54))),
% 13.32/13.48 inference(quant_inst,[status(thm)],[])).
% 13.32/13.48 tff(3936,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s53, s54)) | (~always5(s53)) | always5(s54)),
% 13.32/13.48 inference(modus_ponens,[status(thm)],[3935, 3934])).
% 13.32/13.48 tff(3937,plain,
% 13.32/13.48 ((~always5(s53)) | always5(s54)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[3936, 3890, 3450])).
% 13.32/13.48 tff(3938,plain,
% 13.32/13.48 (~always5(s53)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[3937, 3930])).
% 13.32/13.48 tff(3939,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s52, s53)) | (~always5(s52)) | always5(s53))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s52, s53)) | (~always5(s52)) | always5(s53))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(3940,plain,
% 13.32/13.48 (((~always5(s52)) | (~trans(s52, s53)) | always5(s53)) <=> ((~trans(s52, s53)) | (~always5(s52)) | always5(s53))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(3941,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s52)) | (~trans(s52, s53)) | always5(s53))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s52, s53)) | (~always5(s52)) | always5(s53)))),
% 13.32/13.48 inference(monotonicity,[status(thm)],[3940])).
% 13.32/13.48 tff(3942,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s52)) | (~trans(s52, s53)) | always5(s53))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s52, s53)) | (~always5(s52)) | always5(s53))),
% 13.32/13.48 inference(transitivity,[status(thm)],[3941, 3939])).
% 13.32/13.48 tff(3943,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s52)) | (~trans(s52, s53)) | always5(s53))),
% 13.32/13.48 inference(quant_inst,[status(thm)],[])).
% 13.32/13.48 tff(3944,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s52, s53)) | (~always5(s52)) | always5(s53)),
% 13.32/13.48 inference(modus_ponens,[status(thm)],[3943, 3942])).
% 13.32/13.48 tff(3945,plain,
% 13.32/13.48 ((~always5(s52)) | always5(s53)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[3944, 3890, 3383])).
% 13.32/13.48 tff(3946,plain,
% 13.32/13.48 (~always5(s52)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[3945, 3938])).
% 13.32/13.48 tff(3947,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s51, s52)) | (~always5(s51)) | always5(s52))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s51, s52)) | (~always5(s51)) | always5(s52))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(3948,plain,
% 13.32/13.48 (((~always5(s51)) | (~trans(s51, s52)) | always5(s52)) <=> ((~trans(s51, s52)) | (~always5(s51)) | always5(s52))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(3949,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s51)) | (~trans(s51, s52)) | always5(s52))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s51, s52)) | (~always5(s51)) | always5(s52)))),
% 13.32/13.48 inference(monotonicity,[status(thm)],[3948])).
% 13.32/13.48 tff(3950,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s51)) | (~trans(s51, s52)) | always5(s52))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s51, s52)) | (~always5(s51)) | always5(s52))),
% 13.32/13.48 inference(transitivity,[status(thm)],[3949, 3947])).
% 13.32/13.48 tff(3951,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s51)) | (~trans(s51, s52)) | always5(s52))),
% 13.32/13.48 inference(quant_inst,[status(thm)],[])).
% 13.32/13.48 tff(3952,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s51, s52)) | (~always5(s51)) | always5(s52)),
% 13.32/13.48 inference(modus_ponens,[status(thm)],[3951, 3950])).
% 13.32/13.48 tff(3953,plain,
% 13.32/13.48 ((~always5(s51)) | always5(s52)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[3952, 3890, 3325])).
% 13.32/13.48 tff(3954,plain,
% 13.32/13.48 (~always5(s51)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[3953, 3946])).
% 13.32/13.48 tff(3955,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s50, s51)) | (~always5(s50)) | always5(s51))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s50, s51)) | (~always5(s50)) | always5(s51))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(3956,plain,
% 13.32/13.48 (((~always5(s50)) | (~trans(s50, s51)) | always5(s51)) <=> ((~trans(s50, s51)) | (~always5(s50)) | always5(s51))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(3957,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s50)) | (~trans(s50, s51)) | always5(s51))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s50, s51)) | (~always5(s50)) | always5(s51)))),
% 13.32/13.48 inference(monotonicity,[status(thm)],[3956])).
% 13.32/13.48 tff(3958,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s50)) | (~trans(s50, s51)) | always5(s51))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s50, s51)) | (~always5(s50)) | always5(s51))),
% 13.32/13.48 inference(transitivity,[status(thm)],[3957, 3955])).
% 13.32/13.48 tff(3959,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s50)) | (~trans(s50, s51)) | always5(s51))),
% 13.32/13.48 inference(quant_inst,[status(thm)],[])).
% 13.32/13.48 tff(3960,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s50, s51)) | (~always5(s50)) | always5(s51)),
% 13.32/13.48 inference(modus_ponens,[status(thm)],[3959, 3958])).
% 13.32/13.48 tff(3961,plain,
% 13.32/13.48 ((~always5(s50)) | always5(s51)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[3960, 3890, 3232])).
% 13.32/13.48 tff(3962,plain,
% 13.32/13.48 (~always5(s50)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[3961, 3954])).
% 13.32/13.48 tff(3963,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s49, s50)) | (~always5(s49)) | always5(s50))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s49, s50)) | (~always5(s49)) | always5(s50))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(3964,plain,
% 13.32/13.48 (((~always5(s49)) | (~trans(s49, s50)) | always5(s50)) <=> ((~trans(s49, s50)) | (~always5(s49)) | always5(s50))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(3965,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s49)) | (~trans(s49, s50)) | always5(s50))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s49, s50)) | (~always5(s49)) | always5(s50)))),
% 13.32/13.48 inference(monotonicity,[status(thm)],[3964])).
% 13.32/13.48 tff(3966,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s49)) | (~trans(s49, s50)) | always5(s50))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s49, s50)) | (~always5(s49)) | always5(s50))),
% 13.32/13.48 inference(transitivity,[status(thm)],[3965, 3963])).
% 13.32/13.48 tff(3967,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s49)) | (~trans(s49, s50)) | always5(s50))),
% 13.32/13.48 inference(quant_inst,[status(thm)],[])).
% 13.32/13.48 tff(3968,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s49, s50)) | (~always5(s49)) | always5(s50)),
% 13.32/13.48 inference(modus_ponens,[status(thm)],[3967, 3966])).
% 13.32/13.48 tff(3969,plain,
% 13.32/13.48 ((~always5(s49)) | always5(s50)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[3968, 3890, 3151])).
% 13.32/13.48 tff(3970,plain,
% 13.32/13.48 (~always5(s49)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[3969, 3962])).
% 13.32/13.48 tff(3971,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s48, s49)) | (~always5(s48)) | always5(s49))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s48, s49)) | (~always5(s48)) | always5(s49))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(3972,plain,
% 13.32/13.48 (((~always5(s48)) | (~trans(s48, s49)) | always5(s49)) <=> ((~trans(s48, s49)) | (~always5(s48)) | always5(s49))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(3973,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s48)) | (~trans(s48, s49)) | always5(s49))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s48, s49)) | (~always5(s48)) | always5(s49)))),
% 13.32/13.48 inference(monotonicity,[status(thm)],[3972])).
% 13.32/13.48 tff(3974,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s48)) | (~trans(s48, s49)) | always5(s49))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s48, s49)) | (~always5(s48)) | always5(s49))),
% 13.32/13.48 inference(transitivity,[status(thm)],[3973, 3971])).
% 13.32/13.48 tff(3975,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s48)) | (~trans(s48, s49)) | always5(s49))),
% 13.32/13.48 inference(quant_inst,[status(thm)],[])).
% 13.32/13.48 tff(3976,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s48, s49)) | (~always5(s48)) | always5(s49)),
% 13.32/13.48 inference(modus_ponens,[status(thm)],[3975, 3974])).
% 13.32/13.48 tff(3977,plain,
% 13.32/13.48 ((~always5(s48)) | always5(s49)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[3976, 3890, 3097])).
% 13.32/13.48 tff(3978,plain,
% 13.32/13.48 (~always5(s48)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[3977, 3970])).
% 13.32/13.48 tff(3979,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s47, s48)) | (~always5(s47)) | always5(s48))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s47, s48)) | (~always5(s47)) | always5(s48))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(3980,plain,
% 13.32/13.48 (((~always5(s47)) | (~trans(s47, s48)) | always5(s48)) <=> ((~trans(s47, s48)) | (~always5(s47)) | always5(s48))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(3981,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s47)) | (~trans(s47, s48)) | always5(s48))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s47, s48)) | (~always5(s47)) | always5(s48)))),
% 13.32/13.48 inference(monotonicity,[status(thm)],[3980])).
% 13.32/13.48 tff(3982,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s47)) | (~trans(s47, s48)) | always5(s48))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s47, s48)) | (~always5(s47)) | always5(s48))),
% 13.32/13.48 inference(transitivity,[status(thm)],[3981, 3979])).
% 13.32/13.48 tff(3983,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s47)) | (~trans(s47, s48)) | always5(s48))),
% 13.32/13.48 inference(quant_inst,[status(thm)],[])).
% 13.32/13.48 tff(3984,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s47, s48)) | (~always5(s47)) | always5(s48)),
% 13.32/13.48 inference(modus_ponens,[status(thm)],[3983, 3982])).
% 13.32/13.48 tff(3985,plain,
% 13.32/13.48 ((~always5(s47)) | always5(s48)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[3984, 3890, 3039])).
% 13.32/13.48 tff(3986,plain,
% 13.32/13.48 (~always5(s47)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[3985, 3978])).
% 13.32/13.48 tff(3987,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s46, s47)) | (~always5(s46)) | always5(s47))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s46, s47)) | (~always5(s46)) | always5(s47))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(3988,plain,
% 13.32/13.48 (((~always5(s46)) | (~trans(s46, s47)) | always5(s47)) <=> ((~trans(s46, s47)) | (~always5(s46)) | always5(s47))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(3989,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s46)) | (~trans(s46, s47)) | always5(s47))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s46, s47)) | (~always5(s46)) | always5(s47)))),
% 13.32/13.48 inference(monotonicity,[status(thm)],[3988])).
% 13.32/13.48 tff(3990,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s46)) | (~trans(s46, s47)) | always5(s47))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s46, s47)) | (~always5(s46)) | always5(s47))),
% 13.32/13.48 inference(transitivity,[status(thm)],[3989, 3987])).
% 13.32/13.48 tff(3991,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s46)) | (~trans(s46, s47)) | always5(s47))),
% 13.32/13.48 inference(quant_inst,[status(thm)],[])).
% 13.32/13.48 tff(3992,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s46, s47)) | (~always5(s46)) | always5(s47)),
% 13.32/13.48 inference(modus_ponens,[status(thm)],[3991, 3990])).
% 13.32/13.48 tff(3993,plain,
% 13.32/13.48 ((~always5(s46)) | always5(s47)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[3992, 3890, 2975])).
% 13.32/13.48 tff(3994,plain,
% 13.32/13.48 (~always5(s46)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[3993, 3986])).
% 13.32/13.48 tff(3995,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s45, s46)) | (~always5(s45)) | always5(s46))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s45, s46)) | (~always5(s45)) | always5(s46))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(3996,plain,
% 13.32/13.48 (((~always5(s45)) | (~trans(s45, s46)) | always5(s46)) <=> ((~trans(s45, s46)) | (~always5(s45)) | always5(s46))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(3997,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s45)) | (~trans(s45, s46)) | always5(s46))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s45, s46)) | (~always5(s45)) | always5(s46)))),
% 13.32/13.48 inference(monotonicity,[status(thm)],[3996])).
% 13.32/13.48 tff(3998,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s45)) | (~trans(s45, s46)) | always5(s46))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s45, s46)) | (~always5(s45)) | always5(s46))),
% 13.32/13.48 inference(transitivity,[status(thm)],[3997, 3995])).
% 13.32/13.48 tff(3999,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s45)) | (~trans(s45, s46)) | always5(s46))),
% 13.32/13.48 inference(quant_inst,[status(thm)],[])).
% 13.32/13.48 tff(4000,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s45, s46)) | (~always5(s45)) | always5(s46)),
% 13.32/13.48 inference(modus_ponens,[status(thm)],[3999, 3998])).
% 13.32/13.48 tff(4001,plain,
% 13.32/13.48 ((~always5(s45)) | always5(s46)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[4000, 3890, 2887])).
% 13.32/13.48 tff(4002,plain,
% 13.32/13.48 (~always5(s45)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[4001, 3994])).
% 13.32/13.48 tff(4003,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s44, s45)) | (~always5(s44)) | always5(s45))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s44, s45)) | (~always5(s44)) | always5(s45))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(4004,plain,
% 13.32/13.48 (((~always5(s44)) | (~trans(s44, s45)) | always5(s45)) <=> ((~trans(s44, s45)) | (~always5(s44)) | always5(s45))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(4005,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s44)) | (~trans(s44, s45)) | always5(s45))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s44, s45)) | (~always5(s44)) | always5(s45)))),
% 13.32/13.48 inference(monotonicity,[status(thm)],[4004])).
% 13.32/13.48 tff(4006,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s44)) | (~trans(s44, s45)) | always5(s45))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s44, s45)) | (~always5(s44)) | always5(s45))),
% 13.32/13.48 inference(transitivity,[status(thm)],[4005, 4003])).
% 13.32/13.48 tff(4007,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s44)) | (~trans(s44, s45)) | always5(s45))),
% 13.32/13.48 inference(quant_inst,[status(thm)],[])).
% 13.32/13.48 tff(4008,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s44, s45)) | (~always5(s44)) | always5(s45)),
% 13.32/13.48 inference(modus_ponens,[status(thm)],[4007, 4006])).
% 13.32/13.48 tff(4009,plain,
% 13.32/13.48 ((~always5(s44)) | always5(s45)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[4008, 3890, 2820])).
% 13.32/13.48 tff(4010,plain,
% 13.32/13.48 (~always5(s44)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[4009, 4002])).
% 13.32/13.48 tff(4011,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s43, s44)) | (~always5(s43)) | always5(s44))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s43, s44)) | (~always5(s43)) | always5(s44))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(4012,plain,
% 13.32/13.48 (((~always5(s43)) | (~trans(s43, s44)) | always5(s44)) <=> ((~trans(s43, s44)) | (~always5(s43)) | always5(s44))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(4013,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s43)) | (~trans(s43, s44)) | always5(s44))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s43, s44)) | (~always5(s43)) | always5(s44)))),
% 13.32/13.48 inference(monotonicity,[status(thm)],[4012])).
% 13.32/13.48 tff(4014,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s43)) | (~trans(s43, s44)) | always5(s44))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s43, s44)) | (~always5(s43)) | always5(s44))),
% 13.32/13.48 inference(transitivity,[status(thm)],[4013, 4011])).
% 13.32/13.48 tff(4015,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s43)) | (~trans(s43, s44)) | always5(s44))),
% 13.32/13.48 inference(quant_inst,[status(thm)],[])).
% 13.32/13.48 tff(4016,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s43, s44)) | (~always5(s43)) | always5(s44)),
% 13.32/13.48 inference(modus_ponens,[status(thm)],[4015, 4014])).
% 13.32/13.48 tff(4017,plain,
% 13.32/13.48 ((~always5(s43)) | always5(s44)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[4016, 3890, 1323])).
% 13.32/13.48 tff(4018,plain,
% 13.32/13.48 (~always5(s43)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[4017, 4010])).
% 13.32/13.48 tff(4019,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s42, s43)) | (~always5(s42)) | always5(s43))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s42, s43)) | (~always5(s42)) | always5(s43))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(4020,plain,
% 13.32/13.48 (((~always5(s42)) | (~trans(s42, s43)) | always5(s43)) <=> ((~trans(s42, s43)) | (~always5(s42)) | always5(s43))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(4021,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s42)) | (~trans(s42, s43)) | always5(s43))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s42, s43)) | (~always5(s42)) | always5(s43)))),
% 13.32/13.48 inference(monotonicity,[status(thm)],[4020])).
% 13.32/13.48 tff(4022,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s42)) | (~trans(s42, s43)) | always5(s43))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s42, s43)) | (~always5(s42)) | always5(s43))),
% 13.32/13.48 inference(transitivity,[status(thm)],[4021, 4019])).
% 13.32/13.48 tff(4023,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s42)) | (~trans(s42, s43)) | always5(s43))),
% 13.32/13.48 inference(quant_inst,[status(thm)],[])).
% 13.32/13.48 tff(4024,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s42, s43)) | (~always5(s42)) | always5(s43)),
% 13.32/13.48 inference(modus_ponens,[status(thm)],[4023, 4022])).
% 13.32/13.48 tff(4025,plain,
% 13.32/13.48 ((~always5(s42)) | always5(s43)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[4024, 3890, 1295])).
% 13.32/13.48 tff(4026,plain,
% 13.32/13.48 (~always5(s42)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[4025, 4018])).
% 13.32/13.48 tff(4027,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s41, s42)) | (~always5(s41)) | always5(s42))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s41, s42)) | (~always5(s41)) | always5(s42))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(4028,plain,
% 13.32/13.48 (((~always5(s41)) | (~trans(s41, s42)) | always5(s42)) <=> ((~trans(s41, s42)) | (~always5(s41)) | always5(s42))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(4029,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s41)) | (~trans(s41, s42)) | always5(s42))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s41, s42)) | (~always5(s41)) | always5(s42)))),
% 13.32/13.48 inference(monotonicity,[status(thm)],[4028])).
% 13.32/13.48 tff(4030,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s41)) | (~trans(s41, s42)) | always5(s42))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s41, s42)) | (~always5(s41)) | always5(s42))),
% 13.32/13.48 inference(transitivity,[status(thm)],[4029, 4027])).
% 13.32/13.48 tff(4031,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s41)) | (~trans(s41, s42)) | always5(s42))),
% 13.32/13.48 inference(quant_inst,[status(thm)],[])).
% 13.32/13.48 tff(4032,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s41, s42)) | (~always5(s41)) | always5(s42)),
% 13.32/13.48 inference(modus_ponens,[status(thm)],[4031, 4030])).
% 13.32/13.48 tff(4033,plain,
% 13.32/13.48 ((~always5(s41)) | always5(s42)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[4032, 3890, 1264])).
% 13.32/13.48 tff(4034,plain,
% 13.32/13.48 (~always5(s41)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[4033, 4026])).
% 13.32/13.48 tff(4035,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s40, s41)) | (~always5(s40)) | always5(s41))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s40, s41)) | (~always5(s40)) | always5(s41))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(4036,plain,
% 13.32/13.48 (((~always5(s40)) | (~trans(s40, s41)) | always5(s41)) <=> ((~trans(s40, s41)) | (~always5(s40)) | always5(s41))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(4037,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s40)) | (~trans(s40, s41)) | always5(s41))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s40, s41)) | (~always5(s40)) | always5(s41)))),
% 13.32/13.48 inference(monotonicity,[status(thm)],[4036])).
% 13.32/13.48 tff(4038,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s40)) | (~trans(s40, s41)) | always5(s41))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s40, s41)) | (~always5(s40)) | always5(s41))),
% 13.32/13.48 inference(transitivity,[status(thm)],[4037, 4035])).
% 13.32/13.48 tff(4039,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s40)) | (~trans(s40, s41)) | always5(s41))),
% 13.32/13.48 inference(quant_inst,[status(thm)],[])).
% 13.32/13.48 tff(4040,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s40, s41)) | (~always5(s40)) | always5(s41)),
% 13.32/13.48 inference(modus_ponens,[status(thm)],[4039, 4038])).
% 13.32/13.48 tff(4041,plain,
% 13.32/13.48 ((~always5(s40)) | always5(s41)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[4040, 3890, 1236])).
% 13.32/13.48 tff(4042,plain,
% 13.32/13.48 (~always5(s40)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[4041, 4034])).
% 13.32/13.48 tff(4043,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s39, s40)) | (~always5(s39)) | always5(s40))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s39, s40)) | (~always5(s39)) | always5(s40))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(4044,plain,
% 13.32/13.48 (((~always5(s39)) | (~trans(s39, s40)) | always5(s40)) <=> ((~trans(s39, s40)) | (~always5(s39)) | always5(s40))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(4045,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s39)) | (~trans(s39, s40)) | always5(s40))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s39, s40)) | (~always5(s39)) | always5(s40)))),
% 13.32/13.48 inference(monotonicity,[status(thm)],[4044])).
% 13.32/13.48 tff(4046,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s39)) | (~trans(s39, s40)) | always5(s40))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s39, s40)) | (~always5(s39)) | always5(s40))),
% 13.32/13.48 inference(transitivity,[status(thm)],[4045, 4043])).
% 13.32/13.48 tff(4047,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s39)) | (~trans(s39, s40)) | always5(s40))),
% 13.32/13.48 inference(quant_inst,[status(thm)],[])).
% 13.32/13.48 tff(4048,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s39, s40)) | (~always5(s39)) | always5(s40)),
% 13.32/13.48 inference(modus_ponens,[status(thm)],[4047, 4046])).
% 13.32/13.48 tff(4049,plain,
% 13.32/13.48 ((~always5(s39)) | always5(s40)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[4048, 3890, 1205])).
% 13.32/13.48 tff(4050,plain,
% 13.32/13.48 (~always5(s39)),
% 13.32/13.48 inference(unit_resolution,[status(thm)],[4049, 4042])).
% 13.32/13.48 tff(4051,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s38, s39)) | (~always5(s38)) | always5(s39))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s38, s39)) | (~always5(s38)) | always5(s39))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(4052,plain,
% 13.32/13.48 (((~always5(s38)) | (~trans(s38, s39)) | always5(s39)) <=> ((~trans(s38, s39)) | (~always5(s38)) | always5(s39))),
% 13.32/13.48 inference(rewrite,[status(thm)],[])).
% 13.32/13.48 tff(4053,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s38)) | (~trans(s38, s39)) | always5(s39))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s38, s39)) | (~always5(s38)) | always5(s39)))),
% 13.32/13.48 inference(monotonicity,[status(thm)],[4052])).
% 13.32/13.48 tff(4054,plain,
% 13.32/13.48 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s38)) | (~trans(s38, s39)) | always5(s39))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s38, s39)) | (~always5(s38)) | always5(s39))),
% 13.32/13.48 inference(transitivity,[status(thm)],[4053, 4051])).
% 13.32/13.48 tff(4055,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s38)) | (~trans(s38, s39)) | always5(s39))),
% 13.32/13.48 inference(quant_inst,[status(thm)],[])).
% 13.32/13.48 tff(4056,plain,
% 13.32/13.48 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s38, s39)) | (~always5(s38)) | always5(s39)),
% 13.32/13.48 inference(modus_ponens,[status(thm)],[4055, 4054])).
% 13.32/13.49 tff(4057,plain,
% 13.32/13.49 ((~always5(s38)) | always5(s39)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4056, 3890, 1177])).
% 13.32/13.49 tff(4058,plain,
% 13.32/13.49 (~always5(s38)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4057, 4050])).
% 13.32/13.49 tff(4059,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s37, s38)) | (~always5(s37)) | always5(s38))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s37, s38)) | (~always5(s37)) | always5(s38))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4060,plain,
% 13.32/13.49 (((~always5(s37)) | (~trans(s37, s38)) | always5(s38)) <=> ((~trans(s37, s38)) | (~always5(s37)) | always5(s38))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4061,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s37)) | (~trans(s37, s38)) | always5(s38))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s37, s38)) | (~always5(s37)) | always5(s38)))),
% 13.32/13.49 inference(monotonicity,[status(thm)],[4060])).
% 13.32/13.49 tff(4062,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s37)) | (~trans(s37, s38)) | always5(s38))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s37, s38)) | (~always5(s37)) | always5(s38))),
% 13.32/13.49 inference(transitivity,[status(thm)],[4061, 4059])).
% 13.32/13.49 tff(4063,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s37)) | (~trans(s37, s38)) | always5(s38))),
% 13.32/13.49 inference(quant_inst,[status(thm)],[])).
% 13.32/13.49 tff(4064,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s37, s38)) | (~always5(s37)) | always5(s38)),
% 13.32/13.49 inference(modus_ponens,[status(thm)],[4063, 4062])).
% 13.32/13.49 tff(4065,plain,
% 13.32/13.49 ((~always5(s37)) | always5(s38)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4064, 3890, 1146])).
% 13.32/13.49 tff(4066,plain,
% 13.32/13.49 (~always5(s37)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4065, 4058])).
% 13.32/13.49 tff(4067,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s36, s37)) | (~always5(s36)) | always5(s37))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s36, s37)) | (~always5(s36)) | always5(s37))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4068,plain,
% 13.32/13.49 (((~always5(s36)) | (~trans(s36, s37)) | always5(s37)) <=> ((~trans(s36, s37)) | (~always5(s36)) | always5(s37))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4069,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s36)) | (~trans(s36, s37)) | always5(s37))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s36, s37)) | (~always5(s36)) | always5(s37)))),
% 13.32/13.49 inference(monotonicity,[status(thm)],[4068])).
% 13.32/13.49 tff(4070,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s36)) | (~trans(s36, s37)) | always5(s37))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s36, s37)) | (~always5(s36)) | always5(s37))),
% 13.32/13.49 inference(transitivity,[status(thm)],[4069, 4067])).
% 13.32/13.49 tff(4071,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s36)) | (~trans(s36, s37)) | always5(s37))),
% 13.32/13.49 inference(quant_inst,[status(thm)],[])).
% 13.32/13.49 tff(4072,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s36, s37)) | (~always5(s36)) | always5(s37)),
% 13.32/13.49 inference(modus_ponens,[status(thm)],[4071, 4070])).
% 13.32/13.49 tff(4073,plain,
% 13.32/13.49 ((~always5(s36)) | always5(s37)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4072, 3890, 1118])).
% 13.32/13.49 tff(4074,plain,
% 13.32/13.49 (~always5(s36)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4073, 4066])).
% 13.32/13.49 tff(4075,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s35, s36)) | (~always5(s35)) | always5(s36))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s35, s36)) | (~always5(s35)) | always5(s36))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4076,plain,
% 13.32/13.49 (((~always5(s35)) | (~trans(s35, s36)) | always5(s36)) <=> ((~trans(s35, s36)) | (~always5(s35)) | always5(s36))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4077,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s35)) | (~trans(s35, s36)) | always5(s36))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s35, s36)) | (~always5(s35)) | always5(s36)))),
% 13.32/13.49 inference(monotonicity,[status(thm)],[4076])).
% 13.32/13.49 tff(4078,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s35)) | (~trans(s35, s36)) | always5(s36))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s35, s36)) | (~always5(s35)) | always5(s36))),
% 13.32/13.49 inference(transitivity,[status(thm)],[4077, 4075])).
% 13.32/13.49 tff(4079,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s35)) | (~trans(s35, s36)) | always5(s36))),
% 13.32/13.49 inference(quant_inst,[status(thm)],[])).
% 13.32/13.49 tff(4080,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s35, s36)) | (~always5(s35)) | always5(s36)),
% 13.32/13.49 inference(modus_ponens,[status(thm)],[4079, 4078])).
% 13.32/13.49 tff(4081,plain,
% 13.32/13.49 ((~always5(s35)) | always5(s36)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4080, 3890, 1087])).
% 13.32/13.49 tff(4082,plain,
% 13.32/13.49 (~always5(s35)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4081, 4074])).
% 13.32/13.49 tff(4083,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s34, s35)) | (~always5(s34)) | always5(s35))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s34, s35)) | (~always5(s34)) | always5(s35))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4084,plain,
% 13.32/13.49 (((~always5(s34)) | (~trans(s34, s35)) | always5(s35)) <=> ((~trans(s34, s35)) | (~always5(s34)) | always5(s35))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4085,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s34)) | (~trans(s34, s35)) | always5(s35))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s34, s35)) | (~always5(s34)) | always5(s35)))),
% 13.32/13.49 inference(monotonicity,[status(thm)],[4084])).
% 13.32/13.49 tff(4086,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s34)) | (~trans(s34, s35)) | always5(s35))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s34, s35)) | (~always5(s34)) | always5(s35))),
% 13.32/13.49 inference(transitivity,[status(thm)],[4085, 4083])).
% 13.32/13.49 tff(4087,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s34)) | (~trans(s34, s35)) | always5(s35))),
% 13.32/13.49 inference(quant_inst,[status(thm)],[])).
% 13.32/13.49 tff(4088,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s34, s35)) | (~always5(s34)) | always5(s35)),
% 13.32/13.49 inference(modus_ponens,[status(thm)],[4087, 4086])).
% 13.32/13.49 tff(4089,plain,
% 13.32/13.49 ((~always5(s34)) | always5(s35)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4088, 3890, 1059])).
% 13.32/13.49 tff(4090,plain,
% 13.32/13.49 (~always5(s34)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4089, 4082])).
% 13.32/13.49 tff(4091,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s33, s34)) | (~always5(s33)) | always5(s34))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s33, s34)) | (~always5(s33)) | always5(s34))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4092,plain,
% 13.32/13.49 (((~always5(s33)) | (~trans(s33, s34)) | always5(s34)) <=> ((~trans(s33, s34)) | (~always5(s33)) | always5(s34))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4093,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s33)) | (~trans(s33, s34)) | always5(s34))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s33, s34)) | (~always5(s33)) | always5(s34)))),
% 13.32/13.49 inference(monotonicity,[status(thm)],[4092])).
% 13.32/13.49 tff(4094,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s33)) | (~trans(s33, s34)) | always5(s34))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s33, s34)) | (~always5(s33)) | always5(s34))),
% 13.32/13.49 inference(transitivity,[status(thm)],[4093, 4091])).
% 13.32/13.49 tff(4095,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s33)) | (~trans(s33, s34)) | always5(s34))),
% 13.32/13.49 inference(quant_inst,[status(thm)],[])).
% 13.32/13.49 tff(4096,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s33, s34)) | (~always5(s33)) | always5(s34)),
% 13.32/13.49 inference(modus_ponens,[status(thm)],[4095, 4094])).
% 13.32/13.49 tff(4097,plain,
% 13.32/13.49 ((~always5(s33)) | always5(s34)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4096, 3890, 1028])).
% 13.32/13.49 tff(4098,plain,
% 13.32/13.49 (~always5(s33)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4097, 4090])).
% 13.32/13.49 tff(4099,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s32, s33)) | (~always5(s32)) | always5(s33))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s32, s33)) | (~always5(s32)) | always5(s33))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4100,plain,
% 13.32/13.49 (((~always5(s32)) | (~trans(s32, s33)) | always5(s33)) <=> ((~trans(s32, s33)) | (~always5(s32)) | always5(s33))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4101,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s32)) | (~trans(s32, s33)) | always5(s33))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s32, s33)) | (~always5(s32)) | always5(s33)))),
% 13.32/13.49 inference(monotonicity,[status(thm)],[4100])).
% 13.32/13.49 tff(4102,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s32)) | (~trans(s32, s33)) | always5(s33))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s32, s33)) | (~always5(s32)) | always5(s33))),
% 13.32/13.49 inference(transitivity,[status(thm)],[4101, 4099])).
% 13.32/13.49 tff(4103,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s32)) | (~trans(s32, s33)) | always5(s33))),
% 13.32/13.49 inference(quant_inst,[status(thm)],[])).
% 13.32/13.49 tff(4104,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s32, s33)) | (~always5(s32)) | always5(s33)),
% 13.32/13.49 inference(modus_ponens,[status(thm)],[4103, 4102])).
% 13.32/13.49 tff(4105,plain,
% 13.32/13.49 ((~always5(s32)) | always5(s33)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4104, 3890, 1000])).
% 13.32/13.49 tff(4106,plain,
% 13.32/13.49 (~always5(s32)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4105, 4098])).
% 13.32/13.49 tff(4107,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s31, s32)) | (~always5(s31)) | always5(s32))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s31, s32)) | (~always5(s31)) | always5(s32))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4108,plain,
% 13.32/13.49 (((~always5(s31)) | (~trans(s31, s32)) | always5(s32)) <=> ((~trans(s31, s32)) | (~always5(s31)) | always5(s32))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4109,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s31)) | (~trans(s31, s32)) | always5(s32))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s31, s32)) | (~always5(s31)) | always5(s32)))),
% 13.32/13.49 inference(monotonicity,[status(thm)],[4108])).
% 13.32/13.49 tff(4110,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s31)) | (~trans(s31, s32)) | always5(s32))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s31, s32)) | (~always5(s31)) | always5(s32))),
% 13.32/13.49 inference(transitivity,[status(thm)],[4109, 4107])).
% 13.32/13.49 tff(4111,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s31)) | (~trans(s31, s32)) | always5(s32))),
% 13.32/13.49 inference(quant_inst,[status(thm)],[])).
% 13.32/13.49 tff(4112,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s31, s32)) | (~always5(s31)) | always5(s32)),
% 13.32/13.49 inference(modus_ponens,[status(thm)],[4111, 4110])).
% 13.32/13.49 tff(4113,plain,
% 13.32/13.49 ((~always5(s31)) | always5(s32)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4112, 3890, 969])).
% 13.32/13.49 tff(4114,plain,
% 13.32/13.49 (~always5(s31)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4113, 4106])).
% 13.32/13.49 tff(4115,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s30, s31)) | (~always5(s30)) | always5(s31))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s30, s31)) | (~always5(s30)) | always5(s31))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4116,plain,
% 13.32/13.49 (((~always5(s30)) | (~trans(s30, s31)) | always5(s31)) <=> ((~trans(s30, s31)) | (~always5(s30)) | always5(s31))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4117,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s30)) | (~trans(s30, s31)) | always5(s31))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s30, s31)) | (~always5(s30)) | always5(s31)))),
% 13.32/13.49 inference(monotonicity,[status(thm)],[4116])).
% 13.32/13.49 tff(4118,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s30)) | (~trans(s30, s31)) | always5(s31))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s30, s31)) | (~always5(s30)) | always5(s31))),
% 13.32/13.49 inference(transitivity,[status(thm)],[4117, 4115])).
% 13.32/13.49 tff(4119,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s30)) | (~trans(s30, s31)) | always5(s31))),
% 13.32/13.49 inference(quant_inst,[status(thm)],[])).
% 13.32/13.49 tff(4120,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s30, s31)) | (~always5(s30)) | always5(s31)),
% 13.32/13.49 inference(modus_ponens,[status(thm)],[4119, 4118])).
% 13.32/13.49 tff(4121,plain,
% 13.32/13.49 ((~always5(s30)) | always5(s31)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4120, 3890, 941])).
% 13.32/13.49 tff(4122,plain,
% 13.32/13.49 (~always5(s30)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4121, 4114])).
% 13.32/13.49 tff(4123,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s29, s30)) | (~always5(s29)) | always5(s30))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s29, s30)) | (~always5(s29)) | always5(s30))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4124,plain,
% 13.32/13.49 (((~always5(s29)) | (~trans(s29, s30)) | always5(s30)) <=> ((~trans(s29, s30)) | (~always5(s29)) | always5(s30))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4125,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s29)) | (~trans(s29, s30)) | always5(s30))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s29, s30)) | (~always5(s29)) | always5(s30)))),
% 13.32/13.49 inference(monotonicity,[status(thm)],[4124])).
% 13.32/13.49 tff(4126,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s29)) | (~trans(s29, s30)) | always5(s30))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s29, s30)) | (~always5(s29)) | always5(s30))),
% 13.32/13.49 inference(transitivity,[status(thm)],[4125, 4123])).
% 13.32/13.49 tff(4127,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s29)) | (~trans(s29, s30)) | always5(s30))),
% 13.32/13.49 inference(quant_inst,[status(thm)],[])).
% 13.32/13.49 tff(4128,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s29, s30)) | (~always5(s29)) | always5(s30)),
% 13.32/13.49 inference(modus_ponens,[status(thm)],[4127, 4126])).
% 13.32/13.49 tff(4129,plain,
% 13.32/13.49 ((~always5(s29)) | always5(s30)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4128, 3890, 910])).
% 13.32/13.49 tff(4130,plain,
% 13.32/13.49 (~always5(s29)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4129, 4122])).
% 13.32/13.49 tff(4131,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s28, s29)) | (~always5(s28)) | always5(s29))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s28, s29)) | (~always5(s28)) | always5(s29))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4132,plain,
% 13.32/13.49 (((~always5(s28)) | (~trans(s28, s29)) | always5(s29)) <=> ((~trans(s28, s29)) | (~always5(s28)) | always5(s29))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4133,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s28)) | (~trans(s28, s29)) | always5(s29))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s28, s29)) | (~always5(s28)) | always5(s29)))),
% 13.32/13.49 inference(monotonicity,[status(thm)],[4132])).
% 13.32/13.49 tff(4134,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s28)) | (~trans(s28, s29)) | always5(s29))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s28, s29)) | (~always5(s28)) | always5(s29))),
% 13.32/13.49 inference(transitivity,[status(thm)],[4133, 4131])).
% 13.32/13.49 tff(4135,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s28)) | (~trans(s28, s29)) | always5(s29))),
% 13.32/13.49 inference(quant_inst,[status(thm)],[])).
% 13.32/13.49 tff(4136,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s28, s29)) | (~always5(s28)) | always5(s29)),
% 13.32/13.49 inference(modus_ponens,[status(thm)],[4135, 4134])).
% 13.32/13.49 tff(4137,plain,
% 13.32/13.49 ((~always5(s28)) | always5(s29)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4136, 3890, 882])).
% 13.32/13.49 tff(4138,plain,
% 13.32/13.49 (~always5(s28)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4137, 4130])).
% 13.32/13.49 tff(4139,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s27, s28)) | (~always5(s27)) | always5(s28))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s27, s28)) | (~always5(s27)) | always5(s28))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4140,plain,
% 13.32/13.49 (((~always5(s27)) | (~trans(s27, s28)) | always5(s28)) <=> ((~trans(s27, s28)) | (~always5(s27)) | always5(s28))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4141,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s27)) | (~trans(s27, s28)) | always5(s28))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s27, s28)) | (~always5(s27)) | always5(s28)))),
% 13.32/13.49 inference(monotonicity,[status(thm)],[4140])).
% 13.32/13.49 tff(4142,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s27)) | (~trans(s27, s28)) | always5(s28))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s27, s28)) | (~always5(s27)) | always5(s28))),
% 13.32/13.49 inference(transitivity,[status(thm)],[4141, 4139])).
% 13.32/13.49 tff(4143,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s27)) | (~trans(s27, s28)) | always5(s28))),
% 13.32/13.49 inference(quant_inst,[status(thm)],[])).
% 13.32/13.49 tff(4144,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s27, s28)) | (~always5(s27)) | always5(s28)),
% 13.32/13.49 inference(modus_ponens,[status(thm)],[4143, 4142])).
% 13.32/13.49 tff(4145,plain,
% 13.32/13.49 ((~always5(s27)) | always5(s28)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4144, 3890, 851])).
% 13.32/13.49 tff(4146,plain,
% 13.32/13.49 (~always5(s27)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4145, 4138])).
% 13.32/13.49 tff(4147,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s26, s27)) | (~always5(s26)) | always5(s27))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s26, s27)) | (~always5(s26)) | always5(s27))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4148,plain,
% 13.32/13.49 (((~always5(s26)) | (~trans(s26, s27)) | always5(s27)) <=> ((~trans(s26, s27)) | (~always5(s26)) | always5(s27))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4149,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s26)) | (~trans(s26, s27)) | always5(s27))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s26, s27)) | (~always5(s26)) | always5(s27)))),
% 13.32/13.49 inference(monotonicity,[status(thm)],[4148])).
% 13.32/13.49 tff(4150,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s26)) | (~trans(s26, s27)) | always5(s27))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s26, s27)) | (~always5(s26)) | always5(s27))),
% 13.32/13.49 inference(transitivity,[status(thm)],[4149, 4147])).
% 13.32/13.49 tff(4151,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s26)) | (~trans(s26, s27)) | always5(s27))),
% 13.32/13.49 inference(quant_inst,[status(thm)],[])).
% 13.32/13.49 tff(4152,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s26, s27)) | (~always5(s26)) | always5(s27)),
% 13.32/13.49 inference(modus_ponens,[status(thm)],[4151, 4150])).
% 13.32/13.49 tff(4153,plain,
% 13.32/13.49 ((~always5(s26)) | always5(s27)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4152, 3890, 823])).
% 13.32/13.49 tff(4154,plain,
% 13.32/13.49 (~always5(s26)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4153, 4146])).
% 13.32/13.49 tff(4155,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s25, s26)) | (~always5(s25)) | always5(s26))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s25, s26)) | (~always5(s25)) | always5(s26))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4156,plain,
% 13.32/13.49 (((~always5(s25)) | (~trans(s25, s26)) | always5(s26)) <=> ((~trans(s25, s26)) | (~always5(s25)) | always5(s26))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4157,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s25)) | (~trans(s25, s26)) | always5(s26))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s25, s26)) | (~always5(s25)) | always5(s26)))),
% 13.32/13.49 inference(monotonicity,[status(thm)],[4156])).
% 13.32/13.49 tff(4158,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s25)) | (~trans(s25, s26)) | always5(s26))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s25, s26)) | (~always5(s25)) | always5(s26))),
% 13.32/13.49 inference(transitivity,[status(thm)],[4157, 4155])).
% 13.32/13.49 tff(4159,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s25)) | (~trans(s25, s26)) | always5(s26))),
% 13.32/13.49 inference(quant_inst,[status(thm)],[])).
% 13.32/13.49 tff(4160,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s25, s26)) | (~always5(s25)) | always5(s26)),
% 13.32/13.49 inference(modus_ponens,[status(thm)],[4159, 4158])).
% 13.32/13.49 tff(4161,plain,
% 13.32/13.49 ((~always5(s25)) | always5(s26)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4160, 3890, 792])).
% 13.32/13.49 tff(4162,plain,
% 13.32/13.49 (~always5(s25)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4161, 4154])).
% 13.32/13.49 tff(4163,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s24, s25)) | (~always5(s24)) | always5(s25))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s24, s25)) | (~always5(s24)) | always5(s25))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4164,plain,
% 13.32/13.49 (((~always5(s24)) | (~trans(s24, s25)) | always5(s25)) <=> ((~trans(s24, s25)) | (~always5(s24)) | always5(s25))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4165,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s24)) | (~trans(s24, s25)) | always5(s25))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s24, s25)) | (~always5(s24)) | always5(s25)))),
% 13.32/13.49 inference(monotonicity,[status(thm)],[4164])).
% 13.32/13.49 tff(4166,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s24)) | (~trans(s24, s25)) | always5(s25))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s24, s25)) | (~always5(s24)) | always5(s25))),
% 13.32/13.49 inference(transitivity,[status(thm)],[4165, 4163])).
% 13.32/13.49 tff(4167,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s24)) | (~trans(s24, s25)) | always5(s25))),
% 13.32/13.49 inference(quant_inst,[status(thm)],[])).
% 13.32/13.49 tff(4168,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s24, s25)) | (~always5(s24)) | always5(s25)),
% 13.32/13.49 inference(modus_ponens,[status(thm)],[4167, 4166])).
% 13.32/13.49 tff(4169,plain,
% 13.32/13.49 ((~always5(s24)) | always5(s25)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4168, 3890, 764])).
% 13.32/13.49 tff(4170,plain,
% 13.32/13.49 (~always5(s24)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4169, 4162])).
% 13.32/13.49 tff(4171,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s23, s24)) | (~always5(s23)) | always5(s24))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s23, s24)) | (~always5(s23)) | always5(s24))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4172,plain,
% 13.32/13.49 (((~always5(s23)) | (~trans(s23, s24)) | always5(s24)) <=> ((~trans(s23, s24)) | (~always5(s23)) | always5(s24))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4173,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s23)) | (~trans(s23, s24)) | always5(s24))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s23, s24)) | (~always5(s23)) | always5(s24)))),
% 13.32/13.49 inference(monotonicity,[status(thm)],[4172])).
% 13.32/13.49 tff(4174,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s23)) | (~trans(s23, s24)) | always5(s24))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s23, s24)) | (~always5(s23)) | always5(s24))),
% 13.32/13.49 inference(transitivity,[status(thm)],[4173, 4171])).
% 13.32/13.49 tff(4175,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s23)) | (~trans(s23, s24)) | always5(s24))),
% 13.32/13.49 inference(quant_inst,[status(thm)],[])).
% 13.32/13.49 tff(4176,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s23, s24)) | (~always5(s23)) | always5(s24)),
% 13.32/13.49 inference(modus_ponens,[status(thm)],[4175, 4174])).
% 13.32/13.49 tff(4177,plain,
% 13.32/13.49 ((~always5(s23)) | always5(s24)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4176, 3890, 733])).
% 13.32/13.49 tff(4178,plain,
% 13.32/13.49 (~always5(s23)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4177, 4170])).
% 13.32/13.49 tff(4179,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s22, s23)) | (~always5(s22)) | always5(s23))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s22, s23)) | (~always5(s22)) | always5(s23))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4180,plain,
% 13.32/13.49 (((~always5(s22)) | (~trans(s22, s23)) | always5(s23)) <=> ((~trans(s22, s23)) | (~always5(s22)) | always5(s23))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4181,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s22)) | (~trans(s22, s23)) | always5(s23))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s22, s23)) | (~always5(s22)) | always5(s23)))),
% 13.32/13.49 inference(monotonicity,[status(thm)],[4180])).
% 13.32/13.49 tff(4182,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s22)) | (~trans(s22, s23)) | always5(s23))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s22, s23)) | (~always5(s22)) | always5(s23))),
% 13.32/13.49 inference(transitivity,[status(thm)],[4181, 4179])).
% 13.32/13.49 tff(4183,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s22)) | (~trans(s22, s23)) | always5(s23))),
% 13.32/13.49 inference(quant_inst,[status(thm)],[])).
% 13.32/13.49 tff(4184,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s22, s23)) | (~always5(s22)) | always5(s23)),
% 13.32/13.49 inference(modus_ponens,[status(thm)],[4183, 4182])).
% 13.32/13.49 tff(4185,plain,
% 13.32/13.49 ((~always5(s22)) | always5(s23)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4184, 3890, 705])).
% 13.32/13.49 tff(4186,plain,
% 13.32/13.49 (~always5(s22)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4185, 4178])).
% 13.32/13.49 tff(4187,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s21, s22)) | (~always5(s21)) | always5(s22))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s21, s22)) | (~always5(s21)) | always5(s22))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4188,plain,
% 13.32/13.49 (((~always5(s21)) | (~trans(s21, s22)) | always5(s22)) <=> ((~trans(s21, s22)) | (~always5(s21)) | always5(s22))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4189,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s21)) | (~trans(s21, s22)) | always5(s22))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s21, s22)) | (~always5(s21)) | always5(s22)))),
% 13.32/13.49 inference(monotonicity,[status(thm)],[4188])).
% 13.32/13.49 tff(4190,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s21)) | (~trans(s21, s22)) | always5(s22))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s21, s22)) | (~always5(s21)) | always5(s22))),
% 13.32/13.49 inference(transitivity,[status(thm)],[4189, 4187])).
% 13.32/13.49 tff(4191,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s21)) | (~trans(s21, s22)) | always5(s22))),
% 13.32/13.49 inference(quant_inst,[status(thm)],[])).
% 13.32/13.49 tff(4192,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s21, s22)) | (~always5(s21)) | always5(s22)),
% 13.32/13.49 inference(modus_ponens,[status(thm)],[4191, 4190])).
% 13.32/13.49 tff(4193,plain,
% 13.32/13.49 ((~always5(s21)) | always5(s22)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4192, 3890, 674])).
% 13.32/13.49 tff(4194,plain,
% 13.32/13.49 (~always5(s21)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4193, 4186])).
% 13.32/13.49 tff(4195,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s20, s21)) | (~always5(s20)) | always5(s21))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s20, s21)) | (~always5(s20)) | always5(s21))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4196,plain,
% 13.32/13.49 (((~always5(s20)) | (~trans(s20, s21)) | always5(s21)) <=> ((~trans(s20, s21)) | (~always5(s20)) | always5(s21))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4197,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s20)) | (~trans(s20, s21)) | always5(s21))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s20, s21)) | (~always5(s20)) | always5(s21)))),
% 13.32/13.49 inference(monotonicity,[status(thm)],[4196])).
% 13.32/13.49 tff(4198,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s20)) | (~trans(s20, s21)) | always5(s21))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s20, s21)) | (~always5(s20)) | always5(s21))),
% 13.32/13.49 inference(transitivity,[status(thm)],[4197, 4195])).
% 13.32/13.49 tff(4199,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s20)) | (~trans(s20, s21)) | always5(s21))),
% 13.32/13.49 inference(quant_inst,[status(thm)],[])).
% 13.32/13.49 tff(4200,plain,
% 13.32/13.49 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s20, s21)) | (~always5(s20)) | always5(s21)),
% 13.32/13.49 inference(modus_ponens,[status(thm)],[4199, 4198])).
% 13.32/13.49 tff(4201,plain,
% 13.32/13.49 ((~always5(s20)) | always5(s21)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4200, 3890, 646])).
% 13.32/13.49 tff(4202,plain,
% 13.32/13.49 (~always5(s20)),
% 13.32/13.49 inference(unit_resolution,[status(thm)],[4201, 4194])).
% 13.32/13.49 tff(4203,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s19, s20)) | (~always5(s19)) | always5(s20))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s19, s20)) | (~always5(s19)) | always5(s20))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4204,plain,
% 13.32/13.49 (((~always5(s19)) | (~trans(s19, s20)) | always5(s20)) <=> ((~trans(s19, s20)) | (~always5(s19)) | always5(s20))),
% 13.32/13.49 inference(rewrite,[status(thm)],[])).
% 13.32/13.49 tff(4205,plain,
% 13.32/13.49 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s19)) | (~trans(s19, s20)) | always5(s20))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s19, s20)) | (~always5(s19)) | always5(s20)))),
% 13.32/13.49 inference(monotonicity,[status(thm)],[4204])).
% 13.32/13.50 tff(4206,plain,
% 13.32/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s19)) | (~trans(s19, s20)) | always5(s20))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s19, s20)) | (~always5(s19)) | always5(s20))),
% 13.32/13.50 inference(transitivity,[status(thm)],[4205, 4203])).
% 13.32/13.50 tff(4207,plain,
% 13.32/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s19)) | (~trans(s19, s20)) | always5(s20))),
% 13.32/13.50 inference(quant_inst,[status(thm)],[])).
% 13.32/13.50 tff(4208,plain,
% 13.32/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s19, s20)) | (~always5(s19)) | always5(s20)),
% 13.32/13.50 inference(modus_ponens,[status(thm)],[4207, 4206])).
% 13.32/13.50 tff(4209,plain,
% 13.32/13.50 ((~always5(s19)) | always5(s20)),
% 13.32/13.50 inference(unit_resolution,[status(thm)],[4208, 3890, 615])).
% 13.32/13.50 tff(4210,plain,
% 13.32/13.50 (~always5(s19)),
% 13.32/13.50 inference(unit_resolution,[status(thm)],[4209, 4202])).
% 13.32/13.50 tff(4211,plain,
% 13.32/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s18, s19)) | (~always5(s18)) | always5(s19))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s18, s19)) | (~always5(s18)) | always5(s19))),
% 13.32/13.50 inference(rewrite,[status(thm)],[])).
% 13.32/13.50 tff(4212,plain,
% 13.32/13.50 (((~always5(s18)) | (~trans(s18, s19)) | always5(s19)) <=> ((~trans(s18, s19)) | (~always5(s18)) | always5(s19))),
% 13.32/13.50 inference(rewrite,[status(thm)],[])).
% 13.32/13.50 tff(4213,plain,
% 13.32/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s18)) | (~trans(s18, s19)) | always5(s19))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s18, s19)) | (~always5(s18)) | always5(s19)))),
% 13.32/13.50 inference(monotonicity,[status(thm)],[4212])).
% 13.32/13.50 tff(4214,plain,
% 13.32/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s18)) | (~trans(s18, s19)) | always5(s19))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s18, s19)) | (~always5(s18)) | always5(s19))),
% 13.32/13.50 inference(transitivity,[status(thm)],[4213, 4211])).
% 13.32/13.50 tff(4215,plain,
% 13.32/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s18)) | (~trans(s18, s19)) | always5(s19))),
% 13.32/13.50 inference(quant_inst,[status(thm)],[])).
% 13.32/13.50 tff(4216,plain,
% 13.32/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s18, s19)) | (~always5(s18)) | always5(s19)),
% 13.32/13.50 inference(modus_ponens,[status(thm)],[4215, 4214])).
% 13.32/13.50 tff(4217,plain,
% 13.32/13.50 ((~always5(s18)) | always5(s19)),
% 13.32/13.50 inference(unit_resolution,[status(thm)],[4216, 3890, 587])).
% 13.32/13.50 tff(4218,plain,
% 13.32/13.50 (~always5(s18)),
% 13.32/13.50 inference(unit_resolution,[status(thm)],[4217, 4210])).
% 13.32/13.50 tff(4219,plain,
% 13.32/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s17, s18)) | (~always5(s17)) | always5(s18))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s17, s18)) | (~always5(s17)) | always5(s18))),
% 13.32/13.50 inference(rewrite,[status(thm)],[])).
% 13.32/13.50 tff(4220,plain,
% 13.32/13.50 (((~always5(s17)) | (~trans(s17, s18)) | always5(s18)) <=> ((~trans(s17, s18)) | (~always5(s17)) | always5(s18))),
% 13.32/13.50 inference(rewrite,[status(thm)],[])).
% 13.32/13.50 tff(4221,plain,
% 13.32/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s17)) | (~trans(s17, s18)) | always5(s18))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s17, s18)) | (~always5(s17)) | always5(s18)))),
% 13.32/13.50 inference(monotonicity,[status(thm)],[4220])).
% 13.32/13.50 tff(4222,plain,
% 13.32/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s17)) | (~trans(s17, s18)) | always5(s18))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s17, s18)) | (~always5(s17)) | always5(s18))),
% 13.32/13.50 inference(transitivity,[status(thm)],[4221, 4219])).
% 13.32/13.50 tff(4223,plain,
% 13.32/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s17)) | (~trans(s17, s18)) | always5(s18))),
% 13.32/13.50 inference(quant_inst,[status(thm)],[])).
% 13.32/13.50 tff(4224,plain,
% 13.32/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s17, s18)) | (~always5(s17)) | always5(s18)),
% 13.32/13.50 inference(modus_ponens,[status(thm)],[4223, 4222])).
% 13.32/13.50 tff(4225,plain,
% 13.32/13.50 ((~always5(s17)) | always5(s18)),
% 13.32/13.50 inference(unit_resolution,[status(thm)],[4224, 3890, 556])).
% 13.32/13.50 tff(4226,plain,
% 13.32/13.50 (~always5(s17)),
% 13.32/13.50 inference(unit_resolution,[status(thm)],[4225, 4218])).
% 13.32/13.50 tff(4227,plain,
% 13.32/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s16, s17)) | (~always5(s16)) | always5(s17))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s16, s17)) | (~always5(s16)) | always5(s17))),
% 13.32/13.50 inference(rewrite,[status(thm)],[])).
% 13.32/13.50 tff(4228,plain,
% 13.32/13.50 (((~always5(s16)) | (~trans(s16, s17)) | always5(s17)) <=> ((~trans(s16, s17)) | (~always5(s16)) | always5(s17))),
% 13.32/13.50 inference(rewrite,[status(thm)],[])).
% 13.32/13.50 tff(4229,plain,
% 13.32/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s16)) | (~trans(s16, s17)) | always5(s17))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s16, s17)) | (~always5(s16)) | always5(s17)))),
% 13.32/13.50 inference(monotonicity,[status(thm)],[4228])).
% 13.32/13.50 tff(4230,plain,
% 13.32/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s16)) | (~trans(s16, s17)) | always5(s17))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s16, s17)) | (~always5(s16)) | always5(s17))),
% 13.32/13.50 inference(transitivity,[status(thm)],[4229, 4227])).
% 13.32/13.50 tff(4231,plain,
% 13.32/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s16)) | (~trans(s16, s17)) | always5(s17))),
% 13.32/13.50 inference(quant_inst,[status(thm)],[])).
% 13.32/13.50 tff(4232,plain,
% 13.32/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s16, s17)) | (~always5(s16)) | always5(s17)),
% 13.32/13.50 inference(modus_ponens,[status(thm)],[4231, 4230])).
% 13.32/13.50 tff(4233,plain,
% 13.32/13.50 ((~always5(s16)) | always5(s17)),
% 13.32/13.50 inference(unit_resolution,[status(thm)],[4232, 3890, 528])).
% 13.32/13.50 tff(4234,plain,
% 13.32/13.50 (~always5(s16)),
% 13.32/13.50 inference(unit_resolution,[status(thm)],[4233, 4226])).
% 13.32/13.50 tff(4235,plain,
% 13.32/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s15, s16)) | (~always5(s15)) | always5(s16))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s15, s16)) | (~always5(s15)) | always5(s16))),
% 13.32/13.50 inference(rewrite,[status(thm)],[])).
% 13.32/13.50 tff(4236,plain,
% 13.32/13.50 (((~always5(s15)) | (~trans(s15, s16)) | always5(s16)) <=> ((~trans(s15, s16)) | (~always5(s15)) | always5(s16))),
% 13.32/13.50 inference(rewrite,[status(thm)],[])).
% 13.32/13.50 tff(4237,plain,
% 13.32/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s15)) | (~trans(s15, s16)) | always5(s16))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s15, s16)) | (~always5(s15)) | always5(s16)))),
% 13.32/13.50 inference(monotonicity,[status(thm)],[4236])).
% 13.32/13.50 tff(4238,plain,
% 13.32/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s15)) | (~trans(s15, s16)) | always5(s16))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s15, s16)) | (~always5(s15)) | always5(s16))),
% 13.32/13.50 inference(transitivity,[status(thm)],[4237, 4235])).
% 13.32/13.50 tff(4239,plain,
% 13.32/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s15)) | (~trans(s15, s16)) | always5(s16))),
% 13.32/13.50 inference(quant_inst,[status(thm)],[])).
% 13.32/13.50 tff(4240,plain,
% 13.32/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s15, s16)) | (~always5(s15)) | always5(s16)),
% 13.32/13.50 inference(modus_ponens,[status(thm)],[4239, 4238])).
% 13.32/13.50 tff(4241,plain,
% 13.32/13.50 ((~always5(s15)) | always5(s16)),
% 13.32/13.50 inference(unit_resolution,[status(thm)],[4240, 3890, 499])).
% 13.32/13.50 tff(4242,plain,
% 13.32/13.50 (~always5(s15)),
% 13.32/13.50 inference(unit_resolution,[status(thm)],[4241, 4234])).
% 13.32/13.50 tff(4243,plain,
% 13.32/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s14, s15)) | (~always5(s14)) | always5(s15))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s14, s15)) | (~always5(s14)) | always5(s15))),
% 13.32/13.50 inference(rewrite,[status(thm)],[])).
% 13.32/13.50 tff(4244,plain,
% 13.32/13.50 (((~always5(s14)) | (~trans(s14, s15)) | always5(s15)) <=> ((~trans(s14, s15)) | (~always5(s14)) | always5(s15))),
% 13.32/13.50 inference(rewrite,[status(thm)],[])).
% 13.32/13.50 tff(4245,plain,
% 13.32/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s14)) | (~trans(s14, s15)) | always5(s15))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s14, s15)) | (~always5(s14)) | always5(s15)))),
% 13.32/13.50 inference(monotonicity,[status(thm)],[4244])).
% 13.32/13.50 tff(4246,plain,
% 13.32/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s14)) | (~trans(s14, s15)) | always5(s15))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s14, s15)) | (~always5(s14)) | always5(s15))),
% 13.32/13.50 inference(transitivity,[status(thm)],[4245, 4243])).
% 13.32/13.50 tff(4247,plain,
% 13.32/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s14)) | (~trans(s14, s15)) | always5(s15))),
% 13.32/13.50 inference(quant_inst,[status(thm)],[])).
% 13.32/13.50 tff(4248,plain,
% 13.32/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s14, s15)) | (~always5(s14)) | always5(s15)),
% 13.32/13.50 inference(modus_ponens,[status(thm)],[4247, 4246])).
% 13.32/13.50 tff(4249,plain,
% 13.32/13.50 ((~always5(s14)) | always5(s15)),
% 13.32/13.50 inference(unit_resolution,[status(thm)],[4248, 3890, 473])).
% 13.32/13.50 tff(4250,plain,
% 13.32/13.50 (~always5(s14)),
% 13.32/13.50 inference(unit_resolution,[status(thm)],[4249, 4242])).
% 13.32/13.50 tff(4251,plain,
% 13.32/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s13, s14)) | (~always5(s13)) | always5(s14))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s13, s14)) | (~always5(s13)) | always5(s14))),
% 13.32/13.50 inference(rewrite,[status(thm)],[])).
% 13.32/13.50 tff(4252,plain,
% 13.32/13.50 (((~always5(s13)) | (~trans(s13, s14)) | always5(s14)) <=> ((~trans(s13, s14)) | (~always5(s13)) | always5(s14))),
% 13.32/13.50 inference(rewrite,[status(thm)],[])).
% 13.32/13.50 tff(4253,plain,
% 13.32/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s13)) | (~trans(s13, s14)) | always5(s14))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s13, s14)) | (~always5(s13)) | always5(s14)))),
% 13.32/13.50 inference(monotonicity,[status(thm)],[4252])).
% 13.32/13.50 tff(4254,plain,
% 13.32/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s13)) | (~trans(s13, s14)) | always5(s14))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s13, s14)) | (~always5(s13)) | always5(s14))),
% 13.32/13.50 inference(transitivity,[status(thm)],[4253, 4251])).
% 13.32/13.50 tff(4255,plain,
% 13.32/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s13)) | (~trans(s13, s14)) | always5(s14))),
% 13.32/13.50 inference(quant_inst,[status(thm)],[])).
% 13.32/13.50 tff(4256,plain,
% 13.32/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s13, s14)) | (~always5(s13)) | always5(s14)),
% 13.32/13.50 inference(modus_ponens,[status(thm)],[4255, 4254])).
% 13.32/13.50 tff(4257,plain,
% 13.32/13.50 ((~always5(s13)) | always5(s14)),
% 13.32/13.50 inference(unit_resolution,[status(thm)],[4256, 3890, 444])).
% 13.32/13.50 tff(4258,plain,
% 13.32/13.50 (~always5(s13)),
% 13.32/13.50 inference(unit_resolution,[status(thm)],[4257, 4250])).
% 13.32/13.50 tff(4259,plain,
% 13.32/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s12, s13)) | (~always5(s12)) | always5(s13))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s12, s13)) | (~always5(s12)) | always5(s13))),
% 13.32/13.50 inference(rewrite,[status(thm)],[])).
% 13.32/13.50 tff(4260,plain,
% 13.32/13.50 (((~always5(s12)) | (~trans(s12, s13)) | always5(s13)) <=> ((~trans(s12, s13)) | (~always5(s12)) | always5(s13))),
% 13.32/13.50 inference(rewrite,[status(thm)],[])).
% 13.32/13.50 tff(4261,plain,
% 13.32/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s12)) | (~trans(s12, s13)) | always5(s13))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s12, s13)) | (~always5(s12)) | always5(s13)))),
% 13.35/13.50 inference(monotonicity,[status(thm)],[4260])).
% 13.35/13.50 tff(4262,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s12)) | (~trans(s12, s13)) | always5(s13))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s12, s13)) | (~always5(s12)) | always5(s13))),
% 13.35/13.50 inference(transitivity,[status(thm)],[4261, 4259])).
% 13.35/13.50 tff(4263,plain,
% 13.35/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s12)) | (~trans(s12, s13)) | always5(s13))),
% 13.35/13.50 inference(quant_inst,[status(thm)],[])).
% 13.35/13.50 tff(4264,plain,
% 13.35/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s12, s13)) | (~always5(s12)) | always5(s13)),
% 13.35/13.50 inference(modus_ponens,[status(thm)],[4263, 4262])).
% 13.35/13.50 tff(4265,plain,
% 13.35/13.50 ((~always5(s12)) | always5(s13)),
% 13.35/13.50 inference(unit_resolution,[status(thm)],[4264, 3890, 418])).
% 13.35/13.50 tff(4266,plain,
% 13.35/13.50 (~always5(s12)),
% 13.35/13.50 inference(unit_resolution,[status(thm)],[4265, 4258])).
% 13.35/13.50 tff(4267,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s11, s12)) | (~always5(s11)) | always5(s12))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s11, s12)) | (~always5(s11)) | always5(s12))),
% 13.35/13.50 inference(rewrite,[status(thm)],[])).
% 13.35/13.50 tff(4268,plain,
% 13.35/13.50 (((~always5(s11)) | (~trans(s11, s12)) | always5(s12)) <=> ((~trans(s11, s12)) | (~always5(s11)) | always5(s12))),
% 13.35/13.50 inference(rewrite,[status(thm)],[])).
% 13.35/13.50 tff(4269,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s11)) | (~trans(s11, s12)) | always5(s12))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s11, s12)) | (~always5(s11)) | always5(s12)))),
% 13.35/13.50 inference(monotonicity,[status(thm)],[4268])).
% 13.35/13.50 tff(4270,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s11)) | (~trans(s11, s12)) | always5(s12))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s11, s12)) | (~always5(s11)) | always5(s12))),
% 13.35/13.50 inference(transitivity,[status(thm)],[4269, 4267])).
% 13.35/13.50 tff(4271,plain,
% 13.35/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s11)) | (~trans(s11, s12)) | always5(s12))),
% 13.35/13.50 inference(quant_inst,[status(thm)],[])).
% 13.35/13.50 tff(4272,plain,
% 13.35/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s11, s12)) | (~always5(s11)) | always5(s12)),
% 13.35/13.50 inference(modus_ponens,[status(thm)],[4271, 4270])).
% 13.35/13.50 tff(4273,plain,
% 13.35/13.50 ((~always5(s11)) | always5(s12)),
% 13.35/13.50 inference(unit_resolution,[status(thm)],[4272, 3890, 389])).
% 13.35/13.50 tff(4274,plain,
% 13.35/13.50 (~always5(s11)),
% 13.35/13.50 inference(unit_resolution,[status(thm)],[4273, 4266])).
% 13.35/13.50 tff(4275,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s10, s11)) | (~always5(s10)) | always5(s11))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s10, s11)) | (~always5(s10)) | always5(s11))),
% 13.35/13.50 inference(rewrite,[status(thm)],[])).
% 13.35/13.50 tff(4276,plain,
% 13.35/13.50 (((~always5(s10)) | (~trans(s10, s11)) | always5(s11)) <=> ((~trans(s10, s11)) | (~always5(s10)) | always5(s11))),
% 13.35/13.50 inference(rewrite,[status(thm)],[])).
% 13.35/13.50 tff(4277,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s10)) | (~trans(s10, s11)) | always5(s11))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s10, s11)) | (~always5(s10)) | always5(s11)))),
% 13.35/13.50 inference(monotonicity,[status(thm)],[4276])).
% 13.35/13.50 tff(4278,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s10)) | (~trans(s10, s11)) | always5(s11))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s10, s11)) | (~always5(s10)) | always5(s11))),
% 13.35/13.50 inference(transitivity,[status(thm)],[4277, 4275])).
% 13.35/13.50 tff(4279,plain,
% 13.35/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s10)) | (~trans(s10, s11)) | always5(s11))),
% 13.35/13.50 inference(quant_inst,[status(thm)],[])).
% 13.35/13.50 tff(4280,plain,
% 13.35/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s10, s11)) | (~always5(s10)) | always5(s11)),
% 13.35/13.50 inference(modus_ponens,[status(thm)],[4279, 4278])).
% 13.35/13.50 tff(4281,plain,
% 13.35/13.50 ((~always5(s10)) | always5(s11)),
% 13.35/13.50 inference(unit_resolution,[status(thm)],[4280, 3890, 363])).
% 13.35/13.50 tff(4282,plain,
% 13.35/13.50 (~always5(s10)),
% 13.35/13.50 inference(unit_resolution,[status(thm)],[4281, 4274])).
% 13.35/13.50 tff(4283,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s9, s10)) | (~always5(s9)) | always5(s10))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s9, s10)) | (~always5(s9)) | always5(s10))),
% 13.35/13.50 inference(rewrite,[status(thm)],[])).
% 13.35/13.50 tff(4284,plain,
% 13.35/13.50 (((~always5(s9)) | (~trans(s9, s10)) | always5(s10)) <=> ((~trans(s9, s10)) | (~always5(s9)) | always5(s10))),
% 13.35/13.50 inference(rewrite,[status(thm)],[])).
% 13.35/13.50 tff(4285,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s9)) | (~trans(s9, s10)) | always5(s10))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s9, s10)) | (~always5(s9)) | always5(s10)))),
% 13.35/13.50 inference(monotonicity,[status(thm)],[4284])).
% 13.35/13.50 tff(4286,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s9)) | (~trans(s9, s10)) | always5(s10))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s9, s10)) | (~always5(s9)) | always5(s10))),
% 13.35/13.50 inference(transitivity,[status(thm)],[4285, 4283])).
% 13.35/13.50 tff(4287,plain,
% 13.35/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s9)) | (~trans(s9, s10)) | always5(s10))),
% 13.35/13.50 inference(quant_inst,[status(thm)],[])).
% 13.35/13.50 tff(4288,plain,
% 13.35/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s9, s10)) | (~always5(s9)) | always5(s10)),
% 13.35/13.50 inference(modus_ponens,[status(thm)],[4287, 4286])).
% 13.35/13.50 tff(4289,plain,
% 13.35/13.50 ((~always5(s9)) | always5(s10)),
% 13.35/13.50 inference(unit_resolution,[status(thm)],[4288, 3890, 334])).
% 13.35/13.50 tff(4290,plain,
% 13.35/13.50 (~always5(s9)),
% 13.35/13.50 inference(unit_resolution,[status(thm)],[4289, 4282])).
% 13.35/13.50 tff(4291,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s8, s9)) | (~always5(s8)) | always5(s9))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s8, s9)) | (~always5(s8)) | always5(s9))),
% 13.35/13.50 inference(rewrite,[status(thm)],[])).
% 13.35/13.50 tff(4292,plain,
% 13.35/13.50 (((~always5(s8)) | (~trans(s8, s9)) | always5(s9)) <=> ((~trans(s8, s9)) | (~always5(s8)) | always5(s9))),
% 13.35/13.50 inference(rewrite,[status(thm)],[])).
% 13.35/13.50 tff(4293,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s8)) | (~trans(s8, s9)) | always5(s9))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s8, s9)) | (~always5(s8)) | always5(s9)))),
% 13.35/13.50 inference(monotonicity,[status(thm)],[4292])).
% 13.35/13.50 tff(4294,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s8)) | (~trans(s8, s9)) | always5(s9))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s8, s9)) | (~always5(s8)) | always5(s9))),
% 13.35/13.50 inference(transitivity,[status(thm)],[4293, 4291])).
% 13.35/13.50 tff(4295,plain,
% 13.35/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s8)) | (~trans(s8, s9)) | always5(s9))),
% 13.35/13.50 inference(quant_inst,[status(thm)],[])).
% 13.35/13.50 tff(4296,plain,
% 13.35/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s8, s9)) | (~always5(s8)) | always5(s9)),
% 13.35/13.50 inference(modus_ponens,[status(thm)],[4295, 4294])).
% 13.35/13.50 tff(4297,plain,
% 13.35/13.50 ((~always5(s8)) | always5(s9)),
% 13.35/13.50 inference(unit_resolution,[status(thm)],[4296, 3890, 308])).
% 13.35/13.50 tff(4298,plain,
% 13.35/13.50 (~always5(s8)),
% 13.35/13.50 inference(unit_resolution,[status(thm)],[4297, 4290])).
% 13.35/13.50 tff(4299,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s7, s8)) | (~always5(s7)) | always5(s8))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s7, s8)) | (~always5(s7)) | always5(s8))),
% 13.35/13.50 inference(rewrite,[status(thm)],[])).
% 13.35/13.50 tff(4300,plain,
% 13.35/13.50 (((~always5(s7)) | (~trans(s7, s8)) | always5(s8)) <=> ((~trans(s7, s8)) | (~always5(s7)) | always5(s8))),
% 13.35/13.50 inference(rewrite,[status(thm)],[])).
% 13.35/13.50 tff(4301,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s7)) | (~trans(s7, s8)) | always5(s8))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s7, s8)) | (~always5(s7)) | always5(s8)))),
% 13.35/13.50 inference(monotonicity,[status(thm)],[4300])).
% 13.35/13.50 tff(4302,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s7)) | (~trans(s7, s8)) | always5(s8))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s7, s8)) | (~always5(s7)) | always5(s8))),
% 13.35/13.50 inference(transitivity,[status(thm)],[4301, 4299])).
% 13.35/13.50 tff(4303,plain,
% 13.35/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s7)) | (~trans(s7, s8)) | always5(s8))),
% 13.35/13.50 inference(quant_inst,[status(thm)],[])).
% 13.35/13.50 tff(4304,plain,
% 13.35/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s7, s8)) | (~always5(s7)) | always5(s8)),
% 13.35/13.50 inference(modus_ponens,[status(thm)],[4303, 4302])).
% 13.35/13.50 tff(4305,plain,
% 13.35/13.50 ((~always5(s7)) | always5(s8)),
% 13.35/13.50 inference(unit_resolution,[status(thm)],[4304, 3890, 279])).
% 13.35/13.50 tff(4306,plain,
% 13.35/13.50 (~always5(s7)),
% 13.35/13.50 inference(unit_resolution,[status(thm)],[4305, 4298])).
% 13.35/13.50 tff(4307,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s6, s7)) | (~always5(s6)) | always5(s7))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s6, s7)) | (~always5(s6)) | always5(s7))),
% 13.35/13.50 inference(rewrite,[status(thm)],[])).
% 13.35/13.50 tff(4308,plain,
% 13.35/13.50 (((~always5(s6)) | (~trans(s6, s7)) | always5(s7)) <=> ((~trans(s6, s7)) | (~always5(s6)) | always5(s7))),
% 13.35/13.50 inference(rewrite,[status(thm)],[])).
% 13.35/13.50 tff(4309,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s6)) | (~trans(s6, s7)) | always5(s7))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s6, s7)) | (~always5(s6)) | always5(s7)))),
% 13.35/13.50 inference(monotonicity,[status(thm)],[4308])).
% 13.35/13.50 tff(4310,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s6)) | (~trans(s6, s7)) | always5(s7))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s6, s7)) | (~always5(s6)) | always5(s7))),
% 13.35/13.50 inference(transitivity,[status(thm)],[4309, 4307])).
% 13.35/13.50 tff(4311,plain,
% 13.35/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s6)) | (~trans(s6, s7)) | always5(s7))),
% 13.35/13.50 inference(quant_inst,[status(thm)],[])).
% 13.35/13.50 tff(4312,plain,
% 13.35/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s6, s7)) | (~always5(s6)) | always5(s7)),
% 13.35/13.50 inference(modus_ponens,[status(thm)],[4311, 4310])).
% 13.35/13.50 tff(4313,plain,
% 13.35/13.50 ((~always5(s6)) | always5(s7)),
% 13.35/13.50 inference(unit_resolution,[status(thm)],[4312, 3890, 253])).
% 13.35/13.50 tff(4314,plain,
% 13.35/13.50 (~always5(s6)),
% 13.35/13.50 inference(unit_resolution,[status(thm)],[4313, 4306])).
% 13.35/13.50 tff(4315,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s5, s6)) | (~always5(s5)) | always5(s6))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s5, s6)) | (~always5(s5)) | always5(s6))),
% 13.35/13.50 inference(rewrite,[status(thm)],[])).
% 13.35/13.50 tff(4316,plain,
% 13.35/13.50 (((~always5(s5)) | (~trans(s5, s6)) | always5(s6)) <=> ((~trans(s5, s6)) | (~always5(s5)) | always5(s6))),
% 13.35/13.50 inference(rewrite,[status(thm)],[])).
% 13.35/13.50 tff(4317,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s5)) | (~trans(s5, s6)) | always5(s6))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s5, s6)) | (~always5(s5)) | always5(s6)))),
% 13.35/13.50 inference(monotonicity,[status(thm)],[4316])).
% 13.35/13.50 tff(4318,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s5)) | (~trans(s5, s6)) | always5(s6))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s5, s6)) | (~always5(s5)) | always5(s6))),
% 13.35/13.50 inference(transitivity,[status(thm)],[4317, 4315])).
% 13.35/13.50 tff(4319,plain,
% 13.35/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s5)) | (~trans(s5, s6)) | always5(s6))),
% 13.35/13.50 inference(quant_inst,[status(thm)],[])).
% 13.35/13.50 tff(4320,plain,
% 13.35/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s5, s6)) | (~always5(s5)) | always5(s6)),
% 13.35/13.50 inference(modus_ponens,[status(thm)],[4319, 4318])).
% 13.35/13.50 tff(4321,plain,
% 13.35/13.50 ((~always5(s5)) | always5(s6)),
% 13.35/13.50 inference(unit_resolution,[status(thm)],[4320, 3890, 224])).
% 13.35/13.50 tff(4322,plain,
% 13.35/13.50 (~always5(s5)),
% 13.35/13.50 inference(unit_resolution,[status(thm)],[4321, 4314])).
% 13.35/13.50 tff(4323,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s4, s5)) | (~always5(s4)) | always5(s5))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s4, s5)) | (~always5(s4)) | always5(s5))),
% 13.35/13.50 inference(rewrite,[status(thm)],[])).
% 13.35/13.50 tff(4324,plain,
% 13.35/13.50 (((~always5(s4)) | (~trans(s4, s5)) | always5(s5)) <=> ((~trans(s4, s5)) | (~always5(s4)) | always5(s5))),
% 13.35/13.50 inference(rewrite,[status(thm)],[])).
% 13.35/13.50 tff(4325,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s4)) | (~trans(s4, s5)) | always5(s5))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s4, s5)) | (~always5(s4)) | always5(s5)))),
% 13.35/13.50 inference(monotonicity,[status(thm)],[4324])).
% 13.35/13.50 tff(4326,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s4)) | (~trans(s4, s5)) | always5(s5))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s4, s5)) | (~always5(s4)) | always5(s5))),
% 13.35/13.50 inference(transitivity,[status(thm)],[4325, 4323])).
% 13.35/13.50 tff(4327,plain,
% 13.35/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s4)) | (~trans(s4, s5)) | always5(s5))),
% 13.35/13.50 inference(quant_inst,[status(thm)],[])).
% 13.35/13.50 tff(4328,plain,
% 13.35/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s4, s5)) | (~always5(s4)) | always5(s5)),
% 13.35/13.50 inference(modus_ponens,[status(thm)],[4327, 4326])).
% 13.35/13.50 tff(4329,plain,
% 13.35/13.50 ((~always5(s4)) | always5(s5)),
% 13.35/13.50 inference(unit_resolution,[status(thm)],[4328, 3890, 198])).
% 13.35/13.50 tff(4330,plain,
% 13.35/13.50 (~always5(s4)),
% 13.35/13.50 inference(unit_resolution,[status(thm)],[4329, 4322])).
% 13.35/13.50 tff(4331,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s3, s4)) | (~always5(s3)) | always5(s4))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s3, s4)) | (~always5(s3)) | always5(s4))),
% 13.35/13.50 inference(rewrite,[status(thm)],[])).
% 13.35/13.50 tff(4332,plain,
% 13.35/13.50 (((~always5(s3)) | (~trans(s3, s4)) | always5(s4)) <=> ((~trans(s3, s4)) | (~always5(s3)) | always5(s4))),
% 13.35/13.50 inference(rewrite,[status(thm)],[])).
% 13.35/13.50 tff(4333,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s3)) | (~trans(s3, s4)) | always5(s4))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s3, s4)) | (~always5(s3)) | always5(s4)))),
% 13.35/13.50 inference(monotonicity,[status(thm)],[4332])).
% 13.35/13.50 tff(4334,plain,
% 13.35/13.50 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s3)) | (~trans(s3, s4)) | always5(s4))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s3, s4)) | (~always5(s3)) | always5(s4))),
% 13.35/13.50 inference(transitivity,[status(thm)],[4333, 4331])).
% 13.35/13.50 tff(4335,plain,
% 13.35/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s3)) | (~trans(s3, s4)) | always5(s4))),
% 13.35/13.50 inference(quant_inst,[status(thm)],[])).
% 13.35/13.50 tff(4336,plain,
% 13.35/13.50 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s3, s4)) | (~always5(s3)) | always5(s4)),
% 13.35/13.50 inference(modus_ponens,[status(thm)],[4335, 4334])).
% 13.35/13.50 tff(4337,plain,
% 13.35/13.51 ((~always5(s3)) | always5(s4)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4336, 3890, 169])).
% 13.35/13.51 tff(4338,plain,
% 13.35/13.51 (~always5(s3)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4337, 4330])).
% 13.35/13.51 tff(4339,plain,
% 13.35/13.51 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s2, s3)) | (~always5(s2)) | always5(s3))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s2, s3)) | (~always5(s2)) | always5(s3))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4340,plain,
% 13.35/13.51 (((~always5(s2)) | (~trans(s2, s3)) | always5(s3)) <=> ((~trans(s2, s3)) | (~always5(s2)) | always5(s3))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4341,plain,
% 13.35/13.51 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s2)) | (~trans(s2, s3)) | always5(s3))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s2, s3)) | (~always5(s2)) | always5(s3)))),
% 13.35/13.51 inference(monotonicity,[status(thm)],[4340])).
% 13.35/13.51 tff(4342,plain,
% 13.35/13.51 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s2)) | (~trans(s2, s3)) | always5(s3))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s2, s3)) | (~always5(s2)) | always5(s3))),
% 13.35/13.51 inference(transitivity,[status(thm)],[4341, 4339])).
% 13.35/13.51 tff(4343,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s2)) | (~trans(s2, s3)) | always5(s3))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4344,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s2, s3)) | (~always5(s2)) | always5(s3)),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4343, 4342])).
% 13.35/13.51 tff(4345,plain,
% 13.35/13.51 ((~always5(s2)) | always5(s3)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4344, 3890, 143])).
% 13.35/13.51 tff(4346,plain,
% 13.35/13.51 (~always5(s2)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4345, 4338])).
% 13.35/13.51 tff(4347,plain,
% 13.35/13.51 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s1, s2)) | (~always5(s1)) | always5(s2))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s1, s2)) | (~always5(s1)) | always5(s2))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4348,plain,
% 13.35/13.51 (((~always5(s1)) | (~trans(s1, s2)) | always5(s2)) <=> ((~trans(s1, s2)) | (~always5(s1)) | always5(s2))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4349,plain,
% 13.35/13.51 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s1)) | (~trans(s1, s2)) | always5(s2))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s1, s2)) | (~always5(s1)) | always5(s2)))),
% 13.35/13.51 inference(monotonicity,[status(thm)],[4348])).
% 13.35/13.51 tff(4350,plain,
% 13.35/13.51 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s1)) | (~trans(s1, s2)) | always5(s2))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s1, s2)) | (~always5(s1)) | always5(s2))),
% 13.35/13.51 inference(transitivity,[status(thm)],[4349, 4347])).
% 13.35/13.51 tff(4351,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s1)) | (~trans(s1, s2)) | always5(s2))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4352,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s1, s2)) | (~always5(s1)) | always5(s2)),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4351, 4350])).
% 13.35/13.51 tff(4353,plain,
% 13.35/13.51 ((~always5(s1)) | always5(s2)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4352, 3890, 106])).
% 13.35/13.51 tff(4354,plain,
% 13.35/13.51 (~always5(s1)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4353, 4346])).
% 13.35/13.51 tff(4355,plain,
% 13.35/13.51 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s0, s1)) | (~always5(s0)) | always5(s1))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s0, s1)) | (~always5(s0)) | always5(s1))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4356,plain,
% 13.35/13.51 (((~always5(s0)) | (~trans(s0, s1)) | always5(s1)) <=> ((~trans(s0, s1)) | (~always5(s0)) | always5(s1))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4357,plain,
% 13.35/13.51 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s0)) | (~trans(s0, s1)) | always5(s1))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s0, s1)) | (~always5(s0)) | always5(s1)))),
% 13.35/13.51 inference(monotonicity,[status(thm)],[4356])).
% 13.35/13.51 tff(4358,plain,
% 13.35/13.51 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s0)) | (~trans(s0, s1)) | always5(s1))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s0, s1)) | (~always5(s0)) | always5(s1))),
% 13.35/13.51 inference(transitivity,[status(thm)],[4357, 4355])).
% 13.35/13.51 tff(4359,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s0)) | (~trans(s0, s1)) | always5(s1))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4360,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s0, s1)) | (~always5(s0)) | always5(s1)),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4359, 4358])).
% 13.35/13.51 tff(4361,plain,
% 13.35/13.51 ((~always5(s0)) | always5(s1)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4360, 3890, 52])).
% 13.35/13.51 tff(4362,plain,
% 13.35/13.51 (~always5(s0)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4361, 4354])).
% 13.35/13.51 tff(4363,plain,
% 13.35/13.51 (until6(s0) <=> until6(s0)),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4364,axiom,(until6(s0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty11')).
% 13.35/13.51 tff(4365,plain,
% 13.35/13.51 (until6(s0)),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4364, 4363])).
% 13.35/13.51 tff(4366,plain,
% 13.35/13.51 (^[X: $i] : refl((always5(X) | (~until6(X)) | xuntil7(X)) <=> (always5(X) | (~until6(X)) | xuntil7(X)))),
% 13.35/13.51 inference(bind,[status(th)],[])).
% 13.35/13.51 tff(4367,plain,
% 13.35/13.51 (![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X)) <=> ![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 13.35/13.51 inference(quant_intro,[status(thm)],[4366])).
% 13.35/13.51 tff(4368,plain,
% 13.35/13.51 (![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X)) <=> ![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4369,plain,
% 13.35/13.51 (^[X: $i] : rewrite(((always5(X) | xuntil7(X)) | (~until6(X))) <=> (always5(X) | (~until6(X)) | xuntil7(X)))),
% 13.35/13.51 inference(bind,[status(th)],[])).
% 13.35/13.51 tff(4370,plain,
% 13.35/13.51 (![X: $i] : ((always5(X) | xuntil7(X)) | (~until6(X))) <=> ![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 13.35/13.51 inference(quant_intro,[status(thm)],[4369])).
% 13.35/13.51 tff(4371,axiom,(![X: $i] : ((always5(X) | xuntil7(X)) | (~until6(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty4')).
% 13.35/13.51 tff(4372,plain,
% 13.35/13.51 (![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4371, 4370])).
% 13.35/13.51 tff(4373,plain,
% 13.35/13.51 (![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4372, 4368])).
% 13.35/13.51 tff(4374,plain,(
% 13.35/13.51 ![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 13.35/13.51 inference(skolemize,[status(sab)],[4373])).
% 13.35/13.51 tff(4375,plain,
% 13.35/13.51 (![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4374, 4367])).
% 13.35/13.51 tff(4376,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s0) | always5(s0) | (~until6(s0)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s0) | always5(s0) | (~until6(s0)))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4377,plain,
% 13.35/13.51 ((always5(s0) | (~until6(s0)) | xuntil7(s0)) <=> (xuntil7(s0) | always5(s0) | (~until6(s0)))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4378,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s0) | (~until6(s0)) | xuntil7(s0))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s0) | always5(s0) | (~until6(s0))))),
% 13.35/13.51 inference(monotonicity,[status(thm)],[4377])).
% 13.35/13.51 tff(4379,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s0) | (~until6(s0)) | xuntil7(s0))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s0) | always5(s0) | (~until6(s0)))),
% 13.35/13.51 inference(transitivity,[status(thm)],[4378, 4376])).
% 13.35/13.51 tff(4380,plain,
% 13.35/13.51 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s0) | (~until6(s0)) | xuntil7(s0))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4381,plain,
% 13.35/13.51 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s0) | always5(s0) | (~until6(s0))),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4380, 4379])).
% 13.35/13.51 tff(4382,plain,
% 13.35/13.51 (xuntil7(s0) | always5(s0)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4381, 4375, 4365])).
% 13.35/13.51 tff(4383,plain,
% 13.35/13.51 (xuntil7(s0)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4382, 4362])).
% 13.35/13.51 tff(4384,plain,
% 13.35/13.51 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | (~xuntil7(X)) | until6(Y)) <=> ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y)))),
% 13.35/13.51 inference(bind,[status(th)],[])).
% 13.35/13.51 tff(4385,plain,
% 13.35/13.51 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 13.35/13.51 inference(quant_intro,[status(thm)],[4384])).
% 13.35/13.51 tff(4386,plain,
% 13.35/13.51 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4387,plain,
% 13.35/13.51 (^[Y: $i, X: $i] : rewrite(((until6(Y) | (~succ(X, Y))) | (~xuntil7(X))) <=> ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y)))),
% 13.35/13.51 inference(bind,[status(th)],[])).
% 13.35/13.51 tff(4388,plain,
% 13.35/13.51 (![Y: $i, X: $i] : ((until6(Y) | (~succ(X, Y))) | (~xuntil7(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 13.35/13.51 inference(quant_intro,[status(thm)],[4387])).
% 13.35/13.51 tff(4389,axiom,(![Y: $i, X: $i] : ((until6(Y) | (~succ(X, Y))) | (~xuntil7(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty5')).
% 13.35/13.51 tff(4390,plain,
% 13.35/13.51 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4389, 4388])).
% 13.35/13.51 tff(4391,plain,
% 13.35/13.51 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4390, 4386])).
% 13.35/13.51 tff(4392,plain,(
% 13.35/13.51 ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 13.35/13.51 inference(skolemize,[status(sab)],[4391])).
% 13.35/13.51 tff(4393,plain,
% 13.35/13.51 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4392, 4385])).
% 13.35/13.51 tff(4394,plain,
% 13.35/13.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s0, s1)) | (~xuntil7(s0)) | until6(s1))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s0, s1)) | (~xuntil7(s0)) | until6(s1))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4395,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s0, s1)) | (~xuntil7(s0)) | until6(s1))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4396,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s0, s1)) | (~xuntil7(s0)) | until6(s1)),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4395, 4394])).
% 13.35/13.51 tff(4397,plain,
% 13.35/13.51 ((~xuntil7(s0)) | until6(s1)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4396, 48, 4393])).
% 13.35/13.51 tff(4398,plain,
% 13.35/13.51 (until6(s1)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4397, 4383])).
% 13.35/13.51 tff(4399,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s1) | always5(s1) | (~until6(s1)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s1) | always5(s1) | (~until6(s1)))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4400,plain,
% 13.35/13.51 ((always5(s1) | (~until6(s1)) | xuntil7(s1)) <=> (xuntil7(s1) | always5(s1) | (~until6(s1)))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4401,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s1) | (~until6(s1)) | xuntil7(s1))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s1) | always5(s1) | (~until6(s1))))),
% 13.35/13.51 inference(monotonicity,[status(thm)],[4400])).
% 13.35/13.51 tff(4402,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s1) | (~until6(s1)) | xuntil7(s1))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s1) | always5(s1) | (~until6(s1)))),
% 13.35/13.51 inference(transitivity,[status(thm)],[4401, 4399])).
% 13.35/13.51 tff(4403,plain,
% 13.35/13.51 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s1) | (~until6(s1)) | xuntil7(s1))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4404,plain,
% 13.35/13.51 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s1) | always5(s1) | (~until6(s1))),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4403, 4402])).
% 13.35/13.51 tff(4405,plain,
% 13.35/13.51 (xuntil7(s1)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4404, 4375, 4398, 4354])).
% 13.35/13.51 tff(4406,plain,
% 13.35/13.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s1, s2)) | (~xuntil7(s1)) | until6(s2))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s1, s2)) | (~xuntil7(s1)) | until6(s2))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4407,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s1, s2)) | (~xuntil7(s1)) | until6(s2))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4408,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s1, s2)) | (~xuntil7(s1)) | until6(s2)),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4407, 4406])).
% 13.35/13.51 tff(4409,plain,
% 13.35/13.51 ((~xuntil7(s1)) | until6(s2)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4408, 102, 4393])).
% 13.35/13.51 tff(4410,plain,
% 13.35/13.51 (until6(s2)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4409, 4405])).
% 13.35/13.51 tff(4411,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s2) | always5(s2) | (~until6(s2)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s2) | always5(s2) | (~until6(s2)))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4412,plain,
% 13.35/13.51 ((always5(s2) | (~until6(s2)) | xuntil7(s2)) <=> (xuntil7(s2) | always5(s2) | (~until6(s2)))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4413,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s2) | (~until6(s2)) | xuntil7(s2))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s2) | always5(s2) | (~until6(s2))))),
% 13.35/13.51 inference(monotonicity,[status(thm)],[4412])).
% 13.35/13.51 tff(4414,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s2) | (~until6(s2)) | xuntil7(s2))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s2) | always5(s2) | (~until6(s2)))),
% 13.35/13.51 inference(transitivity,[status(thm)],[4413, 4411])).
% 13.35/13.51 tff(4415,plain,
% 13.35/13.51 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s2) | (~until6(s2)) | xuntil7(s2))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4416,plain,
% 13.35/13.51 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s2) | always5(s2) | (~until6(s2))),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4415, 4414])).
% 13.35/13.51 tff(4417,plain,
% 13.35/13.51 (xuntil7(s2) | (~until6(s2))),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4416, 4375, 4346])).
% 13.35/13.51 tff(4418,plain,
% 13.35/13.51 (xuntil7(s2)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4417, 4410])).
% 13.35/13.51 tff(4419,plain,
% 13.35/13.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s2, s3)) | (~xuntil7(s2)) | until6(s3))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s2, s3)) | (~xuntil7(s2)) | until6(s3))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4420,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s2, s3)) | (~xuntil7(s2)) | until6(s3))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4421,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s2, s3)) | (~xuntil7(s2)) | until6(s3)),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4420, 4419])).
% 13.35/13.51 tff(4422,plain,
% 13.35/13.51 ((~xuntil7(s2)) | until6(s3)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4421, 139, 4393])).
% 13.35/13.51 tff(4423,plain,
% 13.35/13.51 (until6(s3)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4422, 4418])).
% 13.35/13.51 tff(4424,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s3) | always5(s3) | (~until6(s3)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s3) | always5(s3) | (~until6(s3)))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4425,plain,
% 13.35/13.51 ((always5(s3) | (~until6(s3)) | xuntil7(s3)) <=> (xuntil7(s3) | always5(s3) | (~until6(s3)))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4426,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s3) | (~until6(s3)) | xuntil7(s3))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s3) | always5(s3) | (~until6(s3))))),
% 13.35/13.51 inference(monotonicity,[status(thm)],[4425])).
% 13.35/13.51 tff(4427,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s3) | (~until6(s3)) | xuntil7(s3))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s3) | always5(s3) | (~until6(s3)))),
% 13.35/13.51 inference(transitivity,[status(thm)],[4426, 4424])).
% 13.35/13.51 tff(4428,plain,
% 13.35/13.51 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s3) | (~until6(s3)) | xuntil7(s3))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4429,plain,
% 13.35/13.51 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s3) | always5(s3) | (~until6(s3))),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4428, 4427])).
% 13.35/13.51 tff(4430,plain,
% 13.35/13.51 (xuntil7(s3) | (~until6(s3))),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4429, 4375, 4338])).
% 13.35/13.51 tff(4431,plain,
% 13.35/13.51 (xuntil7(s3)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4430, 4423])).
% 13.35/13.51 tff(4432,plain,
% 13.35/13.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s3, s4)) | (~xuntil7(s3)) | until6(s4))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s3, s4)) | (~xuntil7(s3)) | until6(s4))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4433,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s3, s4)) | (~xuntil7(s3)) | until6(s4))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4434,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s3, s4)) | (~xuntil7(s3)) | until6(s4)),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4433, 4432])).
% 13.35/13.51 tff(4435,plain,
% 13.35/13.51 ((~xuntil7(s3)) | until6(s4)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4434, 165, 4393])).
% 13.35/13.51 tff(4436,plain,
% 13.35/13.51 (until6(s4)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4435, 4431])).
% 13.35/13.51 tff(4437,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s4) | always5(s4) | (~until6(s4)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s4) | always5(s4) | (~until6(s4)))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4438,plain,
% 13.35/13.51 ((always5(s4) | (~until6(s4)) | xuntil7(s4)) <=> (xuntil7(s4) | always5(s4) | (~until6(s4)))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4439,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s4) | (~until6(s4)) | xuntil7(s4))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s4) | always5(s4) | (~until6(s4))))),
% 13.35/13.51 inference(monotonicity,[status(thm)],[4438])).
% 13.35/13.51 tff(4440,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s4) | (~until6(s4)) | xuntil7(s4))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s4) | always5(s4) | (~until6(s4)))),
% 13.35/13.51 inference(transitivity,[status(thm)],[4439, 4437])).
% 13.35/13.51 tff(4441,plain,
% 13.35/13.51 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s4) | (~until6(s4)) | xuntil7(s4))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4442,plain,
% 13.35/13.51 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s4) | always5(s4) | (~until6(s4))),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4441, 4440])).
% 13.35/13.51 tff(4443,plain,
% 13.35/13.51 (xuntil7(s4) | (~until6(s4))),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4442, 4375, 4330])).
% 13.35/13.51 tff(4444,plain,
% 13.35/13.51 (xuntil7(s4)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4443, 4436])).
% 13.35/13.51 tff(4445,plain,
% 13.35/13.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s4, s5)) | (~xuntil7(s4)) | until6(s5))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s4, s5)) | (~xuntil7(s4)) | until6(s5))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4446,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s4, s5)) | (~xuntil7(s4)) | until6(s5))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4447,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s4, s5)) | (~xuntil7(s4)) | until6(s5)),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4446, 4445])).
% 13.35/13.51 tff(4448,plain,
% 13.35/13.51 ((~xuntil7(s4)) | until6(s5)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4447, 194, 4393])).
% 13.35/13.51 tff(4449,plain,
% 13.35/13.51 (until6(s5)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4448, 4444])).
% 13.35/13.51 tff(4450,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s5) | always5(s5) | (~until6(s5)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s5) | always5(s5) | (~until6(s5)))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4451,plain,
% 13.35/13.51 ((always5(s5) | (~until6(s5)) | xuntil7(s5)) <=> (xuntil7(s5) | always5(s5) | (~until6(s5)))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4452,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s5) | (~until6(s5)) | xuntil7(s5))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s5) | always5(s5) | (~until6(s5))))),
% 13.35/13.51 inference(monotonicity,[status(thm)],[4451])).
% 13.35/13.51 tff(4453,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s5) | (~until6(s5)) | xuntil7(s5))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s5) | always5(s5) | (~until6(s5)))),
% 13.35/13.51 inference(transitivity,[status(thm)],[4452, 4450])).
% 13.35/13.51 tff(4454,plain,
% 13.35/13.51 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s5) | (~until6(s5)) | xuntil7(s5))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4455,plain,
% 13.35/13.51 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s5) | always5(s5) | (~until6(s5))),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4454, 4453])).
% 13.35/13.51 tff(4456,plain,
% 13.35/13.51 (xuntil7(s5) | (~until6(s5))),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4455, 4375, 4322])).
% 13.35/13.51 tff(4457,plain,
% 13.35/13.51 (xuntil7(s5)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4456, 4449])).
% 13.35/13.51 tff(4458,plain,
% 13.35/13.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s5, s6)) | (~xuntil7(s5)) | until6(s6))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s5, s6)) | (~xuntil7(s5)) | until6(s6))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4459,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s5, s6)) | (~xuntil7(s5)) | until6(s6))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4460,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s5, s6)) | (~xuntil7(s5)) | until6(s6)),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4459, 4458])).
% 13.35/13.51 tff(4461,plain,
% 13.35/13.51 ((~xuntil7(s5)) | until6(s6)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4460, 220, 4393])).
% 13.35/13.51 tff(4462,plain,
% 13.35/13.51 (until6(s6)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4461, 4457])).
% 13.35/13.51 tff(4463,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s6) | always5(s6) | (~until6(s6)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s6) | always5(s6) | (~until6(s6)))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4464,plain,
% 13.35/13.51 ((always5(s6) | (~until6(s6)) | xuntil7(s6)) <=> (xuntil7(s6) | always5(s6) | (~until6(s6)))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4465,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s6) | (~until6(s6)) | xuntil7(s6))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s6) | always5(s6) | (~until6(s6))))),
% 13.35/13.51 inference(monotonicity,[status(thm)],[4464])).
% 13.35/13.51 tff(4466,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s6) | (~until6(s6)) | xuntil7(s6))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s6) | always5(s6) | (~until6(s6)))),
% 13.35/13.51 inference(transitivity,[status(thm)],[4465, 4463])).
% 13.35/13.51 tff(4467,plain,
% 13.35/13.51 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s6) | (~until6(s6)) | xuntil7(s6))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4468,plain,
% 13.35/13.51 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s6) | always5(s6) | (~until6(s6))),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4467, 4466])).
% 13.35/13.51 tff(4469,plain,
% 13.35/13.51 (xuntil7(s6) | (~until6(s6))),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4468, 4375, 4314])).
% 13.35/13.51 tff(4470,plain,
% 13.35/13.51 (xuntil7(s6)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4469, 4462])).
% 13.35/13.51 tff(4471,plain,
% 13.35/13.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s6, s7)) | (~xuntil7(s6)) | until6(s7))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s6, s7)) | (~xuntil7(s6)) | until6(s7))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4472,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s6, s7)) | (~xuntil7(s6)) | until6(s7))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4473,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s6, s7)) | (~xuntil7(s6)) | until6(s7)),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4472, 4471])).
% 13.35/13.51 tff(4474,plain,
% 13.35/13.51 ((~xuntil7(s6)) | until6(s7)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4473, 249, 4393])).
% 13.35/13.51 tff(4475,plain,
% 13.35/13.51 (until6(s7)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4474, 4470])).
% 13.35/13.51 tff(4476,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s7) | always5(s7) | (~until6(s7)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s7) | always5(s7) | (~until6(s7)))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4477,plain,
% 13.35/13.51 ((always5(s7) | (~until6(s7)) | xuntil7(s7)) <=> (xuntil7(s7) | always5(s7) | (~until6(s7)))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4478,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s7) | (~until6(s7)) | xuntil7(s7))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s7) | always5(s7) | (~until6(s7))))),
% 13.35/13.51 inference(monotonicity,[status(thm)],[4477])).
% 13.35/13.51 tff(4479,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s7) | (~until6(s7)) | xuntil7(s7))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s7) | always5(s7) | (~until6(s7)))),
% 13.35/13.51 inference(transitivity,[status(thm)],[4478, 4476])).
% 13.35/13.51 tff(4480,plain,
% 13.35/13.51 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s7) | (~until6(s7)) | xuntil7(s7))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4481,plain,
% 13.35/13.51 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s7) | always5(s7) | (~until6(s7))),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4480, 4479])).
% 13.35/13.51 tff(4482,plain,
% 13.35/13.51 (xuntil7(s7) | (~until6(s7))),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4481, 4375, 4306])).
% 13.35/13.51 tff(4483,plain,
% 13.35/13.51 (xuntil7(s7)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4482, 4475])).
% 13.35/13.51 tff(4484,plain,
% 13.35/13.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s7, s8)) | (~xuntil7(s7)) | until6(s8))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s7, s8)) | (~xuntil7(s7)) | until6(s8))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4485,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s7, s8)) | (~xuntil7(s7)) | until6(s8))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4486,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s7, s8)) | (~xuntil7(s7)) | until6(s8)),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4485, 4484])).
% 13.35/13.51 tff(4487,plain,
% 13.35/13.51 ((~xuntil7(s7)) | until6(s8)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4486, 275, 4393])).
% 13.35/13.51 tff(4488,plain,
% 13.35/13.51 (until6(s8)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4487, 4483])).
% 13.35/13.51 tff(4489,assumption,(~always5(s15)), introduced(assumption)).
% 13.35/13.51 tff(4490,plain,
% 13.35/13.51 (~always5(s14)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4249, 4489])).
% 13.35/13.51 tff(4491,assumption,(~xuntil7(s15)), introduced(assumption)).
% 13.35/13.51 tff(4492,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s15) | always5(s15) | (~until6(s15)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s15) | always5(s15) | (~until6(s15)))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4493,plain,
% 13.35/13.51 ((always5(s15) | (~until6(s15)) | xuntil7(s15)) <=> (xuntil7(s15) | always5(s15) | (~until6(s15)))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4494,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s15) | (~until6(s15)) | xuntil7(s15))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s15) | always5(s15) | (~until6(s15))))),
% 13.35/13.51 inference(monotonicity,[status(thm)],[4493])).
% 13.35/13.51 tff(4495,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s15) | (~until6(s15)) | xuntil7(s15))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s15) | always5(s15) | (~until6(s15)))),
% 13.35/13.51 inference(transitivity,[status(thm)],[4494, 4492])).
% 13.35/13.51 tff(4496,plain,
% 13.35/13.51 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s15) | (~until6(s15)) | xuntil7(s15))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4497,plain,
% 13.35/13.51 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s15) | always5(s15) | (~until6(s15))),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4496, 4495])).
% 13.35/13.51 tff(4498,plain,
% 13.35/13.51 (always5(s15) | (~until6(s15))),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4497, 4375, 4491])).
% 13.35/13.51 tff(4499,plain,
% 13.35/13.51 (~until6(s15)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4498, 4489])).
% 13.35/13.51 tff(4500,plain,
% 13.35/13.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s14, s15)) | (~xuntil7(s14)) | until6(s15))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s14, s15)) | (~xuntil7(s14)) | until6(s15))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4501,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s14, s15)) | (~xuntil7(s14)) | until6(s15))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4502,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s14, s15)) | (~xuntil7(s14)) | until6(s15)),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4501, 4500])).
% 13.35/13.51 tff(4503,plain,
% 13.35/13.51 ((~xuntil7(s14)) | until6(s15)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4502, 469, 4393])).
% 13.35/13.51 tff(4504,plain,
% 13.35/13.51 (~xuntil7(s14)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4503, 4499])).
% 13.35/13.51 tff(4505,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s14) | always5(s14) | (~until6(s14)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s14) | always5(s14) | (~until6(s14)))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4506,plain,
% 13.35/13.51 ((always5(s14) | (~until6(s14)) | xuntil7(s14)) <=> (xuntil7(s14) | always5(s14) | (~until6(s14)))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4507,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s14) | (~until6(s14)) | xuntil7(s14))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s14) | always5(s14) | (~until6(s14))))),
% 13.35/13.51 inference(monotonicity,[status(thm)],[4506])).
% 13.35/13.51 tff(4508,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s14) | (~until6(s14)) | xuntil7(s14))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s14) | always5(s14) | (~until6(s14)))),
% 13.35/13.51 inference(transitivity,[status(thm)],[4507, 4505])).
% 13.35/13.51 tff(4509,plain,
% 13.35/13.51 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s14) | (~until6(s14)) | xuntil7(s14))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4510,plain,
% 13.35/13.51 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s14) | always5(s14) | (~until6(s14))),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4509, 4508])).
% 13.35/13.51 tff(4511,plain,
% 13.35/13.51 (~until6(s14)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4510, 4375, 4504, 4490])).
% 13.35/13.51 tff(4512,plain,
% 13.35/13.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s13, s14)) | (~xuntil7(s13)) | until6(s14))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s13, s14)) | (~xuntil7(s13)) | until6(s14))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4513,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s13, s14)) | (~xuntil7(s13)) | until6(s14))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4514,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s13, s14)) | (~xuntil7(s13)) | until6(s14)),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4513, 4512])).
% 13.35/13.51 tff(4515,plain,
% 13.35/13.51 ((~xuntil7(s13)) | until6(s14)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4514, 440, 4393])).
% 13.35/13.51 tff(4516,plain,
% 13.35/13.51 (~xuntil7(s13)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4515, 4511])).
% 13.35/13.51 tff(4517,plain,
% 13.35/13.51 (~always5(s13)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4257, 4490])).
% 13.35/13.51 tff(4518,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s13) | always5(s13) | (~until6(s13)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s13) | always5(s13) | (~until6(s13)))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4519,plain,
% 13.35/13.51 ((always5(s13) | (~until6(s13)) | xuntil7(s13)) <=> (xuntil7(s13) | always5(s13) | (~until6(s13)))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4520,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s13) | (~until6(s13)) | xuntil7(s13))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s13) | always5(s13) | (~until6(s13))))),
% 13.35/13.51 inference(monotonicity,[status(thm)],[4519])).
% 13.35/13.51 tff(4521,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s13) | (~until6(s13)) | xuntil7(s13))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s13) | always5(s13) | (~until6(s13)))),
% 13.35/13.51 inference(transitivity,[status(thm)],[4520, 4518])).
% 13.35/13.51 tff(4522,plain,
% 13.35/13.51 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s13) | (~until6(s13)) | xuntil7(s13))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4523,plain,
% 13.35/13.51 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s13) | always5(s13) | (~until6(s13))),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4522, 4521])).
% 13.35/13.51 tff(4524,plain,
% 13.35/13.51 (xuntil7(s13) | (~until6(s13))),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4523, 4375, 4517])).
% 13.35/13.51 tff(4525,plain,
% 13.35/13.51 (~until6(s13)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4524, 4516])).
% 13.35/13.51 tff(4526,plain,
% 13.35/13.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s12, s13)) | (~xuntil7(s12)) | until6(s13))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s12, s13)) | (~xuntil7(s12)) | until6(s13))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4527,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s12, s13)) | (~xuntil7(s12)) | until6(s13))),
% 13.35/13.51 inference(quant_inst,[status(thm)],[])).
% 13.35/13.51 tff(4528,plain,
% 13.35/13.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s12, s13)) | (~xuntil7(s12)) | until6(s13)),
% 13.35/13.51 inference(modus_ponens,[status(thm)],[4527, 4526])).
% 13.35/13.51 tff(4529,plain,
% 13.35/13.51 ((~xuntil7(s12)) | until6(s13)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4528, 414, 4393])).
% 13.35/13.51 tff(4530,plain,
% 13.35/13.51 (~xuntil7(s12)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4529, 4525])).
% 13.35/13.51 tff(4531,plain,
% 13.35/13.51 (~always5(s12)),
% 13.35/13.51 inference(unit_resolution,[status(thm)],[4265, 4517])).
% 13.35/13.51 tff(4532,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s12) | always5(s12) | (~until6(s12)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s12) | always5(s12) | (~until6(s12)))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4533,plain,
% 13.35/13.51 ((always5(s12) | (~until6(s12)) | xuntil7(s12)) <=> (xuntil7(s12) | always5(s12) | (~until6(s12)))),
% 13.35/13.51 inference(rewrite,[status(thm)],[])).
% 13.35/13.51 tff(4534,plain,
% 13.35/13.51 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s12) | (~until6(s12)) | xuntil7(s12))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s12) | always5(s12) | (~until6(s12))))),
% 13.35/13.51 inference(monotonicity,[status(thm)],[4533])).
% 13.35/13.52 tff(4535,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s12) | (~until6(s12)) | xuntil7(s12))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s12) | always5(s12) | (~until6(s12)))),
% 13.35/13.52 inference(transitivity,[status(thm)],[4534, 4532])).
% 13.35/13.52 tff(4536,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s12) | (~until6(s12)) | xuntil7(s12))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4537,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s12) | always5(s12) | (~until6(s12))),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4536, 4535])).
% 13.35/13.52 tff(4538,plain,
% 13.35/13.52 (xuntil7(s12) | (~until6(s12))),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4537, 4375, 4531])).
% 13.35/13.52 tff(4539,plain,
% 13.35/13.52 (~until6(s12)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4538, 4530])).
% 13.35/13.52 tff(4540,plain,
% 13.35/13.52 (~always5(s11)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4273, 4531])).
% 13.35/13.52 tff(4541,plain,
% 13.35/13.52 (~always5(s10)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4281, 4540])).
% 13.35/13.52 tff(4542,plain,
% 13.35/13.52 (~always5(s9)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4289, 4541])).
% 13.35/13.52 tff(4543,plain,
% 13.35/13.52 (~always5(s8)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4297, 4542])).
% 13.35/13.52 tff(4544,assumption,(until6(s8)), introduced(assumption)).
% 13.35/13.52 tff(4545,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s8) | always5(s8) | (~until6(s8)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s8) | always5(s8) | (~until6(s8)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4546,plain,
% 13.35/13.52 ((always5(s8) | (~until6(s8)) | xuntil7(s8)) <=> (xuntil7(s8) | always5(s8) | (~until6(s8)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4547,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s8) | (~until6(s8)) | xuntil7(s8))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s8) | always5(s8) | (~until6(s8))))),
% 13.35/13.52 inference(monotonicity,[status(thm)],[4546])).
% 13.35/13.52 tff(4548,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s8) | (~until6(s8)) | xuntil7(s8))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s8) | always5(s8) | (~until6(s8)))),
% 13.35/13.52 inference(transitivity,[status(thm)],[4547, 4545])).
% 13.35/13.52 tff(4549,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s8) | (~until6(s8)) | xuntil7(s8))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4550,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s8) | always5(s8) | (~until6(s8))),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4549, 4548])).
% 13.35/13.52 tff(4551,plain,
% 13.35/13.52 (xuntil7(s8) | always5(s8)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4550, 4375, 4544])).
% 13.35/13.52 tff(4552,plain,
% 13.35/13.52 (xuntil7(s8)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4551, 4543])).
% 13.35/13.52 tff(4553,plain,
% 13.35/13.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s8, s9)) | (~xuntil7(s8)) | until6(s9))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s8, s9)) | (~xuntil7(s8)) | until6(s9))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4554,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s8, s9)) | (~xuntil7(s8)) | until6(s9))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4555,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s8, s9)) | (~xuntil7(s8)) | until6(s9)),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4554, 4553])).
% 13.35/13.52 tff(4556,plain,
% 13.35/13.52 ((~xuntil7(s8)) | until6(s9)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4555, 304, 4393])).
% 13.35/13.52 tff(4557,plain,
% 13.35/13.52 (until6(s9)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4556, 4552])).
% 13.35/13.52 tff(4558,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s9) | always5(s9) | (~until6(s9)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s9) | always5(s9) | (~until6(s9)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4559,plain,
% 13.35/13.52 ((always5(s9) | (~until6(s9)) | xuntil7(s9)) <=> (xuntil7(s9) | always5(s9) | (~until6(s9)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4560,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s9) | (~until6(s9)) | xuntil7(s9))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s9) | always5(s9) | (~until6(s9))))),
% 13.35/13.52 inference(monotonicity,[status(thm)],[4559])).
% 13.35/13.52 tff(4561,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s9) | (~until6(s9)) | xuntil7(s9))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s9) | always5(s9) | (~until6(s9)))),
% 13.35/13.52 inference(transitivity,[status(thm)],[4560, 4558])).
% 13.35/13.52 tff(4562,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s9) | (~until6(s9)) | xuntil7(s9))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4563,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s9) | always5(s9) | (~until6(s9))),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4562, 4561])).
% 13.35/13.52 tff(4564,plain,
% 13.35/13.52 (xuntil7(s9)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4563, 4375, 4557, 4542])).
% 13.35/13.52 tff(4565,plain,
% 13.35/13.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s9, s10)) | (~xuntil7(s9)) | until6(s10))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s9, s10)) | (~xuntil7(s9)) | until6(s10))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4566,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s9, s10)) | (~xuntil7(s9)) | until6(s10))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4567,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s9, s10)) | (~xuntil7(s9)) | until6(s10)),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4566, 4565])).
% 13.35/13.52 tff(4568,plain,
% 13.35/13.52 ((~xuntil7(s9)) | until6(s10)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4567, 330, 4393])).
% 13.35/13.52 tff(4569,plain,
% 13.35/13.52 (until6(s10)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4568, 4564])).
% 13.35/13.52 tff(4570,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s10) | always5(s10) | (~until6(s10)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s10) | always5(s10) | (~until6(s10)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4571,plain,
% 13.35/13.52 ((always5(s10) | (~until6(s10)) | xuntil7(s10)) <=> (xuntil7(s10) | always5(s10) | (~until6(s10)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4572,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s10) | (~until6(s10)) | xuntil7(s10))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s10) | always5(s10) | (~until6(s10))))),
% 13.35/13.52 inference(monotonicity,[status(thm)],[4571])).
% 13.35/13.52 tff(4573,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s10) | (~until6(s10)) | xuntil7(s10))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s10) | always5(s10) | (~until6(s10)))),
% 13.35/13.52 inference(transitivity,[status(thm)],[4572, 4570])).
% 13.35/13.52 tff(4574,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s10) | (~until6(s10)) | xuntil7(s10))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4575,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s10) | always5(s10) | (~until6(s10))),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4574, 4573])).
% 13.35/13.52 tff(4576,plain,
% 13.35/13.52 (xuntil7(s10) | (~until6(s10))),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4575, 4375, 4541])).
% 13.35/13.52 tff(4577,plain,
% 13.35/13.52 (xuntil7(s10)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4576, 4569])).
% 13.35/13.52 tff(4578,plain,
% 13.35/13.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s10, s11)) | (~xuntil7(s10)) | until6(s11))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s10, s11)) | (~xuntil7(s10)) | until6(s11))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4579,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s10, s11)) | (~xuntil7(s10)) | until6(s11))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4580,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s10, s11)) | (~xuntil7(s10)) | until6(s11)),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4579, 4578])).
% 13.35/13.52 tff(4581,plain,
% 13.35/13.52 ((~xuntil7(s10)) | until6(s11)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4580, 359, 4393])).
% 13.35/13.52 tff(4582,plain,
% 13.35/13.52 (until6(s11)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4581, 4577])).
% 13.35/13.52 tff(4583,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s11) | always5(s11) | (~until6(s11)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s11) | always5(s11) | (~until6(s11)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4584,plain,
% 13.35/13.52 ((always5(s11) | (~until6(s11)) | xuntil7(s11)) <=> (xuntil7(s11) | always5(s11) | (~until6(s11)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4585,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s11) | (~until6(s11)) | xuntil7(s11))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s11) | always5(s11) | (~until6(s11))))),
% 13.35/13.52 inference(monotonicity,[status(thm)],[4584])).
% 13.35/13.52 tff(4586,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s11) | (~until6(s11)) | xuntil7(s11))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s11) | always5(s11) | (~until6(s11)))),
% 13.35/13.52 inference(transitivity,[status(thm)],[4585, 4583])).
% 13.35/13.52 tff(4587,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s11) | (~until6(s11)) | xuntil7(s11))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4588,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s11) | always5(s11) | (~until6(s11))),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4587, 4586])).
% 13.35/13.52 tff(4589,plain,
% 13.35/13.52 (xuntil7(s11) | (~until6(s11))),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4588, 4375, 4540])).
% 13.35/13.52 tff(4590,plain,
% 13.35/13.52 (xuntil7(s11)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4589, 4582])).
% 13.35/13.52 tff(4591,plain,
% 13.35/13.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s11, s12)) | (~xuntil7(s11)) | until6(s12))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s11, s12)) | (~xuntil7(s11)) | until6(s12))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4592,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s11, s12)) | (~xuntil7(s11)) | until6(s12))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4593,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s11, s12)) | (~xuntil7(s11)) | until6(s12)),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4592, 4591])).
% 13.35/13.52 tff(4594,plain,
% 13.35/13.52 ((~xuntil7(s11)) | until6(s12)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4593, 385, 4393])).
% 13.35/13.52 tff(4595,plain,
% 13.35/13.52 ($false),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4594, 4590, 4539])).
% 13.35/13.52 tff(4596,plain,(always5(s15) | (~until6(s8)) | xuntil7(s15)), inference(lemma,lemma(discharge,[]))).
% 13.35/13.52 tff(4597,plain,
% 13.35/13.52 (xuntil7(s15)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4596, 4488, 4242])).
% 13.35/13.52 tff(4598,plain,
% 13.35/13.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s15, s16)) | (~xuntil7(s15)) | until6(s16))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s15, s16)) | (~xuntil7(s15)) | until6(s16))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4599,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s15, s16)) | (~xuntil7(s15)) | until6(s16))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4600,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s15, s16)) | (~xuntil7(s15)) | until6(s16)),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4599, 4598])).
% 13.35/13.52 tff(4601,plain,
% 13.35/13.52 ((~xuntil7(s15)) | until6(s16)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4600, 495, 4393])).
% 13.35/13.52 tff(4602,plain,
% 13.35/13.52 (until6(s16)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4601, 4597])).
% 13.35/13.52 tff(4603,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s16) | always5(s16) | (~until6(s16)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s16) | always5(s16) | (~until6(s16)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4604,plain,
% 13.35/13.52 ((always5(s16) | (~until6(s16)) | xuntil7(s16)) <=> (xuntil7(s16) | always5(s16) | (~until6(s16)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4605,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s16) | (~until6(s16)) | xuntil7(s16))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s16) | always5(s16) | (~until6(s16))))),
% 13.35/13.52 inference(monotonicity,[status(thm)],[4604])).
% 13.35/13.52 tff(4606,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s16) | (~until6(s16)) | xuntil7(s16))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s16) | always5(s16) | (~until6(s16)))),
% 13.35/13.52 inference(transitivity,[status(thm)],[4605, 4603])).
% 13.35/13.52 tff(4607,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s16) | (~until6(s16)) | xuntil7(s16))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4608,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s16) | always5(s16) | (~until6(s16))),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4607, 4606])).
% 13.35/13.52 tff(4609,plain,
% 13.35/13.52 (xuntil7(s16) | (~until6(s16))),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4608, 4375, 4234])).
% 13.35/13.52 tff(4610,plain,
% 13.35/13.52 (xuntil7(s16)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4609, 4602])).
% 13.35/13.52 tff(4611,plain,
% 13.35/13.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s16, s17)) | (~xuntil7(s16)) | until6(s17))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s16, s17)) | (~xuntil7(s16)) | until6(s17))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4612,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s16, s17)) | (~xuntil7(s16)) | until6(s17))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4613,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s16, s17)) | (~xuntil7(s16)) | until6(s17)),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4612, 4611])).
% 13.35/13.52 tff(4614,plain,
% 13.35/13.52 ((~xuntil7(s16)) | until6(s17)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4613, 524, 4393])).
% 13.35/13.52 tff(4615,plain,
% 13.35/13.52 (until6(s17)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4614, 4610])).
% 13.35/13.52 tff(4616,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s17) | always5(s17) | (~until6(s17)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s17) | always5(s17) | (~until6(s17)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4617,plain,
% 13.35/13.52 ((always5(s17) | (~until6(s17)) | xuntil7(s17)) <=> (xuntil7(s17) | always5(s17) | (~until6(s17)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4618,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s17) | (~until6(s17)) | xuntil7(s17))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s17) | always5(s17) | (~until6(s17))))),
% 13.35/13.52 inference(monotonicity,[status(thm)],[4617])).
% 13.35/13.52 tff(4619,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s17) | (~until6(s17)) | xuntil7(s17))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s17) | always5(s17) | (~until6(s17)))),
% 13.35/13.52 inference(transitivity,[status(thm)],[4618, 4616])).
% 13.35/13.52 tff(4620,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s17) | (~until6(s17)) | xuntil7(s17))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4621,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s17) | always5(s17) | (~until6(s17))),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4620, 4619])).
% 13.35/13.52 tff(4622,plain,
% 13.35/13.52 (xuntil7(s17) | (~until6(s17))),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4621, 4375, 4226])).
% 13.35/13.52 tff(4623,plain,
% 13.35/13.52 (xuntil7(s17)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4622, 4615])).
% 13.35/13.52 tff(4624,plain,
% 13.35/13.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s17, s18)) | (~xuntil7(s17)) | until6(s18))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s17, s18)) | (~xuntil7(s17)) | until6(s18))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4625,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s17, s18)) | (~xuntil7(s17)) | until6(s18))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4626,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s17, s18)) | (~xuntil7(s17)) | until6(s18)),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4625, 4624])).
% 13.35/13.52 tff(4627,plain,
% 13.35/13.52 ((~xuntil7(s17)) | until6(s18)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4626, 552, 4393])).
% 13.35/13.52 tff(4628,plain,
% 13.35/13.52 (until6(s18)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4627, 4623])).
% 13.35/13.52 tff(4629,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s18) | always5(s18) | (~until6(s18)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s18) | always5(s18) | (~until6(s18)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4630,plain,
% 13.35/13.52 ((always5(s18) | (~until6(s18)) | xuntil7(s18)) <=> (xuntil7(s18) | always5(s18) | (~until6(s18)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4631,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s18) | (~until6(s18)) | xuntil7(s18))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s18) | always5(s18) | (~until6(s18))))),
% 13.35/13.52 inference(monotonicity,[status(thm)],[4630])).
% 13.35/13.52 tff(4632,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s18) | (~until6(s18)) | xuntil7(s18))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s18) | always5(s18) | (~until6(s18)))),
% 13.35/13.52 inference(transitivity,[status(thm)],[4631, 4629])).
% 13.35/13.52 tff(4633,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s18) | (~until6(s18)) | xuntil7(s18))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4634,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s18) | always5(s18) | (~until6(s18))),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4633, 4632])).
% 13.35/13.52 tff(4635,plain,
% 13.35/13.52 (xuntil7(s18) | (~until6(s18))),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4634, 4375, 4218])).
% 13.35/13.52 tff(4636,plain,
% 13.35/13.52 (xuntil7(s18)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4635, 4628])).
% 13.35/13.52 tff(4637,plain,
% 13.35/13.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s18, s19)) | (~xuntil7(s18)) | until6(s19))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s18, s19)) | (~xuntil7(s18)) | until6(s19))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4638,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s18, s19)) | (~xuntil7(s18)) | until6(s19))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4639,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s18, s19)) | (~xuntil7(s18)) | until6(s19)),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4638, 4637])).
% 13.35/13.52 tff(4640,plain,
% 13.35/13.52 ((~xuntil7(s18)) | until6(s19)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4639, 583, 4393])).
% 13.35/13.52 tff(4641,plain,
% 13.35/13.52 (until6(s19)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4640, 4636])).
% 13.35/13.52 tff(4642,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s19) | always5(s19) | (~until6(s19)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s19) | always5(s19) | (~until6(s19)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4643,plain,
% 13.35/13.52 ((always5(s19) | (~until6(s19)) | xuntil7(s19)) <=> (xuntil7(s19) | always5(s19) | (~until6(s19)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4644,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s19) | (~until6(s19)) | xuntil7(s19))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s19) | always5(s19) | (~until6(s19))))),
% 13.35/13.52 inference(monotonicity,[status(thm)],[4643])).
% 13.35/13.52 tff(4645,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s19) | (~until6(s19)) | xuntil7(s19))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s19) | always5(s19) | (~until6(s19)))),
% 13.35/13.52 inference(transitivity,[status(thm)],[4644, 4642])).
% 13.35/13.52 tff(4646,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s19) | (~until6(s19)) | xuntil7(s19))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4647,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s19) | always5(s19) | (~until6(s19))),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4646, 4645])).
% 13.35/13.52 tff(4648,plain,
% 13.35/13.52 (xuntil7(s19) | (~until6(s19))),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4647, 4375, 4210])).
% 13.35/13.52 tff(4649,plain,
% 13.35/13.52 (xuntil7(s19)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4648, 4641])).
% 13.35/13.52 tff(4650,plain,
% 13.35/13.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s19, s20)) | (~xuntil7(s19)) | until6(s20))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s19, s20)) | (~xuntil7(s19)) | until6(s20))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4651,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s19, s20)) | (~xuntil7(s19)) | until6(s20))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4652,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s19, s20)) | (~xuntil7(s19)) | until6(s20)),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4651, 4650])).
% 13.35/13.52 tff(4653,plain,
% 13.35/13.52 ((~xuntil7(s19)) | until6(s20)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4652, 611, 4393])).
% 13.35/13.52 tff(4654,plain,
% 13.35/13.52 (until6(s20)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4653, 4649])).
% 13.35/13.52 tff(4655,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s20) | always5(s20) | (~until6(s20)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s20) | always5(s20) | (~until6(s20)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4656,plain,
% 13.35/13.52 ((always5(s20) | (~until6(s20)) | xuntil7(s20)) <=> (xuntil7(s20) | always5(s20) | (~until6(s20)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4657,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s20) | (~until6(s20)) | xuntil7(s20))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s20) | always5(s20) | (~until6(s20))))),
% 13.35/13.52 inference(monotonicity,[status(thm)],[4656])).
% 13.35/13.52 tff(4658,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s20) | (~until6(s20)) | xuntil7(s20))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s20) | always5(s20) | (~until6(s20)))),
% 13.35/13.52 inference(transitivity,[status(thm)],[4657, 4655])).
% 13.35/13.52 tff(4659,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s20) | (~until6(s20)) | xuntil7(s20))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4660,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s20) | always5(s20) | (~until6(s20))),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4659, 4658])).
% 13.35/13.52 tff(4661,plain,
% 13.35/13.52 (xuntil7(s20) | (~until6(s20))),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4660, 4375, 4202])).
% 13.35/13.52 tff(4662,plain,
% 13.35/13.52 (xuntil7(s20)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4661, 4654])).
% 13.35/13.52 tff(4663,plain,
% 13.35/13.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s20, s21)) | (~xuntil7(s20)) | until6(s21))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s20, s21)) | (~xuntil7(s20)) | until6(s21))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4664,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s20, s21)) | (~xuntil7(s20)) | until6(s21))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4665,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s20, s21)) | (~xuntil7(s20)) | until6(s21)),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4664, 4663])).
% 13.35/13.52 tff(4666,plain,
% 13.35/13.52 ((~xuntil7(s20)) | until6(s21)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4665, 642, 4393])).
% 13.35/13.52 tff(4667,plain,
% 13.35/13.52 (until6(s21)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4666, 4662])).
% 13.35/13.52 tff(4668,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s21) | always5(s21) | (~until6(s21)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s21) | always5(s21) | (~until6(s21)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4669,plain,
% 13.35/13.52 ((always5(s21) | (~until6(s21)) | xuntil7(s21)) <=> (xuntil7(s21) | always5(s21) | (~until6(s21)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4670,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s21) | (~until6(s21)) | xuntil7(s21))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s21) | always5(s21) | (~until6(s21))))),
% 13.35/13.52 inference(monotonicity,[status(thm)],[4669])).
% 13.35/13.52 tff(4671,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s21) | (~until6(s21)) | xuntil7(s21))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s21) | always5(s21) | (~until6(s21)))),
% 13.35/13.52 inference(transitivity,[status(thm)],[4670, 4668])).
% 13.35/13.52 tff(4672,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s21) | (~until6(s21)) | xuntil7(s21))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4673,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s21) | always5(s21) | (~until6(s21))),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4672, 4671])).
% 13.35/13.52 tff(4674,plain,
% 13.35/13.52 (xuntil7(s21) | (~until6(s21))),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4673, 4375, 4194])).
% 13.35/13.52 tff(4675,plain,
% 13.35/13.52 (xuntil7(s21)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4674, 4667])).
% 13.35/13.52 tff(4676,plain,
% 13.35/13.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s21, s22)) | (~xuntil7(s21)) | until6(s22))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s21, s22)) | (~xuntil7(s21)) | until6(s22))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4677,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s21, s22)) | (~xuntil7(s21)) | until6(s22))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4678,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s21, s22)) | (~xuntil7(s21)) | until6(s22)),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4677, 4676])).
% 13.35/13.52 tff(4679,plain,
% 13.35/13.52 ((~xuntil7(s21)) | until6(s22)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4678, 670, 4393])).
% 13.35/13.52 tff(4680,plain,
% 13.35/13.52 (until6(s22)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4679, 4675])).
% 13.35/13.52 tff(4681,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s22) | always5(s22) | (~until6(s22)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s22) | always5(s22) | (~until6(s22)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4682,plain,
% 13.35/13.52 ((always5(s22) | (~until6(s22)) | xuntil7(s22)) <=> (xuntil7(s22) | always5(s22) | (~until6(s22)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4683,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s22) | (~until6(s22)) | xuntil7(s22))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s22) | always5(s22) | (~until6(s22))))),
% 13.35/13.52 inference(monotonicity,[status(thm)],[4682])).
% 13.35/13.52 tff(4684,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s22) | (~until6(s22)) | xuntil7(s22))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s22) | always5(s22) | (~until6(s22)))),
% 13.35/13.52 inference(transitivity,[status(thm)],[4683, 4681])).
% 13.35/13.52 tff(4685,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s22) | (~until6(s22)) | xuntil7(s22))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4686,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s22) | always5(s22) | (~until6(s22))),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4685, 4684])).
% 13.35/13.52 tff(4687,plain,
% 13.35/13.52 (xuntil7(s22) | (~until6(s22))),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4686, 4375, 4186])).
% 13.35/13.52 tff(4688,plain,
% 13.35/13.52 (xuntil7(s22)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4687, 4680])).
% 13.35/13.52 tff(4689,plain,
% 13.35/13.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s22, s23)) | (~xuntil7(s22)) | until6(s23))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s22, s23)) | (~xuntil7(s22)) | until6(s23))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4690,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s22, s23)) | (~xuntil7(s22)) | until6(s23))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4691,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s22, s23)) | (~xuntil7(s22)) | until6(s23)),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4690, 4689])).
% 13.35/13.52 tff(4692,plain,
% 13.35/13.52 ((~xuntil7(s22)) | until6(s23)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4691, 701, 4393])).
% 13.35/13.52 tff(4693,plain,
% 13.35/13.52 (until6(s23)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4692, 4688])).
% 13.35/13.52 tff(4694,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s23) | always5(s23) | (~until6(s23)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s23) | always5(s23) | (~until6(s23)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4695,plain,
% 13.35/13.52 ((always5(s23) | (~until6(s23)) | xuntil7(s23)) <=> (xuntil7(s23) | always5(s23) | (~until6(s23)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4696,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s23) | (~until6(s23)) | xuntil7(s23))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s23) | always5(s23) | (~until6(s23))))),
% 13.35/13.52 inference(monotonicity,[status(thm)],[4695])).
% 13.35/13.52 tff(4697,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s23) | (~until6(s23)) | xuntil7(s23))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s23) | always5(s23) | (~until6(s23)))),
% 13.35/13.52 inference(transitivity,[status(thm)],[4696, 4694])).
% 13.35/13.52 tff(4698,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s23) | (~until6(s23)) | xuntil7(s23))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4699,plain,
% 13.35/13.52 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s23) | always5(s23) | (~until6(s23))),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4698, 4697])).
% 13.35/13.52 tff(4700,plain,
% 13.35/13.52 (xuntil7(s23) | (~until6(s23))),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4699, 4375, 4178])).
% 13.35/13.52 tff(4701,plain,
% 13.35/13.52 (xuntil7(s23)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4700, 4693])).
% 13.35/13.52 tff(4702,plain,
% 13.35/13.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s23, s24)) | (~xuntil7(s23)) | until6(s24))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s23, s24)) | (~xuntil7(s23)) | until6(s24))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4703,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s23, s24)) | (~xuntil7(s23)) | until6(s24))),
% 13.35/13.52 inference(quant_inst,[status(thm)],[])).
% 13.35/13.52 tff(4704,plain,
% 13.35/13.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s23, s24)) | (~xuntil7(s23)) | until6(s24)),
% 13.35/13.52 inference(modus_ponens,[status(thm)],[4703, 4702])).
% 13.35/13.52 tff(4705,plain,
% 13.35/13.52 ((~xuntil7(s23)) | until6(s24)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4704, 729, 4393])).
% 13.35/13.52 tff(4706,plain,
% 13.35/13.52 (until6(s24)),
% 13.35/13.52 inference(unit_resolution,[status(thm)],[4705, 4701])).
% 13.35/13.52 tff(4707,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s24) | always5(s24) | (~until6(s24)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s24) | always5(s24) | (~until6(s24)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4708,plain,
% 13.35/13.52 ((always5(s24) | (~until6(s24)) | xuntil7(s24)) <=> (xuntil7(s24) | always5(s24) | (~until6(s24)))),
% 13.35/13.52 inference(rewrite,[status(thm)],[])).
% 13.35/13.52 tff(4709,plain,
% 13.35/13.52 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s24) | (~until6(s24)) | xuntil7(s24))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s24) | always5(s24) | (~until6(s24))))),
% 13.35/13.53 inference(monotonicity,[status(thm)],[4708])).
% 13.35/13.53 tff(4710,plain,
% 13.35/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s24) | (~until6(s24)) | xuntil7(s24))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s24) | always5(s24) | (~until6(s24)))),
% 13.35/13.53 inference(transitivity,[status(thm)],[4709, 4707])).
% 13.35/13.53 tff(4711,plain,
% 13.35/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s24) | (~until6(s24)) | xuntil7(s24))),
% 13.35/13.53 inference(quant_inst,[status(thm)],[])).
% 13.35/13.53 tff(4712,plain,
% 13.35/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s24) | always5(s24) | (~until6(s24))),
% 13.35/13.53 inference(modus_ponens,[status(thm)],[4711, 4710])).
% 13.35/13.53 tff(4713,plain,
% 13.35/13.53 (xuntil7(s24) | (~until6(s24))),
% 13.35/13.53 inference(unit_resolution,[status(thm)],[4712, 4375, 4170])).
% 13.35/13.53 tff(4714,plain,
% 13.35/13.53 (xuntil7(s24)),
% 13.35/13.53 inference(unit_resolution,[status(thm)],[4713, 4706])).
% 13.35/13.53 tff(4715,plain,
% 13.35/13.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s24, s25)) | (~xuntil7(s24)) | until6(s25))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s24, s25)) | (~xuntil7(s24)) | until6(s25))),
% 13.35/13.53 inference(rewrite,[status(thm)],[])).
% 13.35/13.53 tff(4716,plain,
% 13.35/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s24, s25)) | (~xuntil7(s24)) | until6(s25))),
% 13.35/13.53 inference(quant_inst,[status(thm)],[])).
% 13.35/13.53 tff(4717,plain,
% 13.35/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s24, s25)) | (~xuntil7(s24)) | until6(s25)),
% 13.35/13.53 inference(modus_ponens,[status(thm)],[4716, 4715])).
% 13.35/13.53 tff(4718,plain,
% 13.35/13.53 ((~xuntil7(s24)) | until6(s25)),
% 13.35/13.53 inference(unit_resolution,[status(thm)],[4717, 760, 4393])).
% 13.35/13.53 tff(4719,plain,
% 13.35/13.53 (until6(s25)),
% 13.35/13.53 inference(unit_resolution,[status(thm)],[4718, 4714])).
% 13.35/13.53 tff(4720,plain,
% 13.35/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s25) | always5(s25) | (~until6(s25)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s25) | always5(s25) | (~until6(s25)))),
% 13.35/13.53 inference(rewrite,[status(thm)],[])).
% 13.35/13.53 tff(4721,plain,
% 13.35/13.53 ((always5(s25) | (~until6(s25)) | xuntil7(s25)) <=> (xuntil7(s25) | always5(s25) | (~until6(s25)))),
% 13.35/13.53 inference(rewrite,[status(thm)],[])).
% 13.35/13.53 tff(4722,plain,
% 13.35/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s25) | (~until6(s25)) | xuntil7(s25))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s25) | always5(s25) | (~until6(s25))))),
% 13.35/13.53 inference(monotonicity,[status(thm)],[4721])).
% 13.35/13.53 tff(4723,plain,
% 13.35/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s25) | (~until6(s25)) | xuntil7(s25))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s25) | always5(s25) | (~until6(s25)))),
% 13.35/13.53 inference(transitivity,[status(thm)],[4722, 4720])).
% 13.35/13.53 tff(4724,plain,
% 13.35/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s25) | (~until6(s25)) | xuntil7(s25))),
% 13.35/13.53 inference(quant_inst,[status(thm)],[])).
% 13.35/13.53 tff(4725,plain,
% 13.35/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s25) | always5(s25) | (~until6(s25))),
% 13.35/13.53 inference(modus_ponens,[status(thm)],[4724, 4723])).
% 13.35/13.53 tff(4726,plain,
% 13.35/13.53 (xuntil7(s25) | (~until6(s25))),
% 13.35/13.53 inference(unit_resolution,[status(thm)],[4725, 4375, 4162])).
% 13.35/13.53 tff(4727,plain,
% 13.35/13.53 (xuntil7(s25)),
% 13.35/13.53 inference(unit_resolution,[status(thm)],[4726, 4719])).
% 13.35/13.53 tff(4728,plain,
% 13.35/13.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s25, s26)) | (~xuntil7(s25)) | until6(s26))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s25, s26)) | (~xuntil7(s25)) | until6(s26))),
% 13.35/13.53 inference(rewrite,[status(thm)],[])).
% 13.35/13.53 tff(4729,plain,
% 13.35/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s25, s26)) | (~xuntil7(s25)) | until6(s26))),
% 13.35/13.53 inference(quant_inst,[status(thm)],[])).
% 13.35/13.53 tff(4730,plain,
% 13.35/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s25, s26)) | (~xuntil7(s25)) | until6(s26)),
% 13.35/13.53 inference(modus_ponens,[status(thm)],[4729, 4728])).
% 13.35/13.53 tff(4731,plain,
% 13.35/13.53 ((~xuntil7(s25)) | until6(s26)),
% 13.35/13.53 inference(unit_resolution,[status(thm)],[4730, 788, 4393])).
% 13.35/13.53 tff(4732,plain,
% 13.35/13.53 (until6(s26)),
% 13.35/13.53 inference(unit_resolution,[status(thm)],[4731, 4727])).
% 13.35/13.53 tff(4733,plain,
% 13.35/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s26) | always5(s26) | (~until6(s26)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s26) | always5(s26) | (~until6(s26)))),
% 13.35/13.53 inference(rewrite,[status(thm)],[])).
% 13.35/13.53 tff(4734,plain,
% 13.35/13.53 ((always5(s26) | (~until6(s26)) | xuntil7(s26)) <=> (xuntil7(s26) | always5(s26) | (~until6(s26)))),
% 13.35/13.53 inference(rewrite,[status(thm)],[])).
% 13.35/13.53 tff(4735,plain,
% 13.35/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s26) | (~until6(s26)) | xuntil7(s26))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s26) | always5(s26) | (~until6(s26))))),
% 13.35/13.53 inference(monotonicity,[status(thm)],[4734])).
% 13.35/13.53 tff(4736,plain,
% 13.35/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s26) | (~until6(s26)) | xuntil7(s26))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s26) | always5(s26) | (~until6(s26)))),
% 13.35/13.53 inference(transitivity,[status(thm)],[4735, 4733])).
% 13.35/13.53 tff(4737,plain,
% 13.35/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s26) | (~until6(s26)) | xuntil7(s26))),
% 13.35/13.53 inference(quant_inst,[status(thm)],[])).
% 13.35/13.53 tff(4738,plain,
% 13.35/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s26) | always5(s26) | (~until6(s26))),
% 13.35/13.53 inference(modus_ponens,[status(thm)],[4737, 4736])).
% 13.35/13.53 tff(4739,plain,
% 13.35/13.53 (xuntil7(s26) | (~until6(s26))),
% 13.35/13.53 inference(unit_resolution,[status(thm)],[4738, 4375, 4154])).
% 13.35/13.53 tff(4740,plain,
% 13.35/13.53 (xuntil7(s26)),
% 13.35/13.53 inference(unit_resolution,[status(thm)],[4739, 4732])).
% 13.35/13.53 tff(4741,plain,
% 13.35/13.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s26, s27)) | (~xuntil7(s26)) | until6(s27))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s26, s27)) | (~xuntil7(s26)) | until6(s27))),
% 13.35/13.53 inference(rewrite,[status(thm)],[])).
% 13.35/13.53 tff(4742,plain,
% 13.35/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s26, s27)) | (~xuntil7(s26)) | until6(s27))),
% 13.35/13.53 inference(quant_inst,[status(thm)],[])).
% 13.35/13.53 tff(4743,plain,
% 13.35/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s26, s27)) | (~xuntil7(s26)) | until6(s27)),
% 13.35/13.53 inference(modus_ponens,[status(thm)],[4742, 4741])).
% 13.35/13.53 tff(4744,plain,
% 13.35/13.53 ((~xuntil7(s26)) | until6(s27)),
% 13.35/13.53 inference(unit_resolution,[status(thm)],[4743, 819, 4393])).
% 13.35/13.53 tff(4745,plain,
% 13.35/13.53 (until6(s27)),
% 13.35/13.53 inference(unit_resolution,[status(thm)],[4744, 4740])).
% 13.35/13.53 tff(4746,plain,
% 13.35/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s27) | always5(s27) | (~until6(s27)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s27) | always5(s27) | (~until6(s27)))),
% 13.35/13.53 inference(rewrite,[status(thm)],[])).
% 13.35/13.53 tff(4747,plain,
% 13.35/13.53 ((always5(s27) | (~until6(s27)) | xuntil7(s27)) <=> (xuntil7(s27) | always5(s27) | (~until6(s27)))),
% 13.35/13.53 inference(rewrite,[status(thm)],[])).
% 13.35/13.53 tff(4748,plain,
% 13.35/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s27) | (~until6(s27)) | xuntil7(s27))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s27) | always5(s27) | (~until6(s27))))),
% 13.35/13.53 inference(monotonicity,[status(thm)],[4747])).
% 13.35/13.53 tff(4749,plain,
% 13.35/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s27) | (~until6(s27)) | xuntil7(s27))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s27) | always5(s27) | (~until6(s27)))),
% 13.35/13.53 inference(transitivity,[status(thm)],[4748, 4746])).
% 13.35/13.53 tff(4750,plain,
% 13.35/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s27) | (~until6(s27)) | xuntil7(s27))),
% 13.35/13.53 inference(quant_inst,[status(thm)],[])).
% 13.35/13.53 tff(4751,plain,
% 13.35/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s27) | always5(s27) | (~until6(s27))),
% 13.35/13.53 inference(modus_ponens,[status(thm)],[4750, 4749])).
% 13.35/13.53 tff(4752,plain,
% 13.35/13.53 (xuntil7(s27) | (~until6(s27))),
% 13.35/13.53 inference(unit_resolution,[status(thm)],[4751, 4375, 4146])).
% 13.35/13.53 tff(4753,plain,
% 13.35/13.53 (xuntil7(s27)),
% 13.35/13.53 inference(unit_resolution,[status(thm)],[4752, 4745])).
% 13.35/13.53 tff(4754,plain,
% 13.35/13.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s27, s28)) | (~xuntil7(s27)) | until6(s28))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s27, s28)) | (~xuntil7(s27)) | until6(s28))),
% 13.35/13.53 inference(rewrite,[status(thm)],[])).
% 13.35/13.53 tff(4755,plain,
% 13.35/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s27, s28)) | (~xuntil7(s27)) | until6(s28))),
% 13.35/13.53 inference(quant_inst,[status(thm)],[])).
% 13.35/13.53 tff(4756,plain,
% 13.35/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s27, s28)) | (~xuntil7(s27)) | until6(s28)),
% 13.35/13.53 inference(modus_ponens,[status(thm)],[4755, 4754])).
% 13.35/13.53 tff(4757,plain,
% 13.35/13.53 ((~xuntil7(s27)) | until6(s28)),
% 13.35/13.53 inference(unit_resolution,[status(thm)],[4756, 847, 4393])).
% 13.35/13.53 tff(4758,plain,
% 13.35/13.53 (until6(s28)),
% 13.35/13.53 inference(unit_resolution,[status(thm)],[4757, 4753])).
% 13.35/13.53 tff(4759,plain,
% 13.35/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s28) | always5(s28) | (~until6(s28)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s28) | always5(s28) | (~until6(s28)))),
% 13.35/13.53 inference(rewrite,[status(thm)],[])).
% 13.35/13.53 tff(4760,plain,
% 13.35/13.53 ((always5(s28) | (~until6(s28)) | xuntil7(s28)) <=> (xuntil7(s28) | always5(s28) | (~until6(s28)))),
% 13.35/13.53 inference(rewrite,[status(thm)],[])).
% 13.35/13.53 tff(4761,plain,
% 13.35/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s28) | (~until6(s28)) | xuntil7(s28))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s28) | always5(s28) | (~until6(s28))))),
% 13.35/13.53 inference(monotonicity,[status(thm)],[4760])).
% 13.35/13.53 tff(4762,plain,
% 13.35/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s28) | (~until6(s28)) | xuntil7(s28))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s28) | always5(s28) | (~until6(s28)))),
% 13.35/13.53 inference(transitivity,[status(thm)],[4761, 4759])).
% 13.35/13.53 tff(4763,plain,
% 13.35/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s28) | (~until6(s28)) | xuntil7(s28))),
% 13.35/13.53 inference(quant_inst,[status(thm)],[])).
% 13.35/13.53 tff(4764,plain,
% 13.35/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s28) | always5(s28) | (~until6(s28))),
% 13.35/13.53 inference(modus_ponens,[status(thm)],[4763, 4762])).
% 13.35/13.53 tff(4765,plain,
% 13.35/13.53 (xuntil7(s28) | (~until6(s28))),
% 13.35/13.53 inference(unit_resolution,[status(thm)],[4764, 4375, 4138])).
% 13.35/13.53 tff(4766,plain,
% 13.35/13.53 (xuntil7(s28)),
% 13.35/13.53 inference(unit_resolution,[status(thm)],[4765, 4758])).
% 13.35/13.53 tff(4767,plain,
% 13.35/13.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s28, s29)) | (~xuntil7(s28)) | until6(s29))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s28, s29)) | (~xuntil7(s28)) | until6(s29))),
% 13.35/13.53 inference(rewrite,[status(thm)],[])).
% 13.35/13.53 tff(4768,plain,
% 13.35/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s28, s29)) | (~xuntil7(s28)) | until6(s29))),
% 13.35/13.53 inference(quant_inst,[status(thm)],[])).
% 13.35/13.53 tff(4769,plain,
% 13.35/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s28, s29)) | (~xuntil7(s28)) | until6(s29)),
% 13.35/13.53 inference(modus_ponens,[status(thm)],[4768, 4767])).
% 13.35/13.53 tff(4770,plain,
% 13.35/13.53 ((~xuntil7(s28)) | until6(s29)),
% 13.35/13.53 inference(unit_resolution,[status(thm)],[4769, 878, 4393])).
% 13.35/13.53 tff(4771,plain,
% 13.35/13.53 (until6(s29)),
% 13.35/13.53 inference(unit_resolution,[status(thm)],[4770, 4766])).
% 13.35/13.53 tff(4772,plain,
% 13.35/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s29) | always5(s29) | (~until6(s29)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s29) | always5(s29) | (~until6(s29)))),
% 13.35/13.53 inference(rewrite,[status(thm)],[])).
% 13.35/13.53 tff(4773,plain,
% 13.35/13.53 ((always5(s29) | (~until6(s29)) | xuntil7(s29)) <=> (xuntil7(s29) | always5(s29) | (~until6(s29)))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4774,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s29) | (~until6(s29)) | xuntil7(s29))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s29) | always5(s29) | (~until6(s29))))),
% 13.38/13.53 inference(monotonicity,[status(thm)],[4773])).
% 13.38/13.53 tff(4775,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s29) | (~until6(s29)) | xuntil7(s29))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s29) | always5(s29) | (~until6(s29)))),
% 13.38/13.53 inference(transitivity,[status(thm)],[4774, 4772])).
% 13.38/13.53 tff(4776,plain,
% 13.38/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s29) | (~until6(s29)) | xuntil7(s29))),
% 13.38/13.53 inference(quant_inst,[status(thm)],[])).
% 13.38/13.53 tff(4777,plain,
% 13.38/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s29) | always5(s29) | (~until6(s29))),
% 13.38/13.53 inference(modus_ponens,[status(thm)],[4776, 4775])).
% 13.38/13.53 tff(4778,plain,
% 13.38/13.53 (xuntil7(s29) | (~until6(s29))),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4777, 4375, 4130])).
% 13.38/13.53 tff(4779,plain,
% 13.38/13.53 (xuntil7(s29)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4778, 4771])).
% 13.38/13.53 tff(4780,plain,
% 13.38/13.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s29, s30)) | (~xuntil7(s29)) | until6(s30))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s29, s30)) | (~xuntil7(s29)) | until6(s30))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4781,plain,
% 13.38/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s29, s30)) | (~xuntil7(s29)) | until6(s30))),
% 13.38/13.53 inference(quant_inst,[status(thm)],[])).
% 13.38/13.53 tff(4782,plain,
% 13.38/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s29, s30)) | (~xuntil7(s29)) | until6(s30)),
% 13.38/13.53 inference(modus_ponens,[status(thm)],[4781, 4780])).
% 13.38/13.53 tff(4783,plain,
% 13.38/13.53 ((~xuntil7(s29)) | until6(s30)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4782, 906, 4393])).
% 13.38/13.53 tff(4784,plain,
% 13.38/13.53 (until6(s30)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4783, 4779])).
% 13.38/13.53 tff(4785,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s30) | always5(s30) | (~until6(s30)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s30) | always5(s30) | (~until6(s30)))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4786,plain,
% 13.38/13.53 ((always5(s30) | (~until6(s30)) | xuntil7(s30)) <=> (xuntil7(s30) | always5(s30) | (~until6(s30)))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4787,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s30) | (~until6(s30)) | xuntil7(s30))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s30) | always5(s30) | (~until6(s30))))),
% 13.38/13.53 inference(monotonicity,[status(thm)],[4786])).
% 13.38/13.53 tff(4788,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s30) | (~until6(s30)) | xuntil7(s30))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s30) | always5(s30) | (~until6(s30)))),
% 13.38/13.53 inference(transitivity,[status(thm)],[4787, 4785])).
% 13.38/13.53 tff(4789,plain,
% 13.38/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s30) | (~until6(s30)) | xuntil7(s30))),
% 13.38/13.53 inference(quant_inst,[status(thm)],[])).
% 13.38/13.53 tff(4790,plain,
% 13.38/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s30) | always5(s30) | (~until6(s30))),
% 13.38/13.53 inference(modus_ponens,[status(thm)],[4789, 4788])).
% 13.38/13.53 tff(4791,plain,
% 13.38/13.53 (xuntil7(s30) | (~until6(s30))),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4790, 4375, 4122])).
% 13.38/13.53 tff(4792,plain,
% 13.38/13.53 (xuntil7(s30)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4791, 4784])).
% 13.38/13.53 tff(4793,plain,
% 13.38/13.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s30, s31)) | (~xuntil7(s30)) | until6(s31))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s30, s31)) | (~xuntil7(s30)) | until6(s31))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4794,plain,
% 13.38/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s30, s31)) | (~xuntil7(s30)) | until6(s31))),
% 13.38/13.53 inference(quant_inst,[status(thm)],[])).
% 13.38/13.53 tff(4795,plain,
% 13.38/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s30, s31)) | (~xuntil7(s30)) | until6(s31)),
% 13.38/13.53 inference(modus_ponens,[status(thm)],[4794, 4793])).
% 13.38/13.53 tff(4796,plain,
% 13.38/13.53 ((~xuntil7(s30)) | until6(s31)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4795, 937, 4393])).
% 13.38/13.53 tff(4797,plain,
% 13.38/13.53 (until6(s31)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4796, 4792])).
% 13.38/13.53 tff(4798,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s31) | always5(s31) | (~until6(s31)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s31) | always5(s31) | (~until6(s31)))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4799,plain,
% 13.38/13.53 ((always5(s31) | (~until6(s31)) | xuntil7(s31)) <=> (xuntil7(s31) | always5(s31) | (~until6(s31)))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4800,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s31) | (~until6(s31)) | xuntil7(s31))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s31) | always5(s31) | (~until6(s31))))),
% 13.38/13.53 inference(monotonicity,[status(thm)],[4799])).
% 13.38/13.53 tff(4801,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s31) | (~until6(s31)) | xuntil7(s31))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s31) | always5(s31) | (~until6(s31)))),
% 13.38/13.53 inference(transitivity,[status(thm)],[4800, 4798])).
% 13.38/13.53 tff(4802,plain,
% 13.38/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s31) | (~until6(s31)) | xuntil7(s31))),
% 13.38/13.53 inference(quant_inst,[status(thm)],[])).
% 13.38/13.53 tff(4803,plain,
% 13.38/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s31) | always5(s31) | (~until6(s31))),
% 13.38/13.53 inference(modus_ponens,[status(thm)],[4802, 4801])).
% 13.38/13.53 tff(4804,plain,
% 13.38/13.53 (xuntil7(s31) | (~until6(s31))),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4803, 4375, 4114])).
% 13.38/13.53 tff(4805,plain,
% 13.38/13.53 (xuntil7(s31)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4804, 4797])).
% 13.38/13.53 tff(4806,plain,
% 13.38/13.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s31, s32)) | (~xuntil7(s31)) | until6(s32))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s31, s32)) | (~xuntil7(s31)) | until6(s32))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4807,plain,
% 13.38/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s31, s32)) | (~xuntil7(s31)) | until6(s32))),
% 13.38/13.53 inference(quant_inst,[status(thm)],[])).
% 13.38/13.53 tff(4808,plain,
% 13.38/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s31, s32)) | (~xuntil7(s31)) | until6(s32)),
% 13.38/13.53 inference(modus_ponens,[status(thm)],[4807, 4806])).
% 13.38/13.53 tff(4809,plain,
% 13.38/13.53 ((~xuntil7(s31)) | until6(s32)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4808, 965, 4393])).
% 13.38/13.53 tff(4810,plain,
% 13.38/13.53 (until6(s32)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4809, 4805])).
% 13.38/13.53 tff(4811,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s32) | always5(s32) | (~until6(s32)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s32) | always5(s32) | (~until6(s32)))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4812,plain,
% 13.38/13.53 ((always5(s32) | (~until6(s32)) | xuntil7(s32)) <=> (xuntil7(s32) | always5(s32) | (~until6(s32)))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4813,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s32) | (~until6(s32)) | xuntil7(s32))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s32) | always5(s32) | (~until6(s32))))),
% 13.38/13.53 inference(monotonicity,[status(thm)],[4812])).
% 13.38/13.53 tff(4814,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s32) | (~until6(s32)) | xuntil7(s32))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s32) | always5(s32) | (~until6(s32)))),
% 13.38/13.53 inference(transitivity,[status(thm)],[4813, 4811])).
% 13.38/13.53 tff(4815,plain,
% 13.38/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s32) | (~until6(s32)) | xuntil7(s32))),
% 13.38/13.53 inference(quant_inst,[status(thm)],[])).
% 13.38/13.53 tff(4816,plain,
% 13.38/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s32) | always5(s32) | (~until6(s32))),
% 13.38/13.53 inference(modus_ponens,[status(thm)],[4815, 4814])).
% 13.38/13.53 tff(4817,plain,
% 13.38/13.53 (xuntil7(s32) | (~until6(s32))),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4816, 4375, 4106])).
% 13.38/13.53 tff(4818,plain,
% 13.38/13.53 (xuntil7(s32)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4817, 4810])).
% 13.38/13.53 tff(4819,plain,
% 13.38/13.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s32, s33)) | (~xuntil7(s32)) | until6(s33))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s32, s33)) | (~xuntil7(s32)) | until6(s33))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4820,plain,
% 13.38/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s32, s33)) | (~xuntil7(s32)) | until6(s33))),
% 13.38/13.53 inference(quant_inst,[status(thm)],[])).
% 13.38/13.53 tff(4821,plain,
% 13.38/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s32, s33)) | (~xuntil7(s32)) | until6(s33)),
% 13.38/13.53 inference(modus_ponens,[status(thm)],[4820, 4819])).
% 13.38/13.53 tff(4822,plain,
% 13.38/13.53 ((~xuntil7(s32)) | until6(s33)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4821, 996, 4393])).
% 13.38/13.53 tff(4823,plain,
% 13.38/13.53 (until6(s33)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4822, 4818])).
% 13.38/13.53 tff(4824,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s33) | always5(s33) | (~until6(s33)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s33) | always5(s33) | (~until6(s33)))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4825,plain,
% 13.38/13.53 ((always5(s33) | (~until6(s33)) | xuntil7(s33)) <=> (xuntil7(s33) | always5(s33) | (~until6(s33)))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4826,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s33) | (~until6(s33)) | xuntil7(s33))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s33) | always5(s33) | (~until6(s33))))),
% 13.38/13.53 inference(monotonicity,[status(thm)],[4825])).
% 13.38/13.53 tff(4827,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s33) | (~until6(s33)) | xuntil7(s33))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s33) | always5(s33) | (~until6(s33)))),
% 13.38/13.53 inference(transitivity,[status(thm)],[4826, 4824])).
% 13.38/13.53 tff(4828,plain,
% 13.38/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s33) | (~until6(s33)) | xuntil7(s33))),
% 13.38/13.53 inference(quant_inst,[status(thm)],[])).
% 13.38/13.53 tff(4829,plain,
% 13.38/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s33) | always5(s33) | (~until6(s33))),
% 13.38/13.53 inference(modus_ponens,[status(thm)],[4828, 4827])).
% 13.38/13.53 tff(4830,plain,
% 13.38/13.53 (xuntil7(s33) | (~until6(s33))),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4829, 4375, 4098])).
% 13.38/13.53 tff(4831,plain,
% 13.38/13.53 (xuntil7(s33)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4830, 4823])).
% 13.38/13.53 tff(4832,plain,
% 13.38/13.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s33, s34)) | (~xuntil7(s33)) | until6(s34))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s33, s34)) | (~xuntil7(s33)) | until6(s34))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4833,plain,
% 13.38/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s33, s34)) | (~xuntil7(s33)) | until6(s34))),
% 13.38/13.53 inference(quant_inst,[status(thm)],[])).
% 13.38/13.53 tff(4834,plain,
% 13.38/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s33, s34)) | (~xuntil7(s33)) | until6(s34)),
% 13.38/13.53 inference(modus_ponens,[status(thm)],[4833, 4832])).
% 13.38/13.53 tff(4835,plain,
% 13.38/13.53 ((~xuntil7(s33)) | until6(s34)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4834, 1024, 4393])).
% 13.38/13.53 tff(4836,plain,
% 13.38/13.53 (until6(s34)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4835, 4831])).
% 13.38/13.53 tff(4837,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s34) | always5(s34) | (~until6(s34)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s34) | always5(s34) | (~until6(s34)))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4838,plain,
% 13.38/13.53 ((always5(s34) | (~until6(s34)) | xuntil7(s34)) <=> (xuntil7(s34) | always5(s34) | (~until6(s34)))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4839,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s34) | (~until6(s34)) | xuntil7(s34))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s34) | always5(s34) | (~until6(s34))))),
% 13.38/13.53 inference(monotonicity,[status(thm)],[4838])).
% 13.38/13.53 tff(4840,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s34) | (~until6(s34)) | xuntil7(s34))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s34) | always5(s34) | (~until6(s34)))),
% 13.38/13.53 inference(transitivity,[status(thm)],[4839, 4837])).
% 13.38/13.53 tff(4841,plain,
% 13.38/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s34) | (~until6(s34)) | xuntil7(s34))),
% 13.38/13.53 inference(quant_inst,[status(thm)],[])).
% 13.38/13.53 tff(4842,plain,
% 13.38/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s34) | always5(s34) | (~until6(s34))),
% 13.38/13.53 inference(modus_ponens,[status(thm)],[4841, 4840])).
% 13.38/13.53 tff(4843,plain,
% 13.38/13.53 (xuntil7(s34) | (~until6(s34))),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4842, 4375, 4090])).
% 13.38/13.53 tff(4844,plain,
% 13.38/13.53 (xuntil7(s34)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4843, 4836])).
% 13.38/13.53 tff(4845,plain,
% 13.38/13.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s34, s35)) | (~xuntil7(s34)) | until6(s35))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s34, s35)) | (~xuntil7(s34)) | until6(s35))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4846,plain,
% 13.38/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s34, s35)) | (~xuntil7(s34)) | until6(s35))),
% 13.38/13.53 inference(quant_inst,[status(thm)],[])).
% 13.38/13.53 tff(4847,plain,
% 13.38/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s34, s35)) | (~xuntil7(s34)) | until6(s35)),
% 13.38/13.53 inference(modus_ponens,[status(thm)],[4846, 4845])).
% 13.38/13.53 tff(4848,plain,
% 13.38/13.53 ((~xuntil7(s34)) | until6(s35)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4847, 1055, 4393])).
% 13.38/13.53 tff(4849,plain,
% 13.38/13.53 (until6(s35)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4848, 4844])).
% 13.38/13.53 tff(4850,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s35) | always5(s35) | (~until6(s35)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s35) | always5(s35) | (~until6(s35)))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4851,plain,
% 13.38/13.53 ((always5(s35) | (~until6(s35)) | xuntil7(s35)) <=> (xuntil7(s35) | always5(s35) | (~until6(s35)))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4852,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s35) | (~until6(s35)) | xuntil7(s35))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s35) | always5(s35) | (~until6(s35))))),
% 13.38/13.53 inference(monotonicity,[status(thm)],[4851])).
% 13.38/13.53 tff(4853,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s35) | (~until6(s35)) | xuntil7(s35))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s35) | always5(s35) | (~until6(s35)))),
% 13.38/13.53 inference(transitivity,[status(thm)],[4852, 4850])).
% 13.38/13.53 tff(4854,plain,
% 13.38/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s35) | (~until6(s35)) | xuntil7(s35))),
% 13.38/13.53 inference(quant_inst,[status(thm)],[])).
% 13.38/13.53 tff(4855,plain,
% 13.38/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s35) | always5(s35) | (~until6(s35))),
% 13.38/13.53 inference(modus_ponens,[status(thm)],[4854, 4853])).
% 13.38/13.53 tff(4856,plain,
% 13.38/13.53 (xuntil7(s35) | (~until6(s35))),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4855, 4375, 4082])).
% 13.38/13.53 tff(4857,plain,
% 13.38/13.53 (xuntil7(s35)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4856, 4849])).
% 13.38/13.53 tff(4858,plain,
% 13.38/13.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s35, s36)) | (~xuntil7(s35)) | until6(s36))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s35, s36)) | (~xuntil7(s35)) | until6(s36))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4859,plain,
% 13.38/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s35, s36)) | (~xuntil7(s35)) | until6(s36))),
% 13.38/13.53 inference(quant_inst,[status(thm)],[])).
% 13.38/13.53 tff(4860,plain,
% 13.38/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s35, s36)) | (~xuntil7(s35)) | until6(s36)),
% 13.38/13.53 inference(modus_ponens,[status(thm)],[4859, 4858])).
% 13.38/13.53 tff(4861,plain,
% 13.38/13.53 ((~xuntil7(s35)) | until6(s36)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4860, 1083, 4393])).
% 13.38/13.53 tff(4862,plain,
% 13.38/13.53 (until6(s36)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4861, 4857])).
% 13.38/13.53 tff(4863,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s36) | always5(s36) | (~until6(s36)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s36) | always5(s36) | (~until6(s36)))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4864,plain,
% 13.38/13.53 ((always5(s36) | (~until6(s36)) | xuntil7(s36)) <=> (xuntil7(s36) | always5(s36) | (~until6(s36)))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4865,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s36) | (~until6(s36)) | xuntil7(s36))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s36) | always5(s36) | (~until6(s36))))),
% 13.38/13.53 inference(monotonicity,[status(thm)],[4864])).
% 13.38/13.53 tff(4866,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s36) | (~until6(s36)) | xuntil7(s36))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s36) | always5(s36) | (~until6(s36)))),
% 13.38/13.53 inference(transitivity,[status(thm)],[4865, 4863])).
% 13.38/13.53 tff(4867,plain,
% 13.38/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s36) | (~until6(s36)) | xuntil7(s36))),
% 13.38/13.53 inference(quant_inst,[status(thm)],[])).
% 13.38/13.53 tff(4868,plain,
% 13.38/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s36) | always5(s36) | (~until6(s36))),
% 13.38/13.53 inference(modus_ponens,[status(thm)],[4867, 4866])).
% 13.38/13.53 tff(4869,plain,
% 13.38/13.53 (xuntil7(s36) | (~until6(s36))),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4868, 4375, 4074])).
% 13.38/13.53 tff(4870,plain,
% 13.38/13.53 (xuntil7(s36)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4869, 4862])).
% 13.38/13.53 tff(4871,plain,
% 13.38/13.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s36, s37)) | (~xuntil7(s36)) | until6(s37))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s36, s37)) | (~xuntil7(s36)) | until6(s37))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4872,plain,
% 13.38/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s36, s37)) | (~xuntil7(s36)) | until6(s37))),
% 13.38/13.53 inference(quant_inst,[status(thm)],[])).
% 13.38/13.53 tff(4873,plain,
% 13.38/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s36, s37)) | (~xuntil7(s36)) | until6(s37)),
% 13.38/13.53 inference(modus_ponens,[status(thm)],[4872, 4871])).
% 13.38/13.53 tff(4874,plain,
% 13.38/13.53 ((~xuntil7(s36)) | until6(s37)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4873, 1114, 4393])).
% 13.38/13.53 tff(4875,plain,
% 13.38/13.53 (until6(s37)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4874, 4870])).
% 13.38/13.53 tff(4876,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s37) | always5(s37) | (~until6(s37)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s37) | always5(s37) | (~until6(s37)))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4877,plain,
% 13.38/13.53 ((always5(s37) | (~until6(s37)) | xuntil7(s37)) <=> (xuntil7(s37) | always5(s37) | (~until6(s37)))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4878,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s37) | (~until6(s37)) | xuntil7(s37))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s37) | always5(s37) | (~until6(s37))))),
% 13.38/13.53 inference(monotonicity,[status(thm)],[4877])).
% 13.38/13.53 tff(4879,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s37) | (~until6(s37)) | xuntil7(s37))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s37) | always5(s37) | (~until6(s37)))),
% 13.38/13.53 inference(transitivity,[status(thm)],[4878, 4876])).
% 13.38/13.53 tff(4880,plain,
% 13.38/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s37) | (~until6(s37)) | xuntil7(s37))),
% 13.38/13.53 inference(quant_inst,[status(thm)],[])).
% 13.38/13.53 tff(4881,plain,
% 13.38/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s37) | always5(s37) | (~until6(s37))),
% 13.38/13.53 inference(modus_ponens,[status(thm)],[4880, 4879])).
% 13.38/13.53 tff(4882,plain,
% 13.38/13.53 (xuntil7(s37) | (~until6(s37))),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4881, 4375, 4066])).
% 13.38/13.53 tff(4883,plain,
% 13.38/13.53 (xuntil7(s37)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4882, 4875])).
% 13.38/13.53 tff(4884,plain,
% 13.38/13.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s37, s38)) | (~xuntil7(s37)) | until6(s38))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s37, s38)) | (~xuntil7(s37)) | until6(s38))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4885,plain,
% 13.38/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s37, s38)) | (~xuntil7(s37)) | until6(s38))),
% 13.38/13.53 inference(quant_inst,[status(thm)],[])).
% 13.38/13.53 tff(4886,plain,
% 13.38/13.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s37, s38)) | (~xuntil7(s37)) | until6(s38)),
% 13.38/13.53 inference(modus_ponens,[status(thm)],[4885, 4884])).
% 13.38/13.53 tff(4887,plain,
% 13.38/13.53 ((~xuntil7(s37)) | until6(s38)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4886, 1142, 4393])).
% 13.38/13.53 tff(4888,plain,
% 13.38/13.53 (until6(s38)),
% 13.38/13.53 inference(unit_resolution,[status(thm)],[4887, 4883])).
% 13.38/13.53 tff(4889,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s38) | always5(s38) | (~until6(s38)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s38) | always5(s38) | (~until6(s38)))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4890,plain,
% 13.38/13.53 ((always5(s38) | (~until6(s38)) | xuntil7(s38)) <=> (xuntil7(s38) | always5(s38) | (~until6(s38)))),
% 13.38/13.53 inference(rewrite,[status(thm)],[])).
% 13.38/13.53 tff(4891,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s38) | (~until6(s38)) | xuntil7(s38))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s38) | always5(s38) | (~until6(s38))))),
% 13.38/13.53 inference(monotonicity,[status(thm)],[4890])).
% 13.38/13.53 tff(4892,plain,
% 13.38/13.53 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s38) | (~until6(s38)) | xuntil7(s38))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s38) | always5(s38) | (~until6(s38)))),
% 13.38/13.53 inference(transitivity,[status(thm)],[4891, 4889])).
% 13.38/13.53 tff(4893,plain,
% 13.38/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s38) | (~until6(s38)) | xuntil7(s38))),
% 13.38/13.53 inference(quant_inst,[status(thm)],[])).
% 13.38/13.53 tff(4894,plain,
% 13.38/13.53 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s38) | always5(s38) | (~until6(s38))),
% 13.38/13.53 inference(modus_ponens,[status(thm)],[4893, 4892])).
% 13.38/13.54 tff(4895,plain,
% 13.38/13.54 (xuntil7(s38) | (~until6(s38))),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4894, 4375, 4058])).
% 13.38/13.54 tff(4896,plain,
% 13.38/13.54 (xuntil7(s38)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4895, 4888])).
% 13.38/13.54 tff(4897,plain,
% 13.38/13.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s38, s39)) | (~xuntil7(s38)) | until6(s39))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s38, s39)) | (~xuntil7(s38)) | until6(s39))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(4898,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s38, s39)) | (~xuntil7(s38)) | until6(s39))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(4899,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s38, s39)) | (~xuntil7(s38)) | until6(s39)),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[4898, 4897])).
% 13.38/13.54 tff(4900,plain,
% 13.38/13.54 ((~xuntil7(s38)) | until6(s39)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4899, 1173, 4393])).
% 13.38/13.54 tff(4901,plain,
% 13.38/13.54 (until6(s39)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4900, 4896])).
% 13.38/13.54 tff(4902,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s39) | always5(s39) | (~until6(s39)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s39) | always5(s39) | (~until6(s39)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(4903,plain,
% 13.38/13.54 ((always5(s39) | (~until6(s39)) | xuntil7(s39)) <=> (xuntil7(s39) | always5(s39) | (~until6(s39)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(4904,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s39) | (~until6(s39)) | xuntil7(s39))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s39) | always5(s39) | (~until6(s39))))),
% 13.38/13.54 inference(monotonicity,[status(thm)],[4903])).
% 13.38/13.54 tff(4905,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s39) | (~until6(s39)) | xuntil7(s39))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s39) | always5(s39) | (~until6(s39)))),
% 13.38/13.54 inference(transitivity,[status(thm)],[4904, 4902])).
% 13.38/13.54 tff(4906,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s39) | (~until6(s39)) | xuntil7(s39))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(4907,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s39) | always5(s39) | (~until6(s39))),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[4906, 4905])).
% 13.38/13.54 tff(4908,plain,
% 13.38/13.54 (xuntil7(s39) | (~until6(s39))),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4907, 4375, 4050])).
% 13.38/13.54 tff(4909,plain,
% 13.38/13.54 (xuntil7(s39)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4908, 4901])).
% 13.38/13.54 tff(4910,plain,
% 13.38/13.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s39, s40)) | (~xuntil7(s39)) | until6(s40))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s39, s40)) | (~xuntil7(s39)) | until6(s40))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(4911,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s39, s40)) | (~xuntil7(s39)) | until6(s40))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(4912,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s39, s40)) | (~xuntil7(s39)) | until6(s40)),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[4911, 4910])).
% 13.38/13.54 tff(4913,plain,
% 13.38/13.54 ((~xuntil7(s39)) | until6(s40)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4912, 1201, 4393])).
% 13.38/13.54 tff(4914,plain,
% 13.38/13.54 (until6(s40)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4913, 4909])).
% 13.38/13.54 tff(4915,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s40) | always5(s40) | (~until6(s40)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s40) | always5(s40) | (~until6(s40)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(4916,plain,
% 13.38/13.54 ((always5(s40) | (~until6(s40)) | xuntil7(s40)) <=> (xuntil7(s40) | always5(s40) | (~until6(s40)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(4917,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s40) | (~until6(s40)) | xuntil7(s40))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s40) | always5(s40) | (~until6(s40))))),
% 13.38/13.54 inference(monotonicity,[status(thm)],[4916])).
% 13.38/13.54 tff(4918,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s40) | (~until6(s40)) | xuntil7(s40))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s40) | always5(s40) | (~until6(s40)))),
% 13.38/13.54 inference(transitivity,[status(thm)],[4917, 4915])).
% 13.38/13.54 tff(4919,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s40) | (~until6(s40)) | xuntil7(s40))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(4920,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s40) | always5(s40) | (~until6(s40))),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[4919, 4918])).
% 13.38/13.54 tff(4921,plain,
% 13.38/13.54 (xuntil7(s40) | (~until6(s40))),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4920, 4375, 4042])).
% 13.38/13.54 tff(4922,plain,
% 13.38/13.54 (xuntil7(s40)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4921, 4914])).
% 13.38/13.54 tff(4923,plain,
% 13.38/13.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s40, s41)) | (~xuntil7(s40)) | until6(s41))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s40, s41)) | (~xuntil7(s40)) | until6(s41))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(4924,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s40, s41)) | (~xuntil7(s40)) | until6(s41))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(4925,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s40, s41)) | (~xuntil7(s40)) | until6(s41)),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[4924, 4923])).
% 13.38/13.54 tff(4926,plain,
% 13.38/13.54 ((~xuntil7(s40)) | until6(s41)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4925, 1232, 4393])).
% 13.38/13.54 tff(4927,plain,
% 13.38/13.54 (until6(s41)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4926, 4922])).
% 13.38/13.54 tff(4928,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s41) | always5(s41) | (~until6(s41)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s41) | always5(s41) | (~until6(s41)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(4929,plain,
% 13.38/13.54 ((always5(s41) | (~until6(s41)) | xuntil7(s41)) <=> (xuntil7(s41) | always5(s41) | (~until6(s41)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(4930,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s41) | (~until6(s41)) | xuntil7(s41))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s41) | always5(s41) | (~until6(s41))))),
% 13.38/13.54 inference(monotonicity,[status(thm)],[4929])).
% 13.38/13.54 tff(4931,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s41) | (~until6(s41)) | xuntil7(s41))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s41) | always5(s41) | (~until6(s41)))),
% 13.38/13.54 inference(transitivity,[status(thm)],[4930, 4928])).
% 13.38/13.54 tff(4932,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s41) | (~until6(s41)) | xuntil7(s41))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(4933,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s41) | always5(s41) | (~until6(s41))),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[4932, 4931])).
% 13.38/13.54 tff(4934,plain,
% 13.38/13.54 (xuntil7(s41) | (~until6(s41))),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4933, 4375, 4034])).
% 13.38/13.54 tff(4935,plain,
% 13.38/13.54 (xuntil7(s41)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4934, 4927])).
% 13.38/13.54 tff(4936,plain,
% 13.38/13.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s41, s42)) | (~xuntil7(s41)) | until6(s42))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s41, s42)) | (~xuntil7(s41)) | until6(s42))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(4937,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s41, s42)) | (~xuntil7(s41)) | until6(s42))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(4938,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s41, s42)) | (~xuntil7(s41)) | until6(s42)),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[4937, 4936])).
% 13.38/13.54 tff(4939,plain,
% 13.38/13.54 ((~xuntil7(s41)) | until6(s42)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4938, 1260, 4393])).
% 13.38/13.54 tff(4940,plain,
% 13.38/13.54 (until6(s42)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4939, 4935])).
% 13.38/13.54 tff(4941,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s42) | always5(s42) | (~until6(s42)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s42) | always5(s42) | (~until6(s42)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(4942,plain,
% 13.38/13.54 ((always5(s42) | (~until6(s42)) | xuntil7(s42)) <=> (xuntil7(s42) | always5(s42) | (~until6(s42)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(4943,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s42) | (~until6(s42)) | xuntil7(s42))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s42) | always5(s42) | (~until6(s42))))),
% 13.38/13.54 inference(monotonicity,[status(thm)],[4942])).
% 13.38/13.54 tff(4944,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s42) | (~until6(s42)) | xuntil7(s42))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s42) | always5(s42) | (~until6(s42)))),
% 13.38/13.54 inference(transitivity,[status(thm)],[4943, 4941])).
% 13.38/13.54 tff(4945,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s42) | (~until6(s42)) | xuntil7(s42))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(4946,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s42) | always5(s42) | (~until6(s42))),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[4945, 4944])).
% 13.38/13.54 tff(4947,plain,
% 13.38/13.54 (xuntil7(s42) | (~until6(s42))),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4946, 4375, 4026])).
% 13.38/13.54 tff(4948,plain,
% 13.38/13.54 (xuntil7(s42)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4947, 4940])).
% 13.38/13.54 tff(4949,plain,
% 13.38/13.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s42, s43)) | (~xuntil7(s42)) | until6(s43))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s42, s43)) | (~xuntil7(s42)) | until6(s43))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(4950,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s42, s43)) | (~xuntil7(s42)) | until6(s43))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(4951,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s42, s43)) | (~xuntil7(s42)) | until6(s43)),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[4950, 4949])).
% 13.38/13.54 tff(4952,plain,
% 13.38/13.54 ((~xuntil7(s42)) | until6(s43)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4951, 1291, 4393])).
% 13.38/13.54 tff(4953,plain,
% 13.38/13.54 (until6(s43)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4952, 4948])).
% 13.38/13.54 tff(4954,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s43) | always5(s43) | (~until6(s43)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s43) | always5(s43) | (~until6(s43)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(4955,plain,
% 13.38/13.54 ((always5(s43) | (~until6(s43)) | xuntil7(s43)) <=> (xuntil7(s43) | always5(s43) | (~until6(s43)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(4956,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s43) | (~until6(s43)) | xuntil7(s43))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s43) | always5(s43) | (~until6(s43))))),
% 13.38/13.54 inference(monotonicity,[status(thm)],[4955])).
% 13.38/13.54 tff(4957,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s43) | (~until6(s43)) | xuntil7(s43))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s43) | always5(s43) | (~until6(s43)))),
% 13.38/13.54 inference(transitivity,[status(thm)],[4956, 4954])).
% 13.38/13.54 tff(4958,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s43) | (~until6(s43)) | xuntil7(s43))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(4959,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s43) | always5(s43) | (~until6(s43))),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[4958, 4957])).
% 13.38/13.54 tff(4960,plain,
% 13.38/13.54 (xuntil7(s43) | (~until6(s43))),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4959, 4375, 4018])).
% 13.38/13.54 tff(4961,plain,
% 13.38/13.54 (xuntil7(s43)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4960, 4953])).
% 13.38/13.54 tff(4962,plain,
% 13.38/13.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s43, s44)) | (~xuntil7(s43)) | until6(s44))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s43, s44)) | (~xuntil7(s43)) | until6(s44))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(4963,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s43, s44)) | (~xuntil7(s43)) | until6(s44))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(4964,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s43, s44)) | (~xuntil7(s43)) | until6(s44)),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[4963, 4962])).
% 13.38/13.54 tff(4965,plain,
% 13.38/13.54 ((~xuntil7(s43)) | until6(s44)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4964, 1319, 4393])).
% 13.38/13.54 tff(4966,plain,
% 13.38/13.54 (until6(s44)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4965, 4961])).
% 13.38/13.54 tff(4967,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s44) | always5(s44) | (~until6(s44)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s44) | always5(s44) | (~until6(s44)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(4968,plain,
% 13.38/13.54 ((always5(s44) | (~until6(s44)) | xuntil7(s44)) <=> (xuntil7(s44) | always5(s44) | (~until6(s44)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(4969,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s44) | (~until6(s44)) | xuntil7(s44))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s44) | always5(s44) | (~until6(s44))))),
% 13.38/13.54 inference(monotonicity,[status(thm)],[4968])).
% 13.38/13.54 tff(4970,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s44) | (~until6(s44)) | xuntil7(s44))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s44) | always5(s44) | (~until6(s44)))),
% 13.38/13.54 inference(transitivity,[status(thm)],[4969, 4967])).
% 13.38/13.54 tff(4971,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s44) | (~until6(s44)) | xuntil7(s44))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(4972,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s44) | always5(s44) | (~until6(s44))),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[4971, 4970])).
% 13.38/13.54 tff(4973,plain,
% 13.38/13.54 (xuntil7(s44) | (~until6(s44))),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4972, 4375, 4010])).
% 13.38/13.54 tff(4974,plain,
% 13.38/13.54 (xuntil7(s44)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4973, 4966])).
% 13.38/13.54 tff(4975,plain,
% 13.38/13.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s44, s45)) | (~xuntil7(s44)) | until6(s45))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s44, s45)) | (~xuntil7(s44)) | until6(s45))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(4976,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s44, s45)) | (~xuntil7(s44)) | until6(s45))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(4977,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s44, s45)) | (~xuntil7(s44)) | until6(s45)),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[4976, 4975])).
% 13.38/13.54 tff(4978,plain,
% 13.38/13.54 ((~xuntil7(s44)) | until6(s45)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4977, 2816, 4393])).
% 13.38/13.54 tff(4979,plain,
% 13.38/13.54 (until6(s45)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4978, 4974])).
% 13.38/13.54 tff(4980,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s45) | always5(s45) | (~until6(s45)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s45) | always5(s45) | (~until6(s45)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(4981,plain,
% 13.38/13.54 ((always5(s45) | (~until6(s45)) | xuntil7(s45)) <=> (xuntil7(s45) | always5(s45) | (~until6(s45)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(4982,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s45) | (~until6(s45)) | xuntil7(s45))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s45) | always5(s45) | (~until6(s45))))),
% 13.38/13.54 inference(monotonicity,[status(thm)],[4981])).
% 13.38/13.54 tff(4983,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s45) | (~until6(s45)) | xuntil7(s45))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s45) | always5(s45) | (~until6(s45)))),
% 13.38/13.54 inference(transitivity,[status(thm)],[4982, 4980])).
% 13.38/13.54 tff(4984,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s45) | (~until6(s45)) | xuntil7(s45))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(4985,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s45) | always5(s45) | (~until6(s45))),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[4984, 4983])).
% 13.38/13.54 tff(4986,plain,
% 13.38/13.54 (xuntil7(s45) | (~until6(s45))),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4985, 4375, 4002])).
% 13.38/13.54 tff(4987,plain,
% 13.38/13.54 (xuntil7(s45)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4986, 4979])).
% 13.38/13.54 tff(4988,plain,
% 13.38/13.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s45, s46)) | (~xuntil7(s45)) | until6(s46))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s45, s46)) | (~xuntil7(s45)) | until6(s46))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(4989,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s45, s46)) | (~xuntil7(s45)) | until6(s46))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(4990,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s45, s46)) | (~xuntil7(s45)) | until6(s46)),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[4989, 4988])).
% 13.38/13.54 tff(4991,plain,
% 13.38/13.54 ((~xuntil7(s45)) | until6(s46)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4990, 2883, 4393])).
% 13.38/13.54 tff(4992,plain,
% 13.38/13.54 (until6(s46)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4991, 4987])).
% 13.38/13.54 tff(4993,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s46) | always5(s46) | (~until6(s46)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s46) | always5(s46) | (~until6(s46)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(4994,plain,
% 13.38/13.54 ((always5(s46) | (~until6(s46)) | xuntil7(s46)) <=> (xuntil7(s46) | always5(s46) | (~until6(s46)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(4995,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s46) | (~until6(s46)) | xuntil7(s46))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s46) | always5(s46) | (~until6(s46))))),
% 13.38/13.54 inference(monotonicity,[status(thm)],[4994])).
% 13.38/13.54 tff(4996,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s46) | (~until6(s46)) | xuntil7(s46))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s46) | always5(s46) | (~until6(s46)))),
% 13.38/13.54 inference(transitivity,[status(thm)],[4995, 4993])).
% 13.38/13.54 tff(4997,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s46) | (~until6(s46)) | xuntil7(s46))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(4998,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s46) | always5(s46) | (~until6(s46))),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[4997, 4996])).
% 13.38/13.54 tff(4999,plain,
% 13.38/13.54 (xuntil7(s46) | (~until6(s46))),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4998, 4375, 3994])).
% 13.38/13.54 tff(5000,plain,
% 13.38/13.54 (xuntil7(s46)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[4999, 4992])).
% 13.38/13.54 tff(5001,plain,
% 13.38/13.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s46, s47)) | (~xuntil7(s46)) | until6(s47))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s46, s47)) | (~xuntil7(s46)) | until6(s47))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(5002,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s46, s47)) | (~xuntil7(s46)) | until6(s47))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(5003,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s46, s47)) | (~xuntil7(s46)) | until6(s47)),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[5002, 5001])).
% 13.38/13.54 tff(5004,plain,
% 13.38/13.54 ((~xuntil7(s46)) | until6(s47)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[5003, 2971, 4393])).
% 13.38/13.54 tff(5005,plain,
% 13.38/13.54 (until6(s47)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[5004, 5000])).
% 13.38/13.54 tff(5006,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s47) | always5(s47) | (~until6(s47)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s47) | always5(s47) | (~until6(s47)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(5007,plain,
% 13.38/13.54 ((always5(s47) | (~until6(s47)) | xuntil7(s47)) <=> (xuntil7(s47) | always5(s47) | (~until6(s47)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(5008,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s47) | (~until6(s47)) | xuntil7(s47))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s47) | always5(s47) | (~until6(s47))))),
% 13.38/13.54 inference(monotonicity,[status(thm)],[5007])).
% 13.38/13.54 tff(5009,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s47) | (~until6(s47)) | xuntil7(s47))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s47) | always5(s47) | (~until6(s47)))),
% 13.38/13.54 inference(transitivity,[status(thm)],[5008, 5006])).
% 13.38/13.54 tff(5010,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s47) | (~until6(s47)) | xuntil7(s47))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(5011,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s47) | always5(s47) | (~until6(s47))),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[5010, 5009])).
% 13.38/13.54 tff(5012,plain,
% 13.38/13.54 (xuntil7(s47) | (~until6(s47))),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[5011, 4375, 3986])).
% 13.38/13.54 tff(5013,plain,
% 13.38/13.54 (xuntil7(s47)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[5012, 5005])).
% 13.38/13.54 tff(5014,plain,
% 13.38/13.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s47, s48)) | (~xuntil7(s47)) | until6(s48))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s47, s48)) | (~xuntil7(s47)) | until6(s48))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(5015,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s47, s48)) | (~xuntil7(s47)) | until6(s48))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(5016,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s47, s48)) | (~xuntil7(s47)) | until6(s48)),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[5015, 5014])).
% 13.38/13.54 tff(5017,plain,
% 13.38/13.54 ((~xuntil7(s47)) | until6(s48)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[5016, 3035, 4393])).
% 13.38/13.54 tff(5018,plain,
% 13.38/13.54 (until6(s48)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[5017, 5013])).
% 13.38/13.54 tff(5019,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s48) | always5(s48) | (~until6(s48)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s48) | always5(s48) | (~until6(s48)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(5020,plain,
% 13.38/13.54 ((always5(s48) | (~until6(s48)) | xuntil7(s48)) <=> (xuntil7(s48) | always5(s48) | (~until6(s48)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(5021,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s48) | (~until6(s48)) | xuntil7(s48))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s48) | always5(s48) | (~until6(s48))))),
% 13.38/13.54 inference(monotonicity,[status(thm)],[5020])).
% 13.38/13.54 tff(5022,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s48) | (~until6(s48)) | xuntil7(s48))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s48) | always5(s48) | (~until6(s48)))),
% 13.38/13.54 inference(transitivity,[status(thm)],[5021, 5019])).
% 13.38/13.54 tff(5023,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s48) | (~until6(s48)) | xuntil7(s48))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(5024,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s48) | always5(s48) | (~until6(s48))),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[5023, 5022])).
% 13.38/13.54 tff(5025,plain,
% 13.38/13.54 (xuntil7(s48) | (~until6(s48))),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[5024, 4375, 3978])).
% 13.38/13.54 tff(5026,plain,
% 13.38/13.54 (xuntil7(s48)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[5025, 5018])).
% 13.38/13.54 tff(5027,plain,
% 13.38/13.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s48, s49)) | (~xuntil7(s48)) | until6(s49))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s48, s49)) | (~xuntil7(s48)) | until6(s49))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(5028,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s48, s49)) | (~xuntil7(s48)) | until6(s49))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(5029,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s48, s49)) | (~xuntil7(s48)) | until6(s49)),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[5028, 5027])).
% 13.38/13.54 tff(5030,plain,
% 13.38/13.54 ((~xuntil7(s48)) | until6(s49)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[5029, 3093, 4393])).
% 13.38/13.54 tff(5031,plain,
% 13.38/13.54 (until6(s49)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[5030, 5026])).
% 13.38/13.54 tff(5032,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s49) | always5(s49) | (~until6(s49)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s49) | always5(s49) | (~until6(s49)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(5033,plain,
% 13.38/13.54 ((always5(s49) | (~until6(s49)) | xuntil7(s49)) <=> (xuntil7(s49) | always5(s49) | (~until6(s49)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(5034,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s49) | (~until6(s49)) | xuntil7(s49))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s49) | always5(s49) | (~until6(s49))))),
% 13.38/13.54 inference(monotonicity,[status(thm)],[5033])).
% 13.38/13.54 tff(5035,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s49) | (~until6(s49)) | xuntil7(s49))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s49) | always5(s49) | (~until6(s49)))),
% 13.38/13.54 inference(transitivity,[status(thm)],[5034, 5032])).
% 13.38/13.54 tff(5036,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s49) | (~until6(s49)) | xuntil7(s49))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(5037,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s49) | always5(s49) | (~until6(s49))),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[5036, 5035])).
% 13.38/13.54 tff(5038,plain,
% 13.38/13.54 (xuntil7(s49) | (~until6(s49))),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[5037, 4375, 3970])).
% 13.38/13.54 tff(5039,plain,
% 13.38/13.54 (xuntil7(s49)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[5038, 5031])).
% 13.38/13.54 tff(5040,plain,
% 13.38/13.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s49, s50)) | (~xuntil7(s49)) | until6(s50))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s49, s50)) | (~xuntil7(s49)) | until6(s50))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(5041,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s49, s50)) | (~xuntil7(s49)) | until6(s50))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(5042,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s49, s50)) | (~xuntil7(s49)) | until6(s50)),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[5041, 5040])).
% 13.38/13.54 tff(5043,plain,
% 13.38/13.54 ((~xuntil7(s49)) | until6(s50)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[5042, 3147, 4393])).
% 13.38/13.54 tff(5044,plain,
% 13.38/13.54 (until6(s50)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[5043, 5039])).
% 13.38/13.54 tff(5045,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s50) | always5(s50) | (~until6(s50)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s50) | always5(s50) | (~until6(s50)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(5046,plain,
% 13.38/13.54 ((always5(s50) | (~until6(s50)) | xuntil7(s50)) <=> (xuntil7(s50) | always5(s50) | (~until6(s50)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(5047,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s50) | (~until6(s50)) | xuntil7(s50))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s50) | always5(s50) | (~until6(s50))))),
% 13.38/13.54 inference(monotonicity,[status(thm)],[5046])).
% 13.38/13.54 tff(5048,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s50) | (~until6(s50)) | xuntil7(s50))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s50) | always5(s50) | (~until6(s50)))),
% 13.38/13.54 inference(transitivity,[status(thm)],[5047, 5045])).
% 13.38/13.54 tff(5049,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s50) | (~until6(s50)) | xuntil7(s50))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(5050,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s50) | always5(s50) | (~until6(s50))),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[5049, 5048])).
% 13.38/13.54 tff(5051,plain,
% 13.38/13.54 (xuntil7(s50) | (~until6(s50))),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[5050, 4375, 3962])).
% 13.38/13.54 tff(5052,plain,
% 13.38/13.54 (xuntil7(s50)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[5051, 5044])).
% 13.38/13.54 tff(5053,plain,
% 13.38/13.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s50, s51)) | (~xuntil7(s50)) | until6(s51))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s50, s51)) | (~xuntil7(s50)) | until6(s51))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(5054,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s50, s51)) | (~xuntil7(s50)) | until6(s51))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(5055,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s50, s51)) | (~xuntil7(s50)) | until6(s51)),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[5054, 5053])).
% 13.38/13.54 tff(5056,plain,
% 13.38/13.54 ((~xuntil7(s50)) | until6(s51)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[5055, 3228, 4393])).
% 13.38/13.54 tff(5057,plain,
% 13.38/13.54 (until6(s51)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[5056, 5052])).
% 13.38/13.54 tff(5058,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s51) | always5(s51) | (~until6(s51)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s51) | always5(s51) | (~until6(s51)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(5059,plain,
% 13.38/13.54 ((always5(s51) | (~until6(s51)) | xuntil7(s51)) <=> (xuntil7(s51) | always5(s51) | (~until6(s51)))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(5060,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s51) | (~until6(s51)) | xuntil7(s51))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s51) | always5(s51) | (~until6(s51))))),
% 13.38/13.54 inference(monotonicity,[status(thm)],[5059])).
% 13.38/13.54 tff(5061,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s51) | (~until6(s51)) | xuntil7(s51))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s51) | always5(s51) | (~until6(s51)))),
% 13.38/13.54 inference(transitivity,[status(thm)],[5060, 5058])).
% 13.38/13.54 tff(5062,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s51) | (~until6(s51)) | xuntil7(s51))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(5063,plain,
% 13.38/13.54 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s51) | always5(s51) | (~until6(s51))),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[5062, 5061])).
% 13.38/13.54 tff(5064,plain,
% 13.38/13.54 (xuntil7(s51) | (~until6(s51))),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[5063, 4375, 3954])).
% 13.38/13.54 tff(5065,plain,
% 13.38/13.54 (xuntil7(s51)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[5064, 5057])).
% 13.38/13.54 tff(5066,plain,
% 13.38/13.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s51, s52)) | (~xuntil7(s51)) | until6(s52))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s51, s52)) | (~xuntil7(s51)) | until6(s52))),
% 13.38/13.54 inference(rewrite,[status(thm)],[])).
% 13.38/13.54 tff(5067,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s51, s52)) | (~xuntil7(s51)) | until6(s52))),
% 13.38/13.54 inference(quant_inst,[status(thm)],[])).
% 13.38/13.54 tff(5068,plain,
% 13.38/13.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s51, s52)) | (~xuntil7(s51)) | until6(s52)),
% 13.38/13.54 inference(modus_ponens,[status(thm)],[5067, 5066])).
% 13.38/13.54 tff(5069,plain,
% 13.38/13.54 ((~xuntil7(s51)) | until6(s52)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[5068, 3321, 4393])).
% 13.38/13.54 tff(5070,plain,
% 13.38/13.54 (until6(s52)),
% 13.38/13.54 inference(unit_resolution,[status(thm)],[5069, 5065])).
% 13.38/13.54 tff(5071,plain,
% 13.38/13.54 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s52) | always5(s52) | (~until6(s52)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s52) | always5(s52) | (~until6(s52)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5072,plain,
% 13.38/13.55 ((always5(s52) | (~until6(s52)) | xuntil7(s52)) <=> (xuntil7(s52) | always5(s52) | (~until6(s52)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5073,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s52) | (~until6(s52)) | xuntil7(s52))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s52) | always5(s52) | (~until6(s52))))),
% 13.38/13.55 inference(monotonicity,[status(thm)],[5072])).
% 13.38/13.55 tff(5074,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s52) | (~until6(s52)) | xuntil7(s52))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s52) | always5(s52) | (~until6(s52)))),
% 13.38/13.55 inference(transitivity,[status(thm)],[5073, 5071])).
% 13.38/13.55 tff(5075,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s52) | (~until6(s52)) | xuntil7(s52))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5076,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s52) | always5(s52) | (~until6(s52))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5075, 5074])).
% 13.38/13.55 tff(5077,plain,
% 13.38/13.55 (xuntil7(s52) | (~until6(s52))),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5076, 4375, 3946])).
% 13.38/13.55 tff(5078,plain,
% 13.38/13.55 (xuntil7(s52)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5077, 5070])).
% 13.38/13.55 tff(5079,plain,
% 13.38/13.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s52, s53)) | (~xuntil7(s52)) | until6(s53))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s52, s53)) | (~xuntil7(s52)) | until6(s53))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5080,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s52, s53)) | (~xuntil7(s52)) | until6(s53))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5081,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s52, s53)) | (~xuntil7(s52)) | until6(s53)),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5080, 5079])).
% 13.38/13.55 tff(5082,plain,
% 13.38/13.55 ((~xuntil7(s52)) | until6(s53)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5081, 3379, 4393])).
% 13.38/13.55 tff(5083,plain,
% 13.38/13.55 (until6(s53)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5082, 5078])).
% 13.38/13.55 tff(5084,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s53) | always5(s53) | (~until6(s53)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s53) | always5(s53) | (~until6(s53)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5085,plain,
% 13.38/13.55 ((always5(s53) | (~until6(s53)) | xuntil7(s53)) <=> (xuntil7(s53) | always5(s53) | (~until6(s53)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5086,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s53) | (~until6(s53)) | xuntil7(s53))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s53) | always5(s53) | (~until6(s53))))),
% 13.38/13.55 inference(monotonicity,[status(thm)],[5085])).
% 13.38/13.55 tff(5087,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s53) | (~until6(s53)) | xuntil7(s53))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s53) | always5(s53) | (~until6(s53)))),
% 13.38/13.55 inference(transitivity,[status(thm)],[5086, 5084])).
% 13.38/13.55 tff(5088,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s53) | (~until6(s53)) | xuntil7(s53))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5089,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s53) | always5(s53) | (~until6(s53))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5088, 5087])).
% 13.38/13.55 tff(5090,plain,
% 13.38/13.55 (xuntil7(s53) | (~until6(s53))),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5089, 4375, 3938])).
% 13.38/13.55 tff(5091,plain,
% 13.38/13.55 (xuntil7(s53)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5090, 5083])).
% 13.38/13.55 tff(5092,plain,
% 13.38/13.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s53, s54)) | (~xuntil7(s53)) | until6(s54))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s53, s54)) | (~xuntil7(s53)) | until6(s54))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5093,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s53, s54)) | (~xuntil7(s53)) | until6(s54))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5094,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s53, s54)) | (~xuntil7(s53)) | until6(s54)),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5093, 5092])).
% 13.38/13.55 tff(5095,plain,
% 13.38/13.55 ((~xuntil7(s53)) | until6(s54)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5094, 3446, 4393])).
% 13.38/13.55 tff(5096,plain,
% 13.38/13.55 (until6(s54)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5095, 5091])).
% 13.38/13.55 tff(5097,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s54) | always5(s54) | (~until6(s54)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s54) | always5(s54) | (~until6(s54)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5098,plain,
% 13.38/13.55 ((always5(s54) | (~until6(s54)) | xuntil7(s54)) <=> (xuntil7(s54) | always5(s54) | (~until6(s54)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5099,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s54) | (~until6(s54)) | xuntil7(s54))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s54) | always5(s54) | (~until6(s54))))),
% 13.38/13.55 inference(monotonicity,[status(thm)],[5098])).
% 13.38/13.55 tff(5100,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s54) | (~until6(s54)) | xuntil7(s54))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s54) | always5(s54) | (~until6(s54)))),
% 13.38/13.55 inference(transitivity,[status(thm)],[5099, 5097])).
% 13.38/13.55 tff(5101,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s54) | (~until6(s54)) | xuntil7(s54))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5102,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s54) | always5(s54) | (~until6(s54))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5101, 5100])).
% 13.38/13.55 tff(5103,plain,
% 13.38/13.55 (xuntil7(s54) | (~until6(s54))),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5102, 4375, 3930])).
% 13.38/13.55 tff(5104,plain,
% 13.38/13.55 (xuntil7(s54)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5103, 5096])).
% 13.38/13.55 tff(5105,plain,
% 13.38/13.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s54, s55)) | (~xuntil7(s54)) | until6(s55))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s54, s55)) | (~xuntil7(s54)) | until6(s55))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5106,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s54, s55)) | (~xuntil7(s54)) | until6(s55))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5107,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s54, s55)) | (~xuntil7(s54)) | until6(s55)),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5106, 5105])).
% 13.38/13.55 tff(5108,plain,
% 13.38/13.55 ((~xuntil7(s54)) | until6(s55)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5107, 3508, 4393])).
% 13.38/13.55 tff(5109,plain,
% 13.38/13.55 (until6(s55)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5108, 5104])).
% 13.38/13.55 tff(5110,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s55) | always5(s55) | (~until6(s55)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s55) | always5(s55) | (~until6(s55)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5111,plain,
% 13.38/13.55 ((always5(s55) | (~until6(s55)) | xuntil7(s55)) <=> (xuntil7(s55) | always5(s55) | (~until6(s55)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5112,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s55) | (~until6(s55)) | xuntil7(s55))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s55) | always5(s55) | (~until6(s55))))),
% 13.38/13.55 inference(monotonicity,[status(thm)],[5111])).
% 13.38/13.55 tff(5113,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s55) | (~until6(s55)) | xuntil7(s55))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s55) | always5(s55) | (~until6(s55)))),
% 13.38/13.55 inference(transitivity,[status(thm)],[5112, 5110])).
% 13.38/13.55 tff(5114,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s55) | (~until6(s55)) | xuntil7(s55))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5115,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s55) | always5(s55) | (~until6(s55))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5114, 5113])).
% 13.38/13.55 tff(5116,plain,
% 13.38/13.55 (xuntil7(s55) | (~until6(s55))),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5115, 4375, 3922])).
% 13.38/13.55 tff(5117,plain,
% 13.38/13.55 (xuntil7(s55)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5116, 5109])).
% 13.38/13.55 tff(5118,plain,
% 13.38/13.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s55, s56)) | (~xuntil7(s55)) | until6(s56))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s55, s56)) | (~xuntil7(s55)) | until6(s56))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5119,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s55, s56)) | (~xuntil7(s55)) | until6(s56))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5120,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s55, s56)) | (~xuntil7(s55)) | until6(s56)),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5119, 5118])).
% 13.38/13.55 tff(5121,plain,
% 13.38/13.55 ((~xuntil7(s55)) | until6(s56)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5120, 3572, 4393])).
% 13.38/13.55 tff(5122,plain,
% 13.38/13.55 (until6(s56)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5121, 5117])).
% 13.38/13.55 tff(5123,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s56) | always5(s56) | (~until6(s56)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s56) | always5(s56) | (~until6(s56)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5124,plain,
% 13.38/13.55 ((always5(s56) | (~until6(s56)) | xuntil7(s56)) <=> (xuntil7(s56) | always5(s56) | (~until6(s56)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5125,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s56) | (~until6(s56)) | xuntil7(s56))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s56) | always5(s56) | (~until6(s56))))),
% 13.38/13.55 inference(monotonicity,[status(thm)],[5124])).
% 13.38/13.55 tff(5126,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s56) | (~until6(s56)) | xuntil7(s56))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s56) | always5(s56) | (~until6(s56)))),
% 13.38/13.55 inference(transitivity,[status(thm)],[5125, 5123])).
% 13.38/13.55 tff(5127,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s56) | (~until6(s56)) | xuntil7(s56))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5128,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s56) | always5(s56) | (~until6(s56))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5127, 5126])).
% 13.38/13.55 tff(5129,plain,
% 13.38/13.55 (xuntil7(s56) | (~until6(s56))),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5128, 4375, 3914])).
% 13.38/13.55 tff(5130,plain,
% 13.38/13.55 (xuntil7(s56)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5129, 5122])).
% 13.38/13.55 tff(5131,plain,
% 13.38/13.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s56, s57)) | (~xuntil7(s56)) | until6(s57))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s56, s57)) | (~xuntil7(s56)) | until6(s57))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5132,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s56, s57)) | (~xuntil7(s56)) | until6(s57))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5133,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s56, s57)) | (~xuntil7(s56)) | until6(s57)),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5132, 5131])).
% 13.38/13.55 tff(5134,plain,
% 13.38/13.55 ((~xuntil7(s56)) | until6(s57)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5133, 3638, 4393])).
% 13.38/13.55 tff(5135,plain,
% 13.38/13.55 (until6(s57)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5134, 5130])).
% 13.38/13.55 tff(5136,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s57) | always5(s57) | (~until6(s57)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s57) | always5(s57) | (~until6(s57)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5137,plain,
% 13.38/13.55 ((always5(s57) | (~until6(s57)) | xuntil7(s57)) <=> (xuntil7(s57) | always5(s57) | (~until6(s57)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5138,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s57) | (~until6(s57)) | xuntil7(s57))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s57) | always5(s57) | (~until6(s57))))),
% 13.38/13.55 inference(monotonicity,[status(thm)],[5137])).
% 13.38/13.55 tff(5139,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s57) | (~until6(s57)) | xuntil7(s57))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s57) | always5(s57) | (~until6(s57)))),
% 13.38/13.55 inference(transitivity,[status(thm)],[5138, 5136])).
% 13.38/13.55 tff(5140,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s57) | (~until6(s57)) | xuntil7(s57))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5141,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s57) | always5(s57) | (~until6(s57))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5140, 5139])).
% 13.38/13.55 tff(5142,plain,
% 13.38/13.55 (xuntil7(s57) | (~until6(s57))),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5141, 4375, 3906])).
% 13.38/13.55 tff(5143,plain,
% 13.38/13.55 (xuntil7(s57)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5142, 5135])).
% 13.38/13.55 tff(5144,plain,
% 13.38/13.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s57, s58)) | (~xuntil7(s57)) | until6(s58))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s57, s58)) | (~xuntil7(s57)) | until6(s58))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5145,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s57, s58)) | (~xuntil7(s57)) | until6(s58))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5146,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s57, s58)) | (~xuntil7(s57)) | until6(s58)),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5145, 5144])).
% 13.38/13.55 tff(5147,plain,
% 13.38/13.55 ((~xuntil7(s57)) | until6(s58)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5146, 3729, 4393])).
% 13.38/13.55 tff(5148,plain,
% 13.38/13.55 (until6(s58)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5147, 5143])).
% 13.38/13.55 tff(5149,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s58) | always5(s58) | (~until6(s58)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s58) | always5(s58) | (~until6(s58)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5150,plain,
% 13.38/13.55 ((always5(s58) | (~until6(s58)) | xuntil7(s58)) <=> (xuntil7(s58) | always5(s58) | (~until6(s58)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5151,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s58) | (~until6(s58)) | xuntil7(s58))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s58) | always5(s58) | (~until6(s58))))),
% 13.38/13.55 inference(monotonicity,[status(thm)],[5150])).
% 13.38/13.55 tff(5152,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s58) | (~until6(s58)) | xuntil7(s58))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s58) | always5(s58) | (~until6(s58)))),
% 13.38/13.55 inference(transitivity,[status(thm)],[5151, 5149])).
% 13.38/13.55 tff(5153,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s58) | (~until6(s58)) | xuntil7(s58))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5154,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s58) | always5(s58) | (~until6(s58))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5153, 5152])).
% 13.38/13.55 tff(5155,plain,
% 13.38/13.55 (xuntil7(s58) | (~until6(s58))),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5154, 4375, 3898])).
% 13.38/13.55 tff(5156,plain,
% 13.38/13.55 (xuntil7(s58)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5155, 5148])).
% 13.38/13.55 tff(5157,plain,
% 13.38/13.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s58, s59)) | (~xuntil7(s58)) | until6(s59))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s58, s59)) | (~xuntil7(s58)) | until6(s59))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5158,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s58, s59)) | (~xuntil7(s58)) | until6(s59))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5159,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s58, s59)) | (~xuntil7(s58)) | until6(s59)),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5158, 5157])).
% 13.38/13.55 tff(5160,plain,
% 13.38/13.55 ((~xuntil7(s58)) | until6(s59)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5159, 3813, 4393])).
% 13.38/13.55 tff(5161,plain,
% 13.38/13.55 (until6(s59)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5160, 5156])).
% 13.38/13.55 tff(5162,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s59) | xuntil7(s59) | (~until6(s59)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | always5(s59) | xuntil7(s59) | (~until6(s59)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5163,plain,
% 13.38/13.55 ((always5(s59) | (~until6(s59)) | xuntil7(s59)) <=> (always5(s59) | xuntil7(s59) | (~until6(s59)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5164,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s59) | (~until6(s59)) | xuntil7(s59))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s59) | xuntil7(s59) | (~until6(s59))))),
% 13.38/13.55 inference(monotonicity,[status(thm)],[5163])).
% 13.38/13.55 tff(5165,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s59) | (~until6(s59)) | xuntil7(s59))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | always5(s59) | xuntil7(s59) | (~until6(s59)))),
% 13.38/13.55 inference(transitivity,[status(thm)],[5164, 5162])).
% 13.38/13.55 tff(5166,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s59) | (~until6(s59)) | xuntil7(s59))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5167,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | always5(s59) | xuntil7(s59) | (~until6(s59))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5166, 5165])).
% 13.38/13.55 tff(5168,plain,
% 13.38/13.55 (xuntil7(s59)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5167, 4375, 5161, 3880])).
% 13.38/13.55 tff(5169,plain,
% 13.38/13.55 (^[X: $i] : refl(((~last(X)) | (~xuntil2p9(X))) <=> ((~last(X)) | (~xuntil2p9(X))))),
% 13.38/13.55 inference(bind,[status(th)],[])).
% 13.38/13.55 tff(5170,plain,
% 13.38/13.55 (![X: $i] : ((~last(X)) | (~xuntil2p9(X))) <=> ![X: $i] : ((~last(X)) | (~xuntil2p9(X)))),
% 13.38/13.55 inference(quant_intro,[status(thm)],[5169])).
% 13.38/13.55 tff(5171,plain,
% 13.38/13.55 (![X: $i] : ((~last(X)) | (~xuntil2p9(X))) <=> ![X: $i] : ((~last(X)) | (~xuntil2p9(X)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5172,axiom,(![X: $i] : ((~last(X)) | (~xuntil2p9(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty10')).
% 13.38/13.55 tff(5173,plain,
% 13.38/13.55 (![X: $i] : ((~last(X)) | (~xuntil2p9(X)))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5172, 5171])).
% 13.38/13.55 tff(5174,plain,(
% 13.38/13.55 ![X: $i] : ((~last(X)) | (~xuntil2p9(X)))),
% 13.38/13.55 inference(skolemize,[status(sab)],[5173])).
% 13.38/13.55 tff(5175,plain,
% 13.38/13.55 (![X: $i] : ((~last(X)) | (~xuntil2p9(X)))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5174, 5170])).
% 13.38/13.55 tff(5176,plain,
% 13.38/13.55 (last(s59) <=> last(s59)),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5177,axiom,(last(s59)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound60')).
% 13.38/13.55 tff(5178,plain,
% 13.38/13.55 (last(s59)),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5177, 5176])).
% 13.38/13.55 tff(5179,plain,
% 13.38/13.55 (((~![X: $i] : ((~last(X)) | (~xuntil2p9(X)))) | ((~last(s59)) | (~xuntil2p9(s59)))) <=> ((~![X: $i] : ((~last(X)) | (~xuntil2p9(X)))) | (~last(s59)) | (~xuntil2p9(s59)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5180,plain,
% 13.38/13.55 ((~![X: $i] : ((~last(X)) | (~xuntil2p9(X)))) | ((~last(s59)) | (~xuntil2p9(s59)))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5181,plain,
% 13.38/13.55 ((~![X: $i] : ((~last(X)) | (~xuntil2p9(X)))) | (~last(s59)) | (~xuntil2p9(s59))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5180, 5179])).
% 13.38/13.55 tff(5182,plain,
% 13.38/13.55 (~xuntil2p9(s59)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5181, 5178, 5175])).
% 13.38/13.55 tff(5183,plain,
% 13.38/13.55 (^[X: $i] : refl((always5(X) | xuntil2p9(X) | (~until2p8(X))) <=> (always5(X) | xuntil2p9(X) | (~until2p8(X))))),
% 13.38/13.55 inference(bind,[status(th)],[])).
% 13.38/13.55 tff(5184,plain,
% 13.38/13.55 (![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X))) <=> ![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 13.38/13.55 inference(quant_intro,[status(thm)],[5183])).
% 13.38/13.55 tff(5185,plain,
% 13.38/13.55 (![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X))) <=> ![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5186,plain,
% 13.38/13.55 (^[X: $i] : rewrite(((always5(X) | xuntil2p9(X)) | (~until2p8(X))) <=> (always5(X) | xuntil2p9(X) | (~until2p8(X))))),
% 13.38/13.55 inference(bind,[status(th)],[])).
% 13.38/13.55 tff(5187,plain,
% 13.38/13.55 (![X: $i] : ((always5(X) | xuntil2p9(X)) | (~until2p8(X))) <=> ![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 13.38/13.55 inference(quant_intro,[status(thm)],[5186])).
% 13.38/13.55 tff(5188,axiom,(![X: $i] : ((always5(X) | xuntil2p9(X)) | (~until2p8(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty8')).
% 13.38/13.55 tff(5189,plain,
% 13.38/13.55 (![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5188, 5187])).
% 13.38/13.55 tff(5190,plain,
% 13.38/13.55 (![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5189, 5185])).
% 13.38/13.55 tff(5191,plain,(
% 13.38/13.55 ![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 13.38/13.55 inference(skolemize,[status(sab)],[5190])).
% 13.38/13.55 tff(5192,plain,
% 13.38/13.55 (![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5191, 5184])).
% 13.38/13.55 tff(5193,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s59) | xuntil2p9(s59) | (~until2p8(s59)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s59) | xuntil2p9(s59) | (~until2p8(s59)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5194,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s59) | xuntil2p9(s59) | (~until2p8(s59)))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5195,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s59) | xuntil2p9(s59) | (~until2p8(s59))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5194, 5193])).
% 13.38/13.55 tff(5196,plain,
% 13.38/13.55 (always5(s59) | (~until2p8(s59))),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5195, 5192, 5182])).
% 13.38/13.55 tff(5197,plain,
% 13.38/13.55 (~until2p8(s59)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5196, 3880])).
% 13.38/13.55 tff(5198,plain,
% 13.38/13.55 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X))) <=> ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X))))),
% 13.38/13.55 inference(bind,[status(th)],[])).
% 13.38/13.55 tff(5199,plain,
% 13.38/13.55 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 13.38/13.55 inference(quant_intro,[status(thm)],[5198])).
% 13.38/13.55 tff(5200,plain,
% 13.38/13.55 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5201,plain,
% 13.38/13.55 (^[Y: $i, X: $i] : rewrite(((until2p8(Y) | (~succ(X, Y))) | (~xuntil2p9(X))) <=> ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X))))),
% 13.38/13.55 inference(bind,[status(th)],[])).
% 13.38/13.55 tff(5202,plain,
% 13.38/13.55 (![Y: $i, X: $i] : ((until2p8(Y) | (~succ(X, Y))) | (~xuntil2p9(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 13.38/13.55 inference(quant_intro,[status(thm)],[5201])).
% 13.38/13.55 tff(5203,axiom,(![Y: $i, X: $i] : ((until2p8(Y) | (~succ(X, Y))) | (~xuntil2p9(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty9')).
% 13.38/13.55 tff(5204,plain,
% 13.38/13.55 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5203, 5202])).
% 13.38/13.55 tff(5205,plain,
% 13.38/13.55 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5204, 5200])).
% 13.38/13.55 tff(5206,plain,(
% 13.38/13.55 ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 13.38/13.55 inference(skolemize,[status(sab)],[5205])).
% 13.38/13.55 tff(5207,plain,
% 13.38/13.55 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5206, 5199])).
% 13.38/13.55 tff(5208,plain,
% 13.38/13.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s58, s59)) | until2p8(s59) | (~xuntil2p9(s58)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s58, s59)) | until2p8(s59) | (~xuntil2p9(s58)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5209,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s58, s59)) | until2p8(s59) | (~xuntil2p9(s58)))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5210,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s58, s59)) | until2p8(s59) | (~xuntil2p9(s58))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5209, 5208])).
% 13.38/13.55 tff(5211,plain,
% 13.38/13.55 (until2p8(s59) | (~xuntil2p9(s58))),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5210, 3813, 5207])).
% 13.38/13.55 tff(5212,plain,
% 13.38/13.55 (~xuntil2p9(s58)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5211, 5197])).
% 13.38/13.55 tff(5213,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s58) | xuntil2p9(s58) | (~until2p8(s58)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s58) | xuntil2p9(s58) | (~until2p8(s58)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5214,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s58) | xuntil2p9(s58) | (~until2p8(s58)))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5215,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s58) | xuntil2p9(s58) | (~until2p8(s58))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5214, 5213])).
% 13.38/13.55 tff(5216,plain,
% 13.38/13.55 (~until2p8(s58)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5215, 5192, 5212, 3898])).
% 13.38/13.55 tff(5217,plain,
% 13.38/13.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s57, s58)) | until2p8(s58) | (~xuntil2p9(s57)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s57, s58)) | until2p8(s58) | (~xuntil2p9(s57)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5218,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s57, s58)) | until2p8(s58) | (~xuntil2p9(s57)))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5219,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s57, s58)) | until2p8(s58) | (~xuntil2p9(s57))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5218, 5217])).
% 13.38/13.55 tff(5220,plain,
% 13.38/13.55 (until2p8(s58) | (~xuntil2p9(s57))),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5219, 3729, 5207])).
% 13.38/13.55 tff(5221,plain,
% 13.38/13.55 (~xuntil2p9(s57)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5220, 5216])).
% 13.38/13.55 tff(5222,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s57) | xuntil2p9(s57) | (~until2p8(s57)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s57) | xuntil2p9(s57) | (~until2p8(s57)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5223,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s57) | xuntil2p9(s57) | (~until2p8(s57)))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5224,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s57) | xuntil2p9(s57) | (~until2p8(s57))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5223, 5222])).
% 13.38/13.55 tff(5225,plain,
% 13.38/13.55 (xuntil2p9(s57) | (~until2p8(s57))),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5224, 5192, 3906])).
% 13.38/13.55 tff(5226,plain,
% 13.38/13.55 (~until2p8(s57)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5225, 5221])).
% 13.38/13.55 tff(5227,plain,
% 13.38/13.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s56, s57)) | until2p8(s57) | (~xuntil2p9(s56)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s56, s57)) | until2p8(s57) | (~xuntil2p9(s56)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5228,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s56, s57)) | until2p8(s57) | (~xuntil2p9(s56)))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5229,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s56, s57)) | until2p8(s57) | (~xuntil2p9(s56))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5228, 5227])).
% 13.38/13.55 tff(5230,plain,
% 13.38/13.55 (until2p8(s57) | (~xuntil2p9(s56))),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5229, 3638, 5207])).
% 13.38/13.55 tff(5231,plain,
% 13.38/13.55 (~xuntil2p9(s56)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5230, 5226])).
% 13.38/13.55 tff(5232,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s56) | xuntil2p9(s56) | (~until2p8(s56)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s56) | xuntil2p9(s56) | (~until2p8(s56)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5233,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s56) | xuntil2p9(s56) | (~until2p8(s56)))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5234,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s56) | xuntil2p9(s56) | (~until2p8(s56))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5233, 5232])).
% 13.38/13.55 tff(5235,plain,
% 13.38/13.55 (xuntil2p9(s56) | (~until2p8(s56))),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5234, 5192, 3914])).
% 13.38/13.55 tff(5236,plain,
% 13.38/13.55 (~until2p8(s56)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5235, 5231])).
% 13.38/13.55 tff(5237,plain,
% 13.38/13.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s55, s56)) | until2p8(s56) | (~xuntil2p9(s55)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s55, s56)) | until2p8(s56) | (~xuntil2p9(s55)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5238,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s55, s56)) | until2p8(s56) | (~xuntil2p9(s55)))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5239,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s55, s56)) | until2p8(s56) | (~xuntil2p9(s55))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5238, 5237])).
% 13.38/13.55 tff(5240,plain,
% 13.38/13.55 (until2p8(s56) | (~xuntil2p9(s55))),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5239, 3572, 5207])).
% 13.38/13.55 tff(5241,plain,
% 13.38/13.55 (~xuntil2p9(s55)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5240, 5236])).
% 13.38/13.55 tff(5242,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s55) | xuntil2p9(s55) | (~until2p8(s55)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s55) | xuntil2p9(s55) | (~until2p8(s55)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5243,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s55) | xuntil2p9(s55) | (~until2p8(s55)))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5244,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s55) | xuntil2p9(s55) | (~until2p8(s55))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5243, 5242])).
% 13.38/13.55 tff(5245,plain,
% 13.38/13.55 (xuntil2p9(s55) | (~until2p8(s55))),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5244, 5192, 3922])).
% 13.38/13.55 tff(5246,plain,
% 13.38/13.55 (~until2p8(s55)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5245, 5241])).
% 13.38/13.55 tff(5247,plain,
% 13.38/13.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s54, s55)) | until2p8(s55) | (~xuntil2p9(s54)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s54, s55)) | until2p8(s55) | (~xuntil2p9(s54)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5248,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s54, s55)) | until2p8(s55) | (~xuntil2p9(s54)))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5249,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s54, s55)) | until2p8(s55) | (~xuntil2p9(s54))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5248, 5247])).
% 13.38/13.55 tff(5250,plain,
% 13.38/13.55 (until2p8(s55) | (~xuntil2p9(s54))),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5249, 3508, 5207])).
% 13.38/13.55 tff(5251,plain,
% 13.38/13.55 (~xuntil2p9(s54)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5250, 5246])).
% 13.38/13.55 tff(5252,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s54) | xuntil2p9(s54) | (~until2p8(s54)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s54) | xuntil2p9(s54) | (~until2p8(s54)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5253,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s54) | xuntil2p9(s54) | (~until2p8(s54)))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5254,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s54) | xuntil2p9(s54) | (~until2p8(s54))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5253, 5252])).
% 13.38/13.55 tff(5255,plain,
% 13.38/13.55 (xuntil2p9(s54) | (~until2p8(s54))),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5254, 5192, 3930])).
% 13.38/13.55 tff(5256,plain,
% 13.38/13.55 (~until2p8(s54)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5255, 5251])).
% 13.38/13.55 tff(5257,plain,
% 13.38/13.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s53, s54)) | until2p8(s54) | (~xuntil2p9(s53)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s53, s54)) | until2p8(s54) | (~xuntil2p9(s53)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5258,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s53, s54)) | until2p8(s54) | (~xuntil2p9(s53)))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5259,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s53, s54)) | until2p8(s54) | (~xuntil2p9(s53))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5258, 5257])).
% 13.38/13.55 tff(5260,plain,
% 13.38/13.55 (until2p8(s54) | (~xuntil2p9(s53))),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5259, 3446, 5207])).
% 13.38/13.55 tff(5261,plain,
% 13.38/13.55 (~xuntil2p9(s53)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5260, 5256])).
% 13.38/13.55 tff(5262,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s53) | xuntil2p9(s53) | (~until2p8(s53)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s53) | xuntil2p9(s53) | (~until2p8(s53)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5263,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s53) | xuntil2p9(s53) | (~until2p8(s53)))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5264,plain,
% 13.38/13.55 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s53) | xuntil2p9(s53) | (~until2p8(s53))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5263, 5262])).
% 13.38/13.55 tff(5265,plain,
% 13.38/13.55 (xuntil2p9(s53) | (~until2p8(s53))),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5264, 5192, 3938])).
% 13.38/13.55 tff(5266,plain,
% 13.38/13.55 (~until2p8(s53)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5265, 5261])).
% 13.38/13.55 tff(5267,plain,
% 13.38/13.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s52, s53)) | until2p8(s53) | (~xuntil2p9(s52)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s52, s53)) | until2p8(s53) | (~xuntil2p9(s52)))),
% 13.38/13.55 inference(rewrite,[status(thm)],[])).
% 13.38/13.55 tff(5268,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s52, s53)) | until2p8(s53) | (~xuntil2p9(s52)))),
% 13.38/13.55 inference(quant_inst,[status(thm)],[])).
% 13.38/13.55 tff(5269,plain,
% 13.38/13.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s52, s53)) | until2p8(s53) | (~xuntil2p9(s52))),
% 13.38/13.55 inference(modus_ponens,[status(thm)],[5268, 5267])).
% 13.38/13.55 tff(5270,plain,
% 13.38/13.55 (until2p8(s53) | (~xuntil2p9(s52))),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5269, 3379, 5207])).
% 13.38/13.55 tff(5271,plain,
% 13.38/13.55 (~xuntil2p9(s52)),
% 13.38/13.55 inference(unit_resolution,[status(thm)],[5270, 5266])).
% 13.38/13.55 tff(5272,plain,
% 13.38/13.55 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s52) | xuntil2p9(s52) | (~until2p8(s52)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s52) | xuntil2p9(s52) | (~until2p8(s52)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5273,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s52) | xuntil2p9(s52) | (~until2p8(s52)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5274,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s52) | xuntil2p9(s52) | (~until2p8(s52))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5273, 5272])).
% 13.38/13.56 tff(5275,plain,
% 13.38/13.56 (xuntil2p9(s52) | (~until2p8(s52))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5274, 5192, 3946])).
% 13.38/13.56 tff(5276,plain,
% 13.38/13.56 (~until2p8(s52)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5275, 5271])).
% 13.38/13.56 tff(5277,plain,
% 13.38/13.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s51, s52)) | until2p8(s52) | (~xuntil2p9(s51)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s51, s52)) | until2p8(s52) | (~xuntil2p9(s51)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5278,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s51, s52)) | until2p8(s52) | (~xuntil2p9(s51)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5279,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s51, s52)) | until2p8(s52) | (~xuntil2p9(s51))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5278, 5277])).
% 13.38/13.56 tff(5280,plain,
% 13.38/13.56 (until2p8(s52) | (~xuntil2p9(s51))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5279, 3321, 5207])).
% 13.38/13.56 tff(5281,plain,
% 13.38/13.56 (~xuntil2p9(s51)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5280, 5276])).
% 13.38/13.56 tff(5282,plain,
% 13.38/13.56 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s51) | xuntil2p9(s51) | (~until2p8(s51)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s51) | xuntil2p9(s51) | (~until2p8(s51)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5283,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s51) | xuntil2p9(s51) | (~until2p8(s51)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5284,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s51) | xuntil2p9(s51) | (~until2p8(s51))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5283, 5282])).
% 13.38/13.56 tff(5285,plain,
% 13.38/13.56 (xuntil2p9(s51) | (~until2p8(s51))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5284, 5192, 3954])).
% 13.38/13.56 tff(5286,plain,
% 13.38/13.56 (~until2p8(s51)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5285, 5281])).
% 13.38/13.56 tff(5287,plain,
% 13.38/13.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s50, s51)) | until2p8(s51) | (~xuntil2p9(s50)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s50, s51)) | until2p8(s51) | (~xuntil2p9(s50)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5288,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s50, s51)) | until2p8(s51) | (~xuntil2p9(s50)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5289,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s50, s51)) | until2p8(s51) | (~xuntil2p9(s50))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5288, 5287])).
% 13.38/13.56 tff(5290,plain,
% 13.38/13.56 (until2p8(s51) | (~xuntil2p9(s50))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5289, 3228, 5207])).
% 13.38/13.56 tff(5291,plain,
% 13.38/13.56 (~xuntil2p9(s50)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5290, 5286])).
% 13.38/13.56 tff(5292,plain,
% 13.38/13.56 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s50) | xuntil2p9(s50) | (~until2p8(s50)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s50) | xuntil2p9(s50) | (~until2p8(s50)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5293,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s50) | xuntil2p9(s50) | (~until2p8(s50)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5294,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s50) | xuntil2p9(s50) | (~until2p8(s50))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5293, 5292])).
% 13.38/13.56 tff(5295,plain,
% 13.38/13.56 (xuntil2p9(s50) | (~until2p8(s50))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5294, 5192, 3962])).
% 13.38/13.56 tff(5296,plain,
% 13.38/13.56 (~until2p8(s50)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5295, 5291])).
% 13.38/13.56 tff(5297,plain,
% 13.38/13.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s49, s50)) | until2p8(s50) | (~xuntil2p9(s49)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s49, s50)) | until2p8(s50) | (~xuntil2p9(s49)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5298,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s49, s50)) | until2p8(s50) | (~xuntil2p9(s49)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5299,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s49, s50)) | until2p8(s50) | (~xuntil2p9(s49))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5298, 5297])).
% 13.38/13.56 tff(5300,plain,
% 13.38/13.56 (until2p8(s50) | (~xuntil2p9(s49))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5299, 3147, 5207])).
% 13.38/13.56 tff(5301,plain,
% 13.38/13.56 (~xuntil2p9(s49)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5300, 5296])).
% 13.38/13.56 tff(5302,plain,
% 13.38/13.56 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s49) | xuntil2p9(s49) | (~until2p8(s49)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s49) | xuntil2p9(s49) | (~until2p8(s49)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5303,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s49) | xuntil2p9(s49) | (~until2p8(s49)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5304,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s49) | xuntil2p9(s49) | (~until2p8(s49))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5303, 5302])).
% 13.38/13.56 tff(5305,plain,
% 13.38/13.56 (xuntil2p9(s49) | (~until2p8(s49))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5304, 5192, 3970])).
% 13.38/13.56 tff(5306,plain,
% 13.38/13.56 (~until2p8(s49)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5305, 5301])).
% 13.38/13.56 tff(5307,plain,
% 13.38/13.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s48, s49)) | until2p8(s49) | (~xuntil2p9(s48)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s48, s49)) | until2p8(s49) | (~xuntil2p9(s48)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5308,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s48, s49)) | until2p8(s49) | (~xuntil2p9(s48)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5309,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s48, s49)) | until2p8(s49) | (~xuntil2p9(s48))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5308, 5307])).
% 13.38/13.56 tff(5310,plain,
% 13.38/13.56 (until2p8(s49) | (~xuntil2p9(s48))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5309, 3093, 5207])).
% 13.38/13.56 tff(5311,plain,
% 13.38/13.56 (~xuntil2p9(s48)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5310, 5306])).
% 13.38/13.56 tff(5312,plain,
% 13.38/13.56 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s48) | xuntil2p9(s48) | (~until2p8(s48)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s48) | xuntil2p9(s48) | (~until2p8(s48)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5313,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s48) | xuntil2p9(s48) | (~until2p8(s48)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5314,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s48) | xuntil2p9(s48) | (~until2p8(s48))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5313, 5312])).
% 13.38/13.56 tff(5315,plain,
% 13.38/13.56 (xuntil2p9(s48) | (~until2p8(s48))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5314, 5192, 3978])).
% 13.38/13.56 tff(5316,plain,
% 13.38/13.56 (~until2p8(s48)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5315, 5311])).
% 13.38/13.56 tff(5317,plain,
% 13.38/13.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s47, s48)) | until2p8(s48) | (~xuntil2p9(s47)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s47, s48)) | until2p8(s48) | (~xuntil2p9(s47)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5318,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s47, s48)) | until2p8(s48) | (~xuntil2p9(s47)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5319,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s47, s48)) | until2p8(s48) | (~xuntil2p9(s47))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5318, 5317])).
% 13.38/13.56 tff(5320,plain,
% 13.38/13.56 (until2p8(s48) | (~xuntil2p9(s47))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5319, 3035, 5207])).
% 13.38/13.56 tff(5321,plain,
% 13.38/13.56 (~xuntil2p9(s47)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5320, 5316])).
% 13.38/13.56 tff(5322,plain,
% 13.38/13.56 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s47) | xuntil2p9(s47) | (~until2p8(s47)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s47) | xuntil2p9(s47) | (~until2p8(s47)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5323,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s47) | xuntil2p9(s47) | (~until2p8(s47)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5324,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s47) | xuntil2p9(s47) | (~until2p8(s47))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5323, 5322])).
% 13.38/13.56 tff(5325,plain,
% 13.38/13.56 (xuntil2p9(s47) | (~until2p8(s47))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5324, 5192, 3986])).
% 13.38/13.56 tff(5326,plain,
% 13.38/13.56 (~until2p8(s47)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5325, 5321])).
% 13.38/13.56 tff(5327,plain,
% 13.38/13.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s46, s47)) | until2p8(s47) | (~xuntil2p9(s46)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s46, s47)) | until2p8(s47) | (~xuntil2p9(s46)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5328,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s46, s47)) | until2p8(s47) | (~xuntil2p9(s46)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5329,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s46, s47)) | until2p8(s47) | (~xuntil2p9(s46))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5328, 5327])).
% 13.38/13.56 tff(5330,plain,
% 13.38/13.56 (until2p8(s47) | (~xuntil2p9(s46))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5329, 2971, 5207])).
% 13.38/13.56 tff(5331,plain,
% 13.38/13.56 (~xuntil2p9(s46)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5330, 5326])).
% 13.38/13.56 tff(5332,plain,
% 13.38/13.56 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s46) | xuntil2p9(s46) | (~until2p8(s46)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s46) | xuntil2p9(s46) | (~until2p8(s46)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5333,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s46) | xuntil2p9(s46) | (~until2p8(s46)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5334,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s46) | xuntil2p9(s46) | (~until2p8(s46))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5333, 5332])).
% 13.38/13.56 tff(5335,plain,
% 13.38/13.56 (xuntil2p9(s46) | (~until2p8(s46))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5334, 5192, 3994])).
% 13.38/13.56 tff(5336,plain,
% 13.38/13.56 (~until2p8(s46)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5335, 5331])).
% 13.38/13.56 tff(5337,plain,
% 13.38/13.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s45, s46)) | until2p8(s46) | (~xuntil2p9(s45)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s45, s46)) | until2p8(s46) | (~xuntil2p9(s45)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5338,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s45, s46)) | until2p8(s46) | (~xuntil2p9(s45)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5339,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s45, s46)) | until2p8(s46) | (~xuntil2p9(s45))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5338, 5337])).
% 13.38/13.56 tff(5340,plain,
% 13.38/13.56 (until2p8(s46) | (~xuntil2p9(s45))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5339, 2883, 5207])).
% 13.38/13.56 tff(5341,plain,
% 13.38/13.56 (~xuntil2p9(s45)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5340, 5336])).
% 13.38/13.56 tff(5342,plain,
% 13.38/13.56 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s45) | xuntil2p9(s45) | (~until2p8(s45)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s45) | xuntil2p9(s45) | (~until2p8(s45)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5343,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s45) | xuntil2p9(s45) | (~until2p8(s45)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5344,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s45) | xuntil2p9(s45) | (~until2p8(s45))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5343, 5342])).
% 13.38/13.56 tff(5345,plain,
% 13.38/13.56 (xuntil2p9(s45) | (~until2p8(s45))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5344, 5192, 4002])).
% 13.38/13.56 tff(5346,plain,
% 13.38/13.56 (~until2p8(s45)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5345, 5341])).
% 13.38/13.56 tff(5347,plain,
% 13.38/13.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s44, s45)) | until2p8(s45) | (~xuntil2p9(s44)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s44, s45)) | until2p8(s45) | (~xuntil2p9(s44)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5348,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s44, s45)) | until2p8(s45) | (~xuntil2p9(s44)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5349,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s44, s45)) | until2p8(s45) | (~xuntil2p9(s44))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5348, 5347])).
% 13.38/13.56 tff(5350,plain,
% 13.38/13.56 (until2p8(s45) | (~xuntil2p9(s44))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5349, 2816, 5207])).
% 13.38/13.56 tff(5351,plain,
% 13.38/13.56 (~xuntil2p9(s44)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5350, 5346])).
% 13.38/13.56 tff(5352,plain,
% 13.38/13.56 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s44) | xuntil2p9(s44) | (~until2p8(s44)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s44) | xuntil2p9(s44) | (~until2p8(s44)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5353,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s44) | xuntil2p9(s44) | (~until2p8(s44)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5354,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s44) | xuntil2p9(s44) | (~until2p8(s44))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5353, 5352])).
% 13.38/13.56 tff(5355,plain,
% 13.38/13.56 (xuntil2p9(s44) | (~until2p8(s44))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5354, 5192, 4010])).
% 13.38/13.56 tff(5356,plain,
% 13.38/13.56 (~until2p8(s44)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5355, 5351])).
% 13.38/13.56 tff(5357,plain,
% 13.38/13.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s43, s44)) | until2p8(s44) | (~xuntil2p9(s43)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s43, s44)) | until2p8(s44) | (~xuntil2p9(s43)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5358,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s43, s44)) | until2p8(s44) | (~xuntil2p9(s43)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5359,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s43, s44)) | until2p8(s44) | (~xuntil2p9(s43))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5358, 5357])).
% 13.38/13.56 tff(5360,plain,
% 13.38/13.56 (until2p8(s44) | (~xuntil2p9(s43))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5359, 1319, 5207])).
% 13.38/13.56 tff(5361,plain,
% 13.38/13.56 (~xuntil2p9(s43)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5360, 5356])).
% 13.38/13.56 tff(5362,plain,
% 13.38/13.56 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s43) | xuntil2p9(s43) | (~until2p8(s43)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s43) | xuntil2p9(s43) | (~until2p8(s43)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5363,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s43) | xuntil2p9(s43) | (~until2p8(s43)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5364,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s43) | xuntil2p9(s43) | (~until2p8(s43))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5363, 5362])).
% 13.38/13.56 tff(5365,plain,
% 13.38/13.56 (xuntil2p9(s43) | (~until2p8(s43))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5364, 5192, 4018])).
% 13.38/13.56 tff(5366,plain,
% 13.38/13.56 (~until2p8(s43)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5365, 5361])).
% 13.38/13.56 tff(5367,plain,
% 13.38/13.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s42, s43)) | until2p8(s43) | (~xuntil2p9(s42)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s42, s43)) | until2p8(s43) | (~xuntil2p9(s42)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5368,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s42, s43)) | until2p8(s43) | (~xuntil2p9(s42)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5369,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s42, s43)) | until2p8(s43) | (~xuntil2p9(s42))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5368, 5367])).
% 13.38/13.56 tff(5370,plain,
% 13.38/13.56 (until2p8(s43) | (~xuntil2p9(s42))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5369, 1291, 5207])).
% 13.38/13.56 tff(5371,plain,
% 13.38/13.56 (~xuntil2p9(s42)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5370, 5366])).
% 13.38/13.56 tff(5372,plain,
% 13.38/13.56 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s42) | xuntil2p9(s42) | (~until2p8(s42)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s42) | xuntil2p9(s42) | (~until2p8(s42)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5373,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s42) | xuntil2p9(s42) | (~until2p8(s42)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5374,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s42) | xuntil2p9(s42) | (~until2p8(s42))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5373, 5372])).
% 13.38/13.56 tff(5375,plain,
% 13.38/13.56 (xuntil2p9(s42) | (~until2p8(s42))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5374, 5192, 4026])).
% 13.38/13.56 tff(5376,plain,
% 13.38/13.56 (~until2p8(s42)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5375, 5371])).
% 13.38/13.56 tff(5377,plain,
% 13.38/13.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s41, s42)) | until2p8(s42) | (~xuntil2p9(s41)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s41, s42)) | until2p8(s42) | (~xuntil2p9(s41)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5378,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s41, s42)) | until2p8(s42) | (~xuntil2p9(s41)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5379,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s41, s42)) | until2p8(s42) | (~xuntil2p9(s41))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5378, 5377])).
% 13.38/13.56 tff(5380,plain,
% 13.38/13.56 (until2p8(s42) | (~xuntil2p9(s41))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5379, 1260, 5207])).
% 13.38/13.56 tff(5381,plain,
% 13.38/13.56 (~xuntil2p9(s41)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5380, 5376])).
% 13.38/13.56 tff(5382,plain,
% 13.38/13.56 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s41) | xuntil2p9(s41) | (~until2p8(s41)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s41) | xuntil2p9(s41) | (~until2p8(s41)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5383,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s41) | xuntil2p9(s41) | (~until2p8(s41)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5384,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s41) | xuntil2p9(s41) | (~until2p8(s41))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5383, 5382])).
% 13.38/13.56 tff(5385,plain,
% 13.38/13.56 (xuntil2p9(s41) | (~until2p8(s41))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5384, 5192, 4034])).
% 13.38/13.56 tff(5386,plain,
% 13.38/13.56 (~until2p8(s41)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5385, 5381])).
% 13.38/13.56 tff(5387,plain,
% 13.38/13.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s40, s41)) | until2p8(s41) | (~xuntil2p9(s40)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s40, s41)) | until2p8(s41) | (~xuntil2p9(s40)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5388,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s40, s41)) | until2p8(s41) | (~xuntil2p9(s40)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5389,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s40, s41)) | until2p8(s41) | (~xuntil2p9(s40))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5388, 5387])).
% 13.38/13.56 tff(5390,plain,
% 13.38/13.56 (until2p8(s41) | (~xuntil2p9(s40))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5389, 1232, 5207])).
% 13.38/13.56 tff(5391,plain,
% 13.38/13.56 (~xuntil2p9(s40)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5390, 5386])).
% 13.38/13.56 tff(5392,plain,
% 13.38/13.56 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s40) | xuntil2p9(s40) | (~until2p8(s40)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s40) | xuntil2p9(s40) | (~until2p8(s40)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5393,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s40) | xuntil2p9(s40) | (~until2p8(s40)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5394,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s40) | xuntil2p9(s40) | (~until2p8(s40))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5393, 5392])).
% 13.38/13.56 tff(5395,plain,
% 13.38/13.56 (xuntil2p9(s40) | (~until2p8(s40))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5394, 5192, 4042])).
% 13.38/13.56 tff(5396,plain,
% 13.38/13.56 (~until2p8(s40)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5395, 5391])).
% 13.38/13.56 tff(5397,plain,
% 13.38/13.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s39, s40)) | until2p8(s40) | (~xuntil2p9(s39)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s39, s40)) | until2p8(s40) | (~xuntil2p9(s39)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5398,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s39, s40)) | until2p8(s40) | (~xuntil2p9(s39)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5399,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s39, s40)) | until2p8(s40) | (~xuntil2p9(s39))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5398, 5397])).
% 13.38/13.56 tff(5400,plain,
% 13.38/13.56 (until2p8(s40) | (~xuntil2p9(s39))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5399, 1201, 5207])).
% 13.38/13.56 tff(5401,plain,
% 13.38/13.56 (~xuntil2p9(s39)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5400, 5396])).
% 13.38/13.56 tff(5402,plain,
% 13.38/13.56 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s39) | xuntil2p9(s39) | (~until2p8(s39)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s39) | xuntil2p9(s39) | (~until2p8(s39)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5403,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s39) | xuntil2p9(s39) | (~until2p8(s39)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5404,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s39) | xuntil2p9(s39) | (~until2p8(s39))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5403, 5402])).
% 13.38/13.56 tff(5405,plain,
% 13.38/13.56 (xuntil2p9(s39) | (~until2p8(s39))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5404, 5192, 4050])).
% 13.38/13.56 tff(5406,plain,
% 13.38/13.56 (~until2p8(s39)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5405, 5401])).
% 13.38/13.56 tff(5407,plain,
% 13.38/13.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s38, s39)) | until2p8(s39) | (~xuntil2p9(s38)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s38, s39)) | until2p8(s39) | (~xuntil2p9(s38)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5408,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s38, s39)) | until2p8(s39) | (~xuntil2p9(s38)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5409,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s38, s39)) | until2p8(s39) | (~xuntil2p9(s38))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5408, 5407])).
% 13.38/13.56 tff(5410,plain,
% 13.38/13.56 (until2p8(s39) | (~xuntil2p9(s38))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5409, 1173, 5207])).
% 13.38/13.56 tff(5411,plain,
% 13.38/13.56 (~xuntil2p9(s38)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5410, 5406])).
% 13.38/13.56 tff(5412,plain,
% 13.38/13.56 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s38) | xuntil2p9(s38) | (~until2p8(s38)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s38) | xuntil2p9(s38) | (~until2p8(s38)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5413,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s38) | xuntil2p9(s38) | (~until2p8(s38)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5414,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s38) | xuntil2p9(s38) | (~until2p8(s38))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5413, 5412])).
% 13.38/13.56 tff(5415,plain,
% 13.38/13.56 (xuntil2p9(s38) | (~until2p8(s38))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5414, 5192, 4058])).
% 13.38/13.56 tff(5416,plain,
% 13.38/13.56 (~until2p8(s38)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5415, 5411])).
% 13.38/13.56 tff(5417,plain,
% 13.38/13.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s37, s38)) | until2p8(s38) | (~xuntil2p9(s37)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s37, s38)) | until2p8(s38) | (~xuntil2p9(s37)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5418,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s37, s38)) | until2p8(s38) | (~xuntil2p9(s37)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5419,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s37, s38)) | until2p8(s38) | (~xuntil2p9(s37))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5418, 5417])).
% 13.38/13.56 tff(5420,plain,
% 13.38/13.56 (until2p8(s38) | (~xuntil2p9(s37))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5419, 1142, 5207])).
% 13.38/13.56 tff(5421,plain,
% 13.38/13.56 (~xuntil2p9(s37)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5420, 5416])).
% 13.38/13.56 tff(5422,plain,
% 13.38/13.56 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s37) | xuntil2p9(s37) | (~until2p8(s37)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s37) | xuntil2p9(s37) | (~until2p8(s37)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5423,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s37) | xuntil2p9(s37) | (~until2p8(s37)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5424,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s37) | xuntil2p9(s37) | (~until2p8(s37))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5423, 5422])).
% 13.38/13.56 tff(5425,plain,
% 13.38/13.56 (xuntil2p9(s37) | (~until2p8(s37))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5424, 5192, 4066])).
% 13.38/13.56 tff(5426,plain,
% 13.38/13.56 (~until2p8(s37)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5425, 5421])).
% 13.38/13.56 tff(5427,plain,
% 13.38/13.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s36, s37)) | until2p8(s37) | (~xuntil2p9(s36)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s36, s37)) | until2p8(s37) | (~xuntil2p9(s36)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5428,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s36, s37)) | until2p8(s37) | (~xuntil2p9(s36)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5429,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s36, s37)) | until2p8(s37) | (~xuntil2p9(s36))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5428, 5427])).
% 13.38/13.56 tff(5430,plain,
% 13.38/13.56 (until2p8(s37) | (~xuntil2p9(s36))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5429, 1114, 5207])).
% 13.38/13.56 tff(5431,plain,
% 13.38/13.56 (~xuntil2p9(s36)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5430, 5426])).
% 13.38/13.56 tff(5432,plain,
% 13.38/13.56 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s36) | xuntil2p9(s36) | (~until2p8(s36)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s36) | xuntil2p9(s36) | (~until2p8(s36)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5433,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s36) | xuntil2p9(s36) | (~until2p8(s36)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5434,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s36) | xuntil2p9(s36) | (~until2p8(s36))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5433, 5432])).
% 13.38/13.56 tff(5435,plain,
% 13.38/13.56 (xuntil2p9(s36) | (~until2p8(s36))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5434, 5192, 4074])).
% 13.38/13.56 tff(5436,plain,
% 13.38/13.56 (~until2p8(s36)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5435, 5431])).
% 13.38/13.56 tff(5437,plain,
% 13.38/13.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s35, s36)) | until2p8(s36) | (~xuntil2p9(s35)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s35, s36)) | until2p8(s36) | (~xuntil2p9(s35)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5438,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s35, s36)) | until2p8(s36) | (~xuntil2p9(s35)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5439,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s35, s36)) | until2p8(s36) | (~xuntil2p9(s35))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5438, 5437])).
% 13.38/13.56 tff(5440,plain,
% 13.38/13.56 (until2p8(s36) | (~xuntil2p9(s35))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5439, 1083, 5207])).
% 13.38/13.56 tff(5441,plain,
% 13.38/13.56 (~xuntil2p9(s35)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5440, 5436])).
% 13.38/13.56 tff(5442,plain,
% 13.38/13.56 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s35) | xuntil2p9(s35) | (~until2p8(s35)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s35) | xuntil2p9(s35) | (~until2p8(s35)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5443,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s35) | xuntil2p9(s35) | (~until2p8(s35)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5444,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s35) | xuntil2p9(s35) | (~until2p8(s35))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5443, 5442])).
% 13.38/13.56 tff(5445,plain,
% 13.38/13.56 (xuntil2p9(s35) | (~until2p8(s35))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5444, 5192, 4082])).
% 13.38/13.56 tff(5446,plain,
% 13.38/13.56 (~until2p8(s35)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5445, 5441])).
% 13.38/13.56 tff(5447,plain,
% 13.38/13.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s34, s35)) | until2p8(s35) | (~xuntil2p9(s34)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s34, s35)) | until2p8(s35) | (~xuntil2p9(s34)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5448,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s34, s35)) | until2p8(s35) | (~xuntil2p9(s34)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5449,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s34, s35)) | until2p8(s35) | (~xuntil2p9(s34))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5448, 5447])).
% 13.38/13.56 tff(5450,plain,
% 13.38/13.56 (until2p8(s35) | (~xuntil2p9(s34))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5449, 1055, 5207])).
% 13.38/13.56 tff(5451,plain,
% 13.38/13.56 (~xuntil2p9(s34)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5450, 5446])).
% 13.38/13.56 tff(5452,plain,
% 13.38/13.56 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s34) | xuntil2p9(s34) | (~until2p8(s34)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s34) | xuntil2p9(s34) | (~until2p8(s34)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5453,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s34) | xuntil2p9(s34) | (~until2p8(s34)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5454,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s34) | xuntil2p9(s34) | (~until2p8(s34))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5453, 5452])).
% 13.38/13.56 tff(5455,plain,
% 13.38/13.56 (xuntil2p9(s34) | (~until2p8(s34))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5454, 5192, 4090])).
% 13.38/13.56 tff(5456,plain,
% 13.38/13.56 (~until2p8(s34)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5455, 5451])).
% 13.38/13.56 tff(5457,plain,
% 13.38/13.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s33, s34)) | until2p8(s34) | (~xuntil2p9(s33)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s33, s34)) | until2p8(s34) | (~xuntil2p9(s33)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5458,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s33, s34)) | until2p8(s34) | (~xuntil2p9(s33)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5459,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s33, s34)) | until2p8(s34) | (~xuntil2p9(s33))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5458, 5457])).
% 13.38/13.56 tff(5460,plain,
% 13.38/13.56 (until2p8(s34) | (~xuntil2p9(s33))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5459, 1024, 5207])).
% 13.38/13.56 tff(5461,plain,
% 13.38/13.56 (~xuntil2p9(s33)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5460, 5456])).
% 13.38/13.56 tff(5462,plain,
% 13.38/13.56 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s33) | xuntil2p9(s33) | (~until2p8(s33)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s33) | xuntil2p9(s33) | (~until2p8(s33)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5463,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s33) | xuntil2p9(s33) | (~until2p8(s33)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5464,plain,
% 13.38/13.56 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s33) | xuntil2p9(s33) | (~until2p8(s33))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5463, 5462])).
% 13.38/13.56 tff(5465,plain,
% 13.38/13.56 (xuntil2p9(s33) | (~until2p8(s33))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5464, 5192, 4098])).
% 13.38/13.56 tff(5466,plain,
% 13.38/13.56 (~until2p8(s33)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5465, 5461])).
% 13.38/13.56 tff(5467,plain,
% 13.38/13.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s32, s33)) | until2p8(s33) | (~xuntil2p9(s32)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s32, s33)) | until2p8(s33) | (~xuntil2p9(s32)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.56 tff(5468,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s32, s33)) | until2p8(s33) | (~xuntil2p9(s32)))),
% 13.38/13.56 inference(quant_inst,[status(thm)],[])).
% 13.38/13.56 tff(5469,plain,
% 13.38/13.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s32, s33)) | until2p8(s33) | (~xuntil2p9(s32))),
% 13.38/13.56 inference(modus_ponens,[status(thm)],[5468, 5467])).
% 13.38/13.56 tff(5470,plain,
% 13.38/13.56 (until2p8(s33) | (~xuntil2p9(s32))),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5469, 996, 5207])).
% 13.38/13.56 tff(5471,plain,
% 13.38/13.56 (~xuntil2p9(s32)),
% 13.38/13.56 inference(unit_resolution,[status(thm)],[5470, 5466])).
% 13.38/13.56 tff(5472,plain,
% 13.38/13.56 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s32) | xuntil2p9(s32) | (~until2p8(s32)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s32) | xuntil2p9(s32) | (~until2p8(s32)))),
% 13.38/13.56 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5473,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s32) | xuntil2p9(s32) | (~until2p8(s32)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5474,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s32) | xuntil2p9(s32) | (~until2p8(s32))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5473, 5472])).
% 13.38/13.57 tff(5475,plain,
% 13.38/13.57 (xuntil2p9(s32) | (~until2p8(s32))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5474, 5192, 4106])).
% 13.38/13.57 tff(5476,plain,
% 13.38/13.57 (~until2p8(s32)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5475, 5471])).
% 13.38/13.57 tff(5477,plain,
% 13.38/13.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s31, s32)) | until2p8(s32) | (~xuntil2p9(s31)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s31, s32)) | until2p8(s32) | (~xuntil2p9(s31)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5478,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s31, s32)) | until2p8(s32) | (~xuntil2p9(s31)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5479,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s31, s32)) | until2p8(s32) | (~xuntil2p9(s31))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5478, 5477])).
% 13.38/13.57 tff(5480,plain,
% 13.38/13.57 (until2p8(s32) | (~xuntil2p9(s31))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5479, 965, 5207])).
% 13.38/13.57 tff(5481,plain,
% 13.38/13.57 (~xuntil2p9(s31)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5480, 5476])).
% 13.38/13.57 tff(5482,plain,
% 13.38/13.57 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s31) | xuntil2p9(s31) | (~until2p8(s31)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s31) | xuntil2p9(s31) | (~until2p8(s31)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5483,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s31) | xuntil2p9(s31) | (~until2p8(s31)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5484,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s31) | xuntil2p9(s31) | (~until2p8(s31))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5483, 5482])).
% 13.38/13.57 tff(5485,plain,
% 13.38/13.57 (xuntil2p9(s31) | (~until2p8(s31))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5484, 5192, 4114])).
% 13.38/13.57 tff(5486,plain,
% 13.38/13.57 (~until2p8(s31)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5485, 5481])).
% 13.38/13.57 tff(5487,plain,
% 13.38/13.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s30, s31)) | until2p8(s31) | (~xuntil2p9(s30)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s30, s31)) | until2p8(s31) | (~xuntil2p9(s30)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5488,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s30, s31)) | until2p8(s31) | (~xuntil2p9(s30)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5489,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s30, s31)) | until2p8(s31) | (~xuntil2p9(s30))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5488, 5487])).
% 13.38/13.57 tff(5490,plain,
% 13.38/13.57 (until2p8(s31) | (~xuntil2p9(s30))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5489, 937, 5207])).
% 13.38/13.57 tff(5491,plain,
% 13.38/13.57 (~xuntil2p9(s30)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5490, 5486])).
% 13.38/13.57 tff(5492,plain,
% 13.38/13.57 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s30) | xuntil2p9(s30) | (~until2p8(s30)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s30) | xuntil2p9(s30) | (~until2p8(s30)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5493,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s30) | xuntil2p9(s30) | (~until2p8(s30)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5494,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s30) | xuntil2p9(s30) | (~until2p8(s30))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5493, 5492])).
% 13.38/13.57 tff(5495,plain,
% 13.38/13.57 (xuntil2p9(s30) | (~until2p8(s30))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5494, 5192, 4122])).
% 13.38/13.57 tff(5496,plain,
% 13.38/13.57 (~until2p8(s30)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5495, 5491])).
% 13.38/13.57 tff(5497,plain,
% 13.38/13.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s29, s30)) | until2p8(s30) | (~xuntil2p9(s29)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s29, s30)) | until2p8(s30) | (~xuntil2p9(s29)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5498,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s29, s30)) | until2p8(s30) | (~xuntil2p9(s29)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5499,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s29, s30)) | until2p8(s30) | (~xuntil2p9(s29))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5498, 5497])).
% 13.38/13.57 tff(5500,plain,
% 13.38/13.57 (until2p8(s30) | (~xuntil2p9(s29))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5499, 906, 5207])).
% 13.38/13.57 tff(5501,plain,
% 13.38/13.57 (~xuntil2p9(s29)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5500, 5496])).
% 13.38/13.57 tff(5502,plain,
% 13.38/13.57 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s29) | xuntil2p9(s29) | (~until2p8(s29)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s29) | xuntil2p9(s29) | (~until2p8(s29)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5503,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s29) | xuntil2p9(s29) | (~until2p8(s29)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5504,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s29) | xuntil2p9(s29) | (~until2p8(s29))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5503, 5502])).
% 13.38/13.57 tff(5505,plain,
% 13.38/13.57 (xuntil2p9(s29) | (~until2p8(s29))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5504, 5192, 4130])).
% 13.38/13.57 tff(5506,plain,
% 13.38/13.57 (~until2p8(s29)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5505, 5501])).
% 13.38/13.57 tff(5507,plain,
% 13.38/13.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s28, s29)) | until2p8(s29) | (~xuntil2p9(s28)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s28, s29)) | until2p8(s29) | (~xuntil2p9(s28)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5508,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s28, s29)) | until2p8(s29) | (~xuntil2p9(s28)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5509,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s28, s29)) | until2p8(s29) | (~xuntil2p9(s28))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5508, 5507])).
% 13.38/13.57 tff(5510,plain,
% 13.38/13.57 (until2p8(s29) | (~xuntil2p9(s28))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5509, 878, 5207])).
% 13.38/13.57 tff(5511,plain,
% 13.38/13.57 (~xuntil2p9(s28)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5510, 5506])).
% 13.38/13.57 tff(5512,plain,
% 13.38/13.57 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s28) | xuntil2p9(s28) | (~until2p8(s28)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s28) | xuntil2p9(s28) | (~until2p8(s28)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5513,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s28) | xuntil2p9(s28) | (~until2p8(s28)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5514,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s28) | xuntil2p9(s28) | (~until2p8(s28))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5513, 5512])).
% 13.38/13.57 tff(5515,plain,
% 13.38/13.57 (xuntil2p9(s28) | (~until2p8(s28))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5514, 5192, 4138])).
% 13.38/13.57 tff(5516,plain,
% 13.38/13.57 (~until2p8(s28)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5515, 5511])).
% 13.38/13.57 tff(5517,plain,
% 13.38/13.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s27, s28)) | until2p8(s28) | (~xuntil2p9(s27)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s27, s28)) | until2p8(s28) | (~xuntil2p9(s27)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5518,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s27, s28)) | until2p8(s28) | (~xuntil2p9(s27)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5519,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s27, s28)) | until2p8(s28) | (~xuntil2p9(s27))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5518, 5517])).
% 13.38/13.57 tff(5520,plain,
% 13.38/13.57 (until2p8(s28) | (~xuntil2p9(s27))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5519, 847, 5207])).
% 13.38/13.57 tff(5521,plain,
% 13.38/13.57 (~xuntil2p9(s27)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5520, 5516])).
% 13.38/13.57 tff(5522,plain,
% 13.38/13.57 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s27) | xuntil2p9(s27) | (~until2p8(s27)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s27) | xuntil2p9(s27) | (~until2p8(s27)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5523,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s27) | xuntil2p9(s27) | (~until2p8(s27)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5524,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s27) | xuntil2p9(s27) | (~until2p8(s27))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5523, 5522])).
% 13.38/13.57 tff(5525,plain,
% 13.38/13.57 (xuntil2p9(s27) | (~until2p8(s27))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5524, 5192, 4146])).
% 13.38/13.57 tff(5526,plain,
% 13.38/13.57 (~until2p8(s27)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5525, 5521])).
% 13.38/13.57 tff(5527,plain,
% 13.38/13.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s26, s27)) | until2p8(s27) | (~xuntil2p9(s26)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s26, s27)) | until2p8(s27) | (~xuntil2p9(s26)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5528,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s26, s27)) | until2p8(s27) | (~xuntil2p9(s26)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5529,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s26, s27)) | until2p8(s27) | (~xuntil2p9(s26))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5528, 5527])).
% 13.38/13.57 tff(5530,plain,
% 13.38/13.57 (until2p8(s27) | (~xuntil2p9(s26))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5529, 819, 5207])).
% 13.38/13.57 tff(5531,plain,
% 13.38/13.57 (~xuntil2p9(s26)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5530, 5526])).
% 13.38/13.57 tff(5532,plain,
% 13.38/13.57 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s26) | xuntil2p9(s26) | (~until2p8(s26)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s26) | xuntil2p9(s26) | (~until2p8(s26)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5533,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s26) | xuntil2p9(s26) | (~until2p8(s26)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5534,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s26) | xuntil2p9(s26) | (~until2p8(s26))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5533, 5532])).
% 13.38/13.57 tff(5535,plain,
% 13.38/13.57 (xuntil2p9(s26) | (~until2p8(s26))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5534, 5192, 4154])).
% 13.38/13.57 tff(5536,plain,
% 13.38/13.57 (~until2p8(s26)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5535, 5531])).
% 13.38/13.57 tff(5537,plain,
% 13.38/13.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s25, s26)) | until2p8(s26) | (~xuntil2p9(s25)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s25, s26)) | until2p8(s26) | (~xuntil2p9(s25)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5538,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s25, s26)) | until2p8(s26) | (~xuntil2p9(s25)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5539,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s25, s26)) | until2p8(s26) | (~xuntil2p9(s25))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5538, 5537])).
% 13.38/13.57 tff(5540,plain,
% 13.38/13.57 (until2p8(s26) | (~xuntil2p9(s25))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5539, 788, 5207])).
% 13.38/13.57 tff(5541,plain,
% 13.38/13.57 (~xuntil2p9(s25)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5540, 5536])).
% 13.38/13.57 tff(5542,plain,
% 13.38/13.57 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s25) | xuntil2p9(s25) | (~until2p8(s25)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s25) | xuntil2p9(s25) | (~until2p8(s25)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5543,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s25) | xuntil2p9(s25) | (~until2p8(s25)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5544,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s25) | xuntil2p9(s25) | (~until2p8(s25))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5543, 5542])).
% 13.38/13.57 tff(5545,plain,
% 13.38/13.57 (xuntil2p9(s25) | (~until2p8(s25))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5544, 5192, 4162])).
% 13.38/13.57 tff(5546,plain,
% 13.38/13.57 (~until2p8(s25)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5545, 5541])).
% 13.38/13.57 tff(5547,plain,
% 13.38/13.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s24, s25)) | until2p8(s25) | (~xuntil2p9(s24)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s24, s25)) | until2p8(s25) | (~xuntil2p9(s24)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5548,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s24, s25)) | until2p8(s25) | (~xuntil2p9(s24)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5549,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s24, s25)) | until2p8(s25) | (~xuntil2p9(s24))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5548, 5547])).
% 13.38/13.57 tff(5550,plain,
% 13.38/13.57 (until2p8(s25) | (~xuntil2p9(s24))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5549, 760, 5207])).
% 13.38/13.57 tff(5551,plain,
% 13.38/13.57 (~xuntil2p9(s24)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5550, 5546])).
% 13.38/13.57 tff(5552,plain,
% 13.38/13.57 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s24) | xuntil2p9(s24) | (~until2p8(s24)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s24) | xuntil2p9(s24) | (~until2p8(s24)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5553,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s24) | xuntil2p9(s24) | (~until2p8(s24)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5554,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s24) | xuntil2p9(s24) | (~until2p8(s24))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5553, 5552])).
% 13.38/13.57 tff(5555,plain,
% 13.38/13.57 (xuntil2p9(s24) | (~until2p8(s24))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5554, 5192, 4170])).
% 13.38/13.57 tff(5556,plain,
% 13.38/13.57 (~until2p8(s24)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5555, 5551])).
% 13.38/13.57 tff(5557,plain,
% 13.38/13.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s23, s24)) | until2p8(s24) | (~xuntil2p9(s23)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s23, s24)) | until2p8(s24) | (~xuntil2p9(s23)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5558,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s23, s24)) | until2p8(s24) | (~xuntil2p9(s23)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5559,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s23, s24)) | until2p8(s24) | (~xuntil2p9(s23))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5558, 5557])).
% 13.38/13.57 tff(5560,plain,
% 13.38/13.57 (until2p8(s24) | (~xuntil2p9(s23))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5559, 729, 5207])).
% 13.38/13.57 tff(5561,plain,
% 13.38/13.57 (~xuntil2p9(s23)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5560, 5556])).
% 13.38/13.57 tff(5562,plain,
% 13.38/13.57 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s23) | xuntil2p9(s23) | (~until2p8(s23)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s23) | xuntil2p9(s23) | (~until2p8(s23)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5563,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s23) | xuntil2p9(s23) | (~until2p8(s23)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5564,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s23) | xuntil2p9(s23) | (~until2p8(s23))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5563, 5562])).
% 13.38/13.57 tff(5565,plain,
% 13.38/13.57 (xuntil2p9(s23) | (~until2p8(s23))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5564, 5192, 4178])).
% 13.38/13.57 tff(5566,plain,
% 13.38/13.57 (~until2p8(s23)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5565, 5561])).
% 13.38/13.57 tff(5567,plain,
% 13.38/13.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s22, s23)) | until2p8(s23) | (~xuntil2p9(s22)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s22, s23)) | until2p8(s23) | (~xuntil2p9(s22)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5568,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s22, s23)) | until2p8(s23) | (~xuntil2p9(s22)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5569,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s22, s23)) | until2p8(s23) | (~xuntil2p9(s22))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5568, 5567])).
% 13.38/13.57 tff(5570,plain,
% 13.38/13.57 (until2p8(s23) | (~xuntil2p9(s22))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5569, 701, 5207])).
% 13.38/13.57 tff(5571,plain,
% 13.38/13.57 (~xuntil2p9(s22)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5570, 5566])).
% 13.38/13.57 tff(5572,plain,
% 13.38/13.57 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s22) | xuntil2p9(s22) | (~until2p8(s22)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s22) | xuntil2p9(s22) | (~until2p8(s22)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5573,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s22) | xuntil2p9(s22) | (~until2p8(s22)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5574,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s22) | xuntil2p9(s22) | (~until2p8(s22))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5573, 5572])).
% 13.38/13.57 tff(5575,plain,
% 13.38/13.57 (xuntil2p9(s22) | (~until2p8(s22))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5574, 5192, 4186])).
% 13.38/13.57 tff(5576,plain,
% 13.38/13.57 (~until2p8(s22)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5575, 5571])).
% 13.38/13.57 tff(5577,plain,
% 13.38/13.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s21, s22)) | until2p8(s22) | (~xuntil2p9(s21)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s21, s22)) | until2p8(s22) | (~xuntil2p9(s21)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5578,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s21, s22)) | until2p8(s22) | (~xuntil2p9(s21)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5579,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s21, s22)) | until2p8(s22) | (~xuntil2p9(s21))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5578, 5577])).
% 13.38/13.57 tff(5580,plain,
% 13.38/13.57 (until2p8(s22) | (~xuntil2p9(s21))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5579, 670, 5207])).
% 13.38/13.57 tff(5581,plain,
% 13.38/13.57 (~xuntil2p9(s21)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5580, 5576])).
% 13.38/13.57 tff(5582,plain,
% 13.38/13.57 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s21) | xuntil2p9(s21) | (~until2p8(s21)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s21) | xuntil2p9(s21) | (~until2p8(s21)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5583,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s21) | xuntil2p9(s21) | (~until2p8(s21)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5584,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s21) | xuntil2p9(s21) | (~until2p8(s21))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5583, 5582])).
% 13.38/13.57 tff(5585,plain,
% 13.38/13.57 (xuntil2p9(s21) | (~until2p8(s21))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5584, 5192, 4194])).
% 13.38/13.57 tff(5586,plain,
% 13.38/13.57 (~until2p8(s21)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5585, 5581])).
% 13.38/13.57 tff(5587,plain,
% 13.38/13.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s20, s21)) | until2p8(s21) | (~xuntil2p9(s20)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s20, s21)) | until2p8(s21) | (~xuntil2p9(s20)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5588,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s20, s21)) | until2p8(s21) | (~xuntil2p9(s20)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5589,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s20, s21)) | until2p8(s21) | (~xuntil2p9(s20))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5588, 5587])).
% 13.38/13.57 tff(5590,plain,
% 13.38/13.57 (until2p8(s21) | (~xuntil2p9(s20))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5589, 642, 5207])).
% 13.38/13.57 tff(5591,plain,
% 13.38/13.57 (~xuntil2p9(s20)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5590, 5586])).
% 13.38/13.57 tff(5592,plain,
% 13.38/13.57 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s20) | xuntil2p9(s20) | (~until2p8(s20)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s20) | xuntil2p9(s20) | (~until2p8(s20)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5593,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s20) | xuntil2p9(s20) | (~until2p8(s20)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5594,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s20) | xuntil2p9(s20) | (~until2p8(s20))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5593, 5592])).
% 13.38/13.57 tff(5595,plain,
% 13.38/13.57 (xuntil2p9(s20) | (~until2p8(s20))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5594, 5192, 4202])).
% 13.38/13.57 tff(5596,plain,
% 13.38/13.57 (~until2p8(s20)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5595, 5591])).
% 13.38/13.57 tff(5597,plain,
% 13.38/13.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s19, s20)) | until2p8(s20) | (~xuntil2p9(s19)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s19, s20)) | until2p8(s20) | (~xuntil2p9(s19)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5598,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s19, s20)) | until2p8(s20) | (~xuntil2p9(s19)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5599,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s19, s20)) | until2p8(s20) | (~xuntil2p9(s19))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5598, 5597])).
% 13.38/13.57 tff(5600,plain,
% 13.38/13.57 (until2p8(s20) | (~xuntil2p9(s19))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5599, 611, 5207])).
% 13.38/13.57 tff(5601,plain,
% 13.38/13.57 (~xuntil2p9(s19)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5600, 5596])).
% 13.38/13.57 tff(5602,plain,
% 13.38/13.57 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s19) | xuntil2p9(s19) | (~until2p8(s19)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s19) | xuntil2p9(s19) | (~until2p8(s19)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5603,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s19) | xuntil2p9(s19) | (~until2p8(s19)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5604,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s19) | xuntil2p9(s19) | (~until2p8(s19))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5603, 5602])).
% 13.38/13.57 tff(5605,plain,
% 13.38/13.57 (xuntil2p9(s19) | (~until2p8(s19))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5604, 5192, 4210])).
% 13.38/13.57 tff(5606,plain,
% 13.38/13.57 (~until2p8(s19)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5605, 5601])).
% 13.38/13.57 tff(5607,plain,
% 13.38/13.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s18, s19)) | until2p8(s19) | (~xuntil2p9(s18)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s18, s19)) | until2p8(s19) | (~xuntil2p9(s18)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5608,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s18, s19)) | until2p8(s19) | (~xuntil2p9(s18)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5609,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s18, s19)) | until2p8(s19) | (~xuntil2p9(s18))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5608, 5607])).
% 13.38/13.57 tff(5610,plain,
% 13.38/13.57 (until2p8(s19) | (~xuntil2p9(s18))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5609, 583, 5207])).
% 13.38/13.57 tff(5611,plain,
% 13.38/13.57 (~xuntil2p9(s18)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5610, 5606])).
% 13.38/13.57 tff(5612,plain,
% 13.38/13.57 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s18) | xuntil2p9(s18) | (~until2p8(s18)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s18) | xuntil2p9(s18) | (~until2p8(s18)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5613,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s18) | xuntil2p9(s18) | (~until2p8(s18)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5614,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s18) | xuntil2p9(s18) | (~until2p8(s18))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5613, 5612])).
% 13.38/13.57 tff(5615,plain,
% 13.38/13.57 (xuntil2p9(s18) | (~until2p8(s18))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5614, 5192, 4218])).
% 13.38/13.57 tff(5616,plain,
% 13.38/13.57 (~until2p8(s18)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5615, 5611])).
% 13.38/13.57 tff(5617,plain,
% 13.38/13.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s17, s18)) | until2p8(s18) | (~xuntil2p9(s17)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s17, s18)) | until2p8(s18) | (~xuntil2p9(s17)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5618,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s17, s18)) | until2p8(s18) | (~xuntil2p9(s17)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5619,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s17, s18)) | until2p8(s18) | (~xuntil2p9(s17))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5618, 5617])).
% 13.38/13.57 tff(5620,plain,
% 13.38/13.57 (until2p8(s18) | (~xuntil2p9(s17))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5619, 552, 5207])).
% 13.38/13.57 tff(5621,plain,
% 13.38/13.57 (~xuntil2p9(s17)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5620, 5616])).
% 13.38/13.57 tff(5622,plain,
% 13.38/13.57 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s17) | xuntil2p9(s17) | (~until2p8(s17)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s17) | xuntil2p9(s17) | (~until2p8(s17)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5623,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s17) | xuntil2p9(s17) | (~until2p8(s17)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5624,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s17) | xuntil2p9(s17) | (~until2p8(s17))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5623, 5622])).
% 13.38/13.57 tff(5625,plain,
% 13.38/13.57 (xuntil2p9(s17) | (~until2p8(s17))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5624, 5192, 4226])).
% 13.38/13.57 tff(5626,plain,
% 13.38/13.57 (~until2p8(s17)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5625, 5621])).
% 13.38/13.57 tff(5627,plain,
% 13.38/13.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s16, s17)) | until2p8(s17) | (~xuntil2p9(s16)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s16, s17)) | until2p8(s17) | (~xuntil2p9(s16)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5628,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s16, s17)) | until2p8(s17) | (~xuntil2p9(s16)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5629,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s16, s17)) | until2p8(s17) | (~xuntil2p9(s16))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5628, 5627])).
% 13.38/13.57 tff(5630,plain,
% 13.38/13.57 (until2p8(s17) | (~xuntil2p9(s16))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5629, 524, 5207])).
% 13.38/13.57 tff(5631,plain,
% 13.38/13.57 (~xuntil2p9(s16)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5630, 5626])).
% 13.38/13.57 tff(5632,plain,
% 13.38/13.57 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s16) | xuntil2p9(s16) | (~until2p8(s16)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s16) | xuntil2p9(s16) | (~until2p8(s16)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5633,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s16) | xuntil2p9(s16) | (~until2p8(s16)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5634,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s16) | xuntil2p9(s16) | (~until2p8(s16))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5633, 5632])).
% 13.38/13.57 tff(5635,plain,
% 13.38/13.57 (xuntil2p9(s16) | (~until2p8(s16))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5634, 5192, 4234])).
% 13.38/13.57 tff(5636,plain,
% 13.38/13.57 (~until2p8(s16)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5635, 5631])).
% 13.38/13.57 tff(5637,plain,
% 13.38/13.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s15, s16)) | until2p8(s16) | (~xuntil2p9(s15)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s15, s16)) | until2p8(s16) | (~xuntil2p9(s15)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5638,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s15, s16)) | until2p8(s16) | (~xuntil2p9(s15)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5639,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s15, s16)) | until2p8(s16) | (~xuntil2p9(s15))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5638, 5637])).
% 13.38/13.57 tff(5640,plain,
% 13.38/13.57 (until2p8(s16) | (~xuntil2p9(s15))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5639, 495, 5207])).
% 13.38/13.57 tff(5641,plain,
% 13.38/13.57 (~xuntil2p9(s15)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5640, 5636])).
% 13.38/13.57 tff(5642,plain,
% 13.38/13.57 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s15) | xuntil2p9(s15) | (~until2p8(s15)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s15) | xuntil2p9(s15) | (~until2p8(s15)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5643,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s15) | xuntil2p9(s15) | (~until2p8(s15)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5644,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s15) | xuntil2p9(s15) | (~until2p8(s15))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5643, 5642])).
% 13.38/13.57 tff(5645,plain,
% 13.38/13.57 (xuntil2p9(s15) | (~until2p8(s15))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5644, 5192, 4242])).
% 13.38/13.57 tff(5646,plain,
% 13.38/13.57 (~until2p8(s15)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5645, 5641])).
% 13.38/13.57 tff(5647,plain,
% 13.38/13.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s14, s15)) | until2p8(s15) | (~xuntil2p9(s14)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s14, s15)) | until2p8(s15) | (~xuntil2p9(s14)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5648,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s14, s15)) | until2p8(s15) | (~xuntil2p9(s14)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5649,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s14, s15)) | until2p8(s15) | (~xuntil2p9(s14))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5648, 5647])).
% 13.38/13.57 tff(5650,plain,
% 13.38/13.57 (until2p8(s15) | (~xuntil2p9(s14))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5649, 469, 5207])).
% 13.38/13.57 tff(5651,plain,
% 13.38/13.57 (~xuntil2p9(s14)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5650, 5646])).
% 13.38/13.57 tff(5652,plain,
% 13.38/13.57 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s14) | xuntil2p9(s14) | (~until2p8(s14)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s14) | xuntil2p9(s14) | (~until2p8(s14)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5653,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s14) | xuntil2p9(s14) | (~until2p8(s14)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5654,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s14) | xuntil2p9(s14) | (~until2p8(s14))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5653, 5652])).
% 13.38/13.57 tff(5655,plain,
% 13.38/13.57 (xuntil2p9(s14) | (~until2p8(s14))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5654, 5192, 4250])).
% 13.38/13.57 tff(5656,plain,
% 13.38/13.57 (~until2p8(s14)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5655, 5651])).
% 13.38/13.57 tff(5657,plain,
% 13.38/13.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s13, s14)) | until2p8(s14) | (~xuntil2p9(s13)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s13, s14)) | until2p8(s14) | (~xuntil2p9(s13)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5658,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s13, s14)) | until2p8(s14) | (~xuntil2p9(s13)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5659,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s13, s14)) | until2p8(s14) | (~xuntil2p9(s13))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5658, 5657])).
% 13.38/13.57 tff(5660,plain,
% 13.38/13.57 (until2p8(s14) | (~xuntil2p9(s13))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5659, 440, 5207])).
% 13.38/13.57 tff(5661,plain,
% 13.38/13.57 (~xuntil2p9(s13)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5660, 5656])).
% 13.38/13.57 tff(5662,plain,
% 13.38/13.57 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s13) | xuntil2p9(s13) | (~until2p8(s13)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s13) | xuntil2p9(s13) | (~until2p8(s13)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5663,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s13) | xuntil2p9(s13) | (~until2p8(s13)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5664,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s13) | xuntil2p9(s13) | (~until2p8(s13))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5663, 5662])).
% 13.38/13.57 tff(5665,plain,
% 13.38/13.57 (xuntil2p9(s13) | (~until2p8(s13))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5664, 5192, 4258])).
% 13.38/13.57 tff(5666,plain,
% 13.38/13.57 (~until2p8(s13)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5665, 5661])).
% 13.38/13.57 tff(5667,plain,
% 13.38/13.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s12, s13)) | until2p8(s13) | (~xuntil2p9(s12)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s12, s13)) | until2p8(s13) | (~xuntil2p9(s12)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5668,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s12, s13)) | until2p8(s13) | (~xuntil2p9(s12)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5669,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s12, s13)) | until2p8(s13) | (~xuntil2p9(s12))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5668, 5667])).
% 13.38/13.57 tff(5670,plain,
% 13.38/13.57 (until2p8(s13) | (~xuntil2p9(s12))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5669, 414, 5207])).
% 13.38/13.57 tff(5671,plain,
% 13.38/13.57 (~xuntil2p9(s12)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5670, 5666])).
% 13.38/13.57 tff(5672,plain,
% 13.38/13.57 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s12) | xuntil2p9(s12) | (~until2p8(s12)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s12) | xuntil2p9(s12) | (~until2p8(s12)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5673,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s12) | xuntil2p9(s12) | (~until2p8(s12)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5674,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s12) | xuntil2p9(s12) | (~until2p8(s12))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5673, 5672])).
% 13.38/13.57 tff(5675,plain,
% 13.38/13.57 (xuntil2p9(s12) | (~until2p8(s12))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5674, 5192, 4266])).
% 13.38/13.57 tff(5676,plain,
% 13.38/13.57 (~until2p8(s12)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5675, 5671])).
% 13.38/13.57 tff(5677,plain,
% 13.38/13.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s11, s12)) | until2p8(s12) | (~xuntil2p9(s11)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s11, s12)) | until2p8(s12) | (~xuntil2p9(s11)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5678,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s11, s12)) | until2p8(s12) | (~xuntil2p9(s11)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5679,plain,
% 13.38/13.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s11, s12)) | until2p8(s12) | (~xuntil2p9(s11))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5678, 5677])).
% 13.38/13.57 tff(5680,plain,
% 13.38/13.57 (until2p8(s12) | (~xuntil2p9(s11))),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5679, 385, 5207])).
% 13.38/13.57 tff(5681,plain,
% 13.38/13.57 (~xuntil2p9(s11)),
% 13.38/13.57 inference(unit_resolution,[status(thm)],[5680, 5676])).
% 13.38/13.57 tff(5682,plain,
% 13.38/13.57 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s11) | xuntil2p9(s11) | (~until2p8(s11)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s11) | xuntil2p9(s11) | (~until2p8(s11)))),
% 13.38/13.57 inference(rewrite,[status(thm)],[])).
% 13.38/13.57 tff(5683,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s11) | xuntil2p9(s11) | (~until2p8(s11)))),
% 13.38/13.57 inference(quant_inst,[status(thm)],[])).
% 13.38/13.57 tff(5684,plain,
% 13.38/13.57 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s11) | xuntil2p9(s11) | (~until2p8(s11))),
% 13.38/13.57 inference(modus_ponens,[status(thm)],[5683, 5682])).
% 13.38/13.57 tff(5685,plain,
% 13.38/13.57 (xuntil2p9(s11) | (~until2p8(s11))),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5684, 5192, 4274])).
% 13.38/13.58 tff(5686,plain,
% 13.38/13.58 (~until2p8(s11)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5685, 5681])).
% 13.38/13.58 tff(5687,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s10, s11)) | until2p8(s11) | (~xuntil2p9(s10)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s10, s11)) | until2p8(s11) | (~xuntil2p9(s10)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5688,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s10, s11)) | until2p8(s11) | (~xuntil2p9(s10)))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5689,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s10, s11)) | until2p8(s11) | (~xuntil2p9(s10))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5688, 5687])).
% 13.38/13.58 tff(5690,plain,
% 13.38/13.58 (until2p8(s11) | (~xuntil2p9(s10))),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5689, 359, 5207])).
% 13.38/13.58 tff(5691,plain,
% 13.38/13.58 (~xuntil2p9(s10)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5690, 5686])).
% 13.38/13.58 tff(5692,plain,
% 13.38/13.58 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s10) | xuntil2p9(s10) | (~until2p8(s10)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s10) | xuntil2p9(s10) | (~until2p8(s10)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5693,plain,
% 13.38/13.58 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s10) | xuntil2p9(s10) | (~until2p8(s10)))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5694,plain,
% 13.38/13.58 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s10) | xuntil2p9(s10) | (~until2p8(s10))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5693, 5692])).
% 13.38/13.58 tff(5695,plain,
% 13.38/13.58 (xuntil2p9(s10) | (~until2p8(s10))),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5694, 5192, 4282])).
% 13.38/13.58 tff(5696,plain,
% 13.38/13.58 (~until2p8(s10)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5695, 5691])).
% 13.38/13.58 tff(5697,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s9, s10)) | until2p8(s10) | (~xuntil2p9(s9)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s9, s10)) | until2p8(s10) | (~xuntil2p9(s9)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5698,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s9, s10)) | until2p8(s10) | (~xuntil2p9(s9)))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5699,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s9, s10)) | until2p8(s10) | (~xuntil2p9(s9))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5698, 5697])).
% 13.38/13.58 tff(5700,plain,
% 13.38/13.58 (until2p8(s10) | (~xuntil2p9(s9))),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5699, 330, 5207])).
% 13.38/13.58 tff(5701,plain,
% 13.38/13.58 (~xuntil2p9(s9)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5700, 5696])).
% 13.38/13.58 tff(5702,plain,
% 13.38/13.58 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s9) | xuntil2p9(s9) | (~until2p8(s9)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s9) | xuntil2p9(s9) | (~until2p8(s9)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5703,plain,
% 13.38/13.58 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s9) | xuntil2p9(s9) | (~until2p8(s9)))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5704,plain,
% 13.38/13.58 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s9) | xuntil2p9(s9) | (~until2p8(s9))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5703, 5702])).
% 13.38/13.58 tff(5705,plain,
% 13.38/13.58 (xuntil2p9(s9) | (~until2p8(s9))),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5704, 5192, 4290])).
% 13.38/13.58 tff(5706,plain,
% 13.38/13.58 (~until2p8(s9)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5705, 5701])).
% 13.38/13.58 tff(5707,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s8, s9)) | until2p8(s9) | (~xuntil2p9(s8)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s8, s9)) | until2p8(s9) | (~xuntil2p9(s8)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5708,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s8, s9)) | until2p8(s9) | (~xuntil2p9(s8)))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5709,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s8, s9)) | until2p8(s9) | (~xuntil2p9(s8))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5708, 5707])).
% 13.38/13.58 tff(5710,plain,
% 13.38/13.58 (until2p8(s9) | (~xuntil2p9(s8))),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5709, 304, 5207])).
% 13.38/13.58 tff(5711,plain,
% 13.38/13.58 (~xuntil2p9(s8)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5710, 5706])).
% 13.38/13.58 tff(5712,plain,
% 13.38/13.58 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s8) | xuntil2p9(s8) | (~until2p8(s8)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s8) | xuntil2p9(s8) | (~until2p8(s8)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5713,plain,
% 13.38/13.58 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s8) | xuntil2p9(s8) | (~until2p8(s8)))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5714,plain,
% 13.38/13.58 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s8) | xuntil2p9(s8) | (~until2p8(s8))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5713, 5712])).
% 13.38/13.58 tff(5715,plain,
% 13.38/13.58 (xuntil2p9(s8) | (~until2p8(s8))),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5714, 5192, 4298])).
% 13.38/13.58 tff(5716,plain,
% 13.38/13.58 (~until2p8(s8)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5715, 5711])).
% 13.38/13.58 tff(5717,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s7, s8)) | until2p8(s8) | (~xuntil2p9(s7)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s7, s8)) | until2p8(s8) | (~xuntil2p9(s7)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5718,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s7, s8)) | until2p8(s8) | (~xuntil2p9(s7)))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5719,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s7, s8)) | until2p8(s8) | (~xuntil2p9(s7))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5718, 5717])).
% 13.38/13.58 tff(5720,plain,
% 13.38/13.58 (until2p8(s8) | (~xuntil2p9(s7))),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5719, 275, 5207])).
% 13.38/13.58 tff(5721,plain,
% 13.38/13.58 (~xuntil2p9(s7)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5720, 5716])).
% 13.38/13.58 tff(5722,plain,
% 13.38/13.58 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s7) | xuntil2p9(s7) | (~until2p8(s7)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s7) | xuntil2p9(s7) | (~until2p8(s7)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5723,plain,
% 13.38/13.58 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s7) | xuntil2p9(s7) | (~until2p8(s7)))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5724,plain,
% 13.38/13.58 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s7) | xuntil2p9(s7) | (~until2p8(s7))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5723, 5722])).
% 13.38/13.58 tff(5725,plain,
% 13.38/13.58 (xuntil2p9(s7) | (~until2p8(s7))),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5724, 5192, 4306])).
% 13.38/13.58 tff(5726,plain,
% 13.38/13.58 (~until2p8(s7)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5725, 5721])).
% 13.38/13.58 tff(5727,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s6, s7)) | until2p8(s7) | (~xuntil2p9(s6)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s6, s7)) | until2p8(s7) | (~xuntil2p9(s6)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5728,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s6, s7)) | until2p8(s7) | (~xuntil2p9(s6)))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5729,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s6, s7)) | until2p8(s7) | (~xuntil2p9(s6))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5728, 5727])).
% 13.38/13.58 tff(5730,plain,
% 13.38/13.58 (until2p8(s7) | (~xuntil2p9(s6))),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5729, 249, 5207])).
% 13.38/13.58 tff(5731,plain,
% 13.38/13.58 (~xuntil2p9(s6)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5730, 5726])).
% 13.38/13.58 tff(5732,plain,
% 13.38/13.58 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s6) | xuntil2p9(s6) | (~until2p8(s6)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s6) | xuntil2p9(s6) | (~until2p8(s6)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5733,plain,
% 13.38/13.58 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s6) | xuntil2p9(s6) | (~until2p8(s6)))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5734,plain,
% 13.38/13.58 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s6) | xuntil2p9(s6) | (~until2p8(s6))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5733, 5732])).
% 13.38/13.58 tff(5735,plain,
% 13.38/13.58 (xuntil2p9(s6) | (~until2p8(s6))),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5734, 5192, 4314])).
% 13.38/13.58 tff(5736,plain,
% 13.38/13.58 (~until2p8(s6)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5735, 5731])).
% 13.38/13.58 tff(5737,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s5, s6)) | until2p8(s6) | (~xuntil2p9(s5)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s5, s6)) | until2p8(s6) | (~xuntil2p9(s5)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5738,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s5, s6)) | until2p8(s6) | (~xuntil2p9(s5)))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5739,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s5, s6)) | until2p8(s6) | (~xuntil2p9(s5))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5738, 5737])).
% 13.38/13.58 tff(5740,plain,
% 13.38/13.58 (until2p8(s6) | (~xuntil2p9(s5))),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5739, 220, 5207])).
% 13.38/13.58 tff(5741,plain,
% 13.38/13.58 (~xuntil2p9(s5)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5740, 5736])).
% 13.38/13.58 tff(5742,plain,
% 13.38/13.58 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s5) | xuntil2p9(s5) | (~until2p8(s5)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s5) | xuntil2p9(s5) | (~until2p8(s5)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5743,plain,
% 13.38/13.58 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s5) | xuntil2p9(s5) | (~until2p8(s5)))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5744,plain,
% 13.38/13.58 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s5) | xuntil2p9(s5) | (~until2p8(s5))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5743, 5742])).
% 13.38/13.58 tff(5745,plain,
% 13.38/13.58 (xuntil2p9(s5) | (~until2p8(s5))),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5744, 5192, 4322])).
% 13.38/13.58 tff(5746,plain,
% 13.38/13.58 (~until2p8(s5)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5745, 5741])).
% 13.38/13.58 tff(5747,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s4, s5)) | until2p8(s5) | (~xuntil2p9(s4)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s4, s5)) | until2p8(s5) | (~xuntil2p9(s4)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5748,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s4, s5)) | until2p8(s5) | (~xuntil2p9(s4)))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5749,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s4, s5)) | until2p8(s5) | (~xuntil2p9(s4))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5748, 5747])).
% 13.38/13.58 tff(5750,plain,
% 13.38/13.58 (until2p8(s5) | (~xuntil2p9(s4))),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5749, 194, 5207])).
% 13.38/13.58 tff(5751,plain,
% 13.38/13.58 (~xuntil2p9(s4)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5750, 5746])).
% 13.38/13.58 tff(5752,plain,
% 13.38/13.58 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s4) | xuntil2p9(s4) | (~until2p8(s4)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s4) | xuntil2p9(s4) | (~until2p8(s4)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5753,plain,
% 13.38/13.58 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s4) | xuntil2p9(s4) | (~until2p8(s4)))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5754,plain,
% 13.38/13.58 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s4) | xuntil2p9(s4) | (~until2p8(s4))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5753, 5752])).
% 13.38/13.58 tff(5755,plain,
% 13.38/13.58 (xuntil2p9(s4) | (~until2p8(s4))),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5754, 5192, 4330])).
% 13.38/13.58 tff(5756,plain,
% 13.38/13.58 (~until2p8(s4)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5755, 5751])).
% 13.38/13.58 tff(5757,plain,
% 13.38/13.58 (^[Y: $i, X: $i] : refl(((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y)) <=> ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y)))),
% 13.38/13.58 inference(bind,[status(th)],[])).
% 13.38/13.58 tff(5758,plain,
% 13.38/13.58 (![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y)) <=> ![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))),
% 13.38/13.58 inference(quant_intro,[status(thm)],[5757])).
% 13.38/13.58 tff(5759,plain,
% 13.38/13.58 (![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y)) <=> ![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5760,plain,
% 13.38/13.58 (^[Y: $i, X: $i] : trans(monotonicity(rewrite(((until2p8(Y) | (~trans(X, Y))) | (~last(X))) <=> ((~last(X)) | (~trans(X, Y)) | until2p8(Y))), ((((until2p8(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil7(X))) <=> (((~last(X)) | (~trans(X, Y)) | until2p8(Y)) | (~xuntil7(X))))), rewrite((((~last(X)) | (~trans(X, Y)) | until2p8(Y)) | (~xuntil7(X))) <=> ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))), ((((until2p8(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil7(X))) <=> ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))))),
% 13.38/13.58 inference(bind,[status(th)],[])).
% 13.38/13.58 tff(5761,plain,
% 13.38/13.58 (![Y: $i, X: $i] : (((until2p8(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil7(X))) <=> ![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))),
% 13.38/13.58 inference(quant_intro,[status(thm)],[5760])).
% 13.38/13.58 tff(5762,axiom,(![Y: $i, X: $i] : (((until2p8(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil7(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty7')).
% 13.38/13.58 tff(5763,plain,
% 13.38/13.58 (![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5762, 5761])).
% 13.38/13.58 tff(5764,plain,
% 13.38/13.58 (![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5763, 5759])).
% 13.38/13.58 tff(5765,plain,(
% 13.38/13.58 ![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))),
% 13.38/13.58 inference(skolemize,[status(sab)],[5764])).
% 13.38/13.58 tff(5766,plain,
% 13.38/13.58 (![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5765, 5758])).
% 13.38/13.58 tff(5767,assumption,(xuntil7(s59)), introduced(assumption)).
% 13.38/13.58 tff(5768,assumption,(~until2p8(s37)), introduced(assumption)).
% 13.38/13.58 tff(5769,assumption,(trans(s59, s37)), introduced(assumption)).
% 13.38/13.58 tff(5770,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s37) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s37)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s37) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s37)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5771,plain,
% 13.38/13.58 (((~last(s59)) | (~trans(s59, s37)) | (~xuntil7(s59)) | until2p8(s37)) <=> (until2p8(s37) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s37)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5772,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s37)) | (~xuntil7(s59)) | until2p8(s37))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s37) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s37))))),
% 13.38/13.58 inference(monotonicity,[status(thm)],[5771])).
% 13.38/13.58 tff(5773,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s37)) | (~xuntil7(s59)) | until2p8(s37))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s37) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s37)))),
% 13.38/13.58 inference(transitivity,[status(thm)],[5772, 5770])).
% 13.38/13.58 tff(5774,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s37)) | (~xuntil7(s59)) | until2p8(s37))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5775,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s37) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s37))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5774, 5773])).
% 13.38/13.58 tff(5776,plain,
% 13.38/13.58 ($false),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5775, 5178, 5769, 5766, 5768, 5767])).
% 13.38/13.58 tff(5777,plain,((~trans(s59, s37)) | until2p8(s37) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.58 tff(5778,plain,
% 13.38/13.58 (~trans(s59, s37)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5777, 5426, 5168])).
% 13.38/13.58 tff(5779,assumption,(~until2p8(s25)), introduced(assumption)).
% 13.38/13.58 tff(5780,assumption,(trans(s59, s25)), introduced(assumption)).
% 13.38/13.58 tff(5781,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s25) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s25)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s25) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s25)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5782,plain,
% 13.38/13.58 (((~last(s59)) | (~trans(s59, s25)) | (~xuntil7(s59)) | until2p8(s25)) <=> (until2p8(s25) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s25)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5783,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s25)) | (~xuntil7(s59)) | until2p8(s25))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s25) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s25))))),
% 13.38/13.58 inference(monotonicity,[status(thm)],[5782])).
% 13.38/13.58 tff(5784,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s25)) | (~xuntil7(s59)) | until2p8(s25))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s25) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s25)))),
% 13.38/13.58 inference(transitivity,[status(thm)],[5783, 5781])).
% 13.38/13.58 tff(5785,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s25)) | (~xuntil7(s59)) | until2p8(s25))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5786,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s25) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s25))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5785, 5784])).
% 13.38/13.58 tff(5787,plain,
% 13.38/13.58 ($false),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5786, 5178, 5780, 5766, 5779, 5767])).
% 13.38/13.58 tff(5788,plain,((~trans(s59, s25)) | until2p8(s25) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.58 tff(5789,plain,
% 13.38/13.58 (~trans(s59, s25)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5788, 5546, 5168])).
% 13.38/13.58 tff(5790,assumption,(~until2p8(s55)), introduced(assumption)).
% 13.38/13.58 tff(5791,assumption,(trans(s59, s55)), introduced(assumption)).
% 13.38/13.58 tff(5792,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s55) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s55)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s55) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s55)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5793,plain,
% 13.38/13.58 (((~last(s59)) | (~trans(s59, s55)) | (~xuntil7(s59)) | until2p8(s55)) <=> (until2p8(s55) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s55)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5794,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s55)) | (~xuntil7(s59)) | until2p8(s55))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s55) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s55))))),
% 13.38/13.58 inference(monotonicity,[status(thm)],[5793])).
% 13.38/13.58 tff(5795,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s55)) | (~xuntil7(s59)) | until2p8(s55))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s55) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s55)))),
% 13.38/13.58 inference(transitivity,[status(thm)],[5794, 5792])).
% 13.38/13.58 tff(5796,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s55)) | (~xuntil7(s59)) | until2p8(s55))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5797,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s55) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s55))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5796, 5795])).
% 13.38/13.58 tff(5798,plain,
% 13.38/13.58 ($false),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5797, 5178, 5791, 5766, 5790, 5767])).
% 13.38/13.58 tff(5799,plain,((~trans(s59, s55)) | until2p8(s55) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.58 tff(5800,plain,
% 13.38/13.58 (~trans(s59, s55)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5799, 5246, 5168])).
% 13.38/13.58 tff(5801,assumption,(~until2p8(s51)), introduced(assumption)).
% 13.38/13.58 tff(5802,assumption,(trans(s59, s51)), introduced(assumption)).
% 13.38/13.58 tff(5803,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s51) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s51)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s51) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s51)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5804,plain,
% 13.38/13.58 (((~last(s59)) | (~trans(s59, s51)) | (~xuntil7(s59)) | until2p8(s51)) <=> (until2p8(s51) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s51)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5805,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s51)) | (~xuntil7(s59)) | until2p8(s51))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s51) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s51))))),
% 13.38/13.58 inference(monotonicity,[status(thm)],[5804])).
% 13.38/13.58 tff(5806,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s51)) | (~xuntil7(s59)) | until2p8(s51))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s51) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s51)))),
% 13.38/13.58 inference(transitivity,[status(thm)],[5805, 5803])).
% 13.38/13.58 tff(5807,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s51)) | (~xuntil7(s59)) | until2p8(s51))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5808,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s51) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s51))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5807, 5806])).
% 13.38/13.58 tff(5809,plain,
% 13.38/13.58 ($false),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5808, 5178, 5802, 5766, 5801, 5767])).
% 13.38/13.58 tff(5810,plain,((~trans(s59, s51)) | until2p8(s51) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.58 tff(5811,plain,
% 13.38/13.58 (~trans(s59, s51)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5810, 5286, 5168])).
% 13.38/13.58 tff(5812,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s3, s4)) | until2p8(s4) | (~xuntil2p9(s3)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s3, s4)) | until2p8(s4) | (~xuntil2p9(s3)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5813,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s3, s4)) | until2p8(s4) | (~xuntil2p9(s3)))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5814,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s3, s4)) | until2p8(s4) | (~xuntil2p9(s3))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5813, 5812])).
% 13.38/13.58 tff(5815,plain,
% 13.38/13.58 (until2p8(s4) | (~xuntil2p9(s3))),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5814, 165, 5207])).
% 13.38/13.58 tff(5816,plain,
% 13.38/13.58 (~xuntil2p9(s3)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5815, 5756])).
% 13.38/13.58 tff(5817,plain,
% 13.38/13.58 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s3) | xuntil2p9(s3) | (~until2p8(s3)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s3) | xuntil2p9(s3) | (~until2p8(s3)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5818,plain,
% 13.38/13.58 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s3) | xuntil2p9(s3) | (~until2p8(s3)))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5819,plain,
% 13.38/13.58 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s3) | xuntil2p9(s3) | (~until2p8(s3))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5818, 5817])).
% 13.38/13.58 tff(5820,plain,
% 13.38/13.58 (xuntil2p9(s3) | (~until2p8(s3))),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5819, 5192, 4338])).
% 13.38/13.58 tff(5821,plain,
% 13.38/13.58 (~until2p8(s3)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5820, 5816])).
% 13.38/13.58 tff(5822,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s2, s3)) | until2p8(s3) | (~xuntil2p9(s2)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s2, s3)) | until2p8(s3) | (~xuntil2p9(s2)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5823,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s2, s3)) | until2p8(s3) | (~xuntil2p9(s2)))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5824,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s2, s3)) | until2p8(s3) | (~xuntil2p9(s2))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5823, 5822])).
% 13.38/13.58 tff(5825,plain,
% 13.38/13.58 (until2p8(s3) | (~xuntil2p9(s2))),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5824, 139, 5207])).
% 13.38/13.58 tff(5826,plain,
% 13.38/13.58 (~xuntil2p9(s2)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5825, 5821])).
% 13.38/13.58 tff(5827,plain,
% 13.38/13.58 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s2) | xuntil2p9(s2) | (~until2p8(s2)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s2) | xuntil2p9(s2) | (~until2p8(s2)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5828,plain,
% 13.38/13.58 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s2) | xuntil2p9(s2) | (~until2p8(s2)))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5829,plain,
% 13.38/13.58 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s2) | xuntil2p9(s2) | (~until2p8(s2))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5828, 5827])).
% 13.38/13.58 tff(5830,plain,
% 13.38/13.58 (xuntil2p9(s2) | (~until2p8(s2))),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5829, 5192, 4346])).
% 13.38/13.58 tff(5831,plain,
% 13.38/13.58 (~until2p8(s2)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5830, 5826])).
% 13.38/13.58 tff(5832,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s1, s2)) | until2p8(s2) | (~xuntil2p9(s1)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s1, s2)) | until2p8(s2) | (~xuntil2p9(s1)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5833,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s1, s2)) | until2p8(s2) | (~xuntil2p9(s1)))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5834,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s1, s2)) | until2p8(s2) | (~xuntil2p9(s1))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5833, 5832])).
% 13.38/13.58 tff(5835,plain,
% 13.38/13.58 (until2p8(s2) | (~xuntil2p9(s1))),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5834, 102, 5207])).
% 13.38/13.58 tff(5836,plain,
% 13.38/13.58 (~xuntil2p9(s1)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5835, 5831])).
% 13.38/13.58 tff(5837,plain,
% 13.38/13.58 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s1) | xuntil2p9(s1) | (~until2p8(s1)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s1) | xuntil2p9(s1) | (~until2p8(s1)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5838,plain,
% 13.38/13.58 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s1) | xuntil2p9(s1) | (~until2p8(s1)))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5839,plain,
% 13.38/13.58 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s1) | xuntil2p9(s1) | (~until2p8(s1))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5838, 5837])).
% 13.38/13.58 tff(5840,plain,
% 13.38/13.58 (xuntil2p9(s1) | (~until2p8(s1))),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5839, 5192, 4354])).
% 13.38/13.58 tff(5841,plain,
% 13.38/13.58 (~until2p8(s1)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5840, 5836])).
% 13.38/13.58 tff(5842,assumption,(~until2p8(s1)), introduced(assumption)).
% 13.38/13.58 tff(5843,assumption,(trans(s59, s1)), introduced(assumption)).
% 13.38/13.58 tff(5844,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s1) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s1)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s1) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s1)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5845,plain,
% 13.38/13.58 (((~last(s59)) | (~trans(s59, s1)) | (~xuntil7(s59)) | until2p8(s1)) <=> (until2p8(s1) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s1)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5846,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s1)) | (~xuntil7(s59)) | until2p8(s1))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s1) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s1))))),
% 13.38/13.58 inference(monotonicity,[status(thm)],[5845])).
% 13.38/13.58 tff(5847,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s1)) | (~xuntil7(s59)) | until2p8(s1))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s1) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s1)))),
% 13.38/13.58 inference(transitivity,[status(thm)],[5846, 5844])).
% 13.38/13.58 tff(5848,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s1)) | (~xuntil7(s59)) | until2p8(s1))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5849,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s1) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s1))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5848, 5847])).
% 13.38/13.58 tff(5850,plain,
% 13.38/13.58 ($false),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5849, 5178, 5843, 5766, 5842, 5767])).
% 13.38/13.58 tff(5851,plain,((~trans(s59, s1)) | until2p8(s1) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.58 tff(5852,plain,
% 13.38/13.58 (~trans(s59, s1)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5851, 5841, 5168])).
% 13.38/13.58 tff(5853,assumption,(~until2p8(s9)), introduced(assumption)).
% 13.38/13.58 tff(5854,assumption,(trans(s59, s9)), introduced(assumption)).
% 13.38/13.58 tff(5855,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s9) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s9)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s9) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s9)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5856,plain,
% 13.38/13.58 (((~last(s59)) | (~trans(s59, s9)) | (~xuntil7(s59)) | until2p8(s9)) <=> (until2p8(s9) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s9)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5857,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s9)) | (~xuntil7(s59)) | until2p8(s9))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s9) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s9))))),
% 13.38/13.58 inference(monotonicity,[status(thm)],[5856])).
% 13.38/13.58 tff(5858,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s9)) | (~xuntil7(s59)) | until2p8(s9))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s9) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s9)))),
% 13.38/13.58 inference(transitivity,[status(thm)],[5857, 5855])).
% 13.38/13.58 tff(5859,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s9)) | (~xuntil7(s59)) | until2p8(s9))),
% 13.38/13.58 inference(quant_inst,[status(thm)],[])).
% 13.38/13.58 tff(5860,plain,
% 13.38/13.58 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s9) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s9))),
% 13.38/13.58 inference(modus_ponens,[status(thm)],[5859, 5858])).
% 13.38/13.58 tff(5861,plain,
% 13.38/13.58 ($false),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5860, 5178, 5854, 5766, 5853, 5767])).
% 13.38/13.58 tff(5862,plain,((~trans(s59, s9)) | until2p8(s9) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.58 tff(5863,plain,
% 13.38/13.58 (~trans(s59, s9)),
% 13.38/13.58 inference(unit_resolution,[status(thm)],[5862, 5706, 5168])).
% 13.38/13.58 tff(5864,assumption,(~until2p8(s26)), introduced(assumption)).
% 13.38/13.58 tff(5865,assumption,(trans(s59, s26)), introduced(assumption)).
% 13.38/13.58 tff(5866,plain,
% 13.38/13.58 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s26) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s26)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s26) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s26)))),
% 13.38/13.58 inference(rewrite,[status(thm)],[])).
% 13.38/13.58 tff(5867,plain,
% 13.38/13.58 (((~last(s59)) | (~trans(s59, s26)) | (~xuntil7(s59)) | until2p8(s26)) <=> (until2p8(s26) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s26)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(5868,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s26)) | (~xuntil7(s59)) | until2p8(s26))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s26) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s26))))),
% 13.38/13.59 inference(monotonicity,[status(thm)],[5867])).
% 13.38/13.59 tff(5869,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s26)) | (~xuntil7(s59)) | until2p8(s26))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s26) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s26)))),
% 13.38/13.59 inference(transitivity,[status(thm)],[5868, 5866])).
% 13.38/13.59 tff(5870,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s26)) | (~xuntil7(s59)) | until2p8(s26))),
% 13.38/13.59 inference(quant_inst,[status(thm)],[])).
% 13.38/13.59 tff(5871,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s26) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s26))),
% 13.38/13.59 inference(modus_ponens,[status(thm)],[5870, 5869])).
% 13.38/13.59 tff(5872,plain,
% 13.38/13.59 ($false),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[5871, 5178, 5865, 5766, 5864, 5767])).
% 13.38/13.59 tff(5873,plain,((~trans(s59, s26)) | until2p8(s26) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.59 tff(5874,plain,
% 13.38/13.59 (~trans(s59, s26)),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[5873, 5536, 5168])).
% 13.38/13.59 tff(5875,assumption,(~until2p8(s56)), introduced(assumption)).
% 13.38/13.59 tff(5876,assumption,(trans(s59, s56)), introduced(assumption)).
% 13.38/13.59 tff(5877,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s56) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s56)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s56) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s56)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(5878,plain,
% 13.38/13.59 (((~last(s59)) | (~trans(s59, s56)) | (~xuntil7(s59)) | until2p8(s56)) <=> (until2p8(s56) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s56)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(5879,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s56)) | (~xuntil7(s59)) | until2p8(s56))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s56) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s56))))),
% 13.38/13.59 inference(monotonicity,[status(thm)],[5878])).
% 13.38/13.59 tff(5880,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s56)) | (~xuntil7(s59)) | until2p8(s56))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s56) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s56)))),
% 13.38/13.59 inference(transitivity,[status(thm)],[5879, 5877])).
% 13.38/13.59 tff(5881,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s56)) | (~xuntil7(s59)) | until2p8(s56))),
% 13.38/13.59 inference(quant_inst,[status(thm)],[])).
% 13.38/13.59 tff(5882,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s56) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s56))),
% 13.38/13.59 inference(modus_ponens,[status(thm)],[5881, 5880])).
% 13.38/13.59 tff(5883,plain,
% 13.38/13.59 ($false),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[5882, 5178, 5876, 5766, 5875, 5767])).
% 13.38/13.59 tff(5884,plain,((~trans(s59, s56)) | until2p8(s56) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.59 tff(5885,plain,
% 13.38/13.59 (~trans(s59, s56)),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[5884, 5236, 5168])).
% 13.38/13.59 tff(5886,assumption,(~until2p8(s48)), introduced(assumption)).
% 13.38/13.59 tff(5887,assumption,(trans(s59, s48)), introduced(assumption)).
% 13.38/13.59 tff(5888,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s48) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s48)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s48) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s48)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(5889,plain,
% 13.38/13.59 (((~last(s59)) | (~trans(s59, s48)) | (~xuntil7(s59)) | until2p8(s48)) <=> (until2p8(s48) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s48)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(5890,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s48)) | (~xuntil7(s59)) | until2p8(s48))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s48) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s48))))),
% 13.38/13.59 inference(monotonicity,[status(thm)],[5889])).
% 13.38/13.59 tff(5891,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s48)) | (~xuntil7(s59)) | until2p8(s48))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s48) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s48)))),
% 13.38/13.59 inference(transitivity,[status(thm)],[5890, 5888])).
% 13.38/13.59 tff(5892,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s48)) | (~xuntil7(s59)) | until2p8(s48))),
% 13.38/13.59 inference(quant_inst,[status(thm)],[])).
% 13.38/13.59 tff(5893,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s48) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s48))),
% 13.38/13.59 inference(modus_ponens,[status(thm)],[5892, 5891])).
% 13.38/13.59 tff(5894,plain,
% 13.38/13.59 ($false),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[5893, 5178, 5887, 5766, 5886, 5767])).
% 13.38/13.59 tff(5895,plain,((~trans(s59, s48)) | until2p8(s48) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.59 tff(5896,plain,
% 13.38/13.59 (~trans(s59, s48)),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[5895, 5316, 5168])).
% 13.38/13.59 tff(5897,assumption,(~until2p8(s10)), introduced(assumption)).
% 13.38/13.59 tff(5898,assumption,(trans(s59, s10)), introduced(assumption)).
% 13.38/13.59 tff(5899,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s10) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s10)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s10) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s10)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(5900,plain,
% 13.38/13.59 (((~last(s59)) | (~trans(s59, s10)) | (~xuntil7(s59)) | until2p8(s10)) <=> (until2p8(s10) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s10)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(5901,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s10)) | (~xuntil7(s59)) | until2p8(s10))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s10) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s10))))),
% 13.38/13.59 inference(monotonicity,[status(thm)],[5900])).
% 13.38/13.59 tff(5902,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s10)) | (~xuntil7(s59)) | until2p8(s10))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s10) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s10)))),
% 13.38/13.59 inference(transitivity,[status(thm)],[5901, 5899])).
% 13.38/13.59 tff(5903,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s10)) | (~xuntil7(s59)) | until2p8(s10))),
% 13.38/13.59 inference(quant_inst,[status(thm)],[])).
% 13.38/13.59 tff(5904,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s10) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s10))),
% 13.38/13.59 inference(modus_ponens,[status(thm)],[5903, 5902])).
% 13.38/13.59 tff(5905,plain,
% 13.38/13.59 ($false),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[5904, 5178, 5898, 5766, 5897, 5767])).
% 13.38/13.59 tff(5906,plain,((~trans(s59, s10)) | until2p8(s10) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.59 tff(5907,plain,
% 13.38/13.59 (~trans(s59, s10)),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[5906, 5696, 5168])).
% 13.38/13.59 tff(5908,assumption,(~until2p8(s32)), introduced(assumption)).
% 13.38/13.59 tff(5909,assumption,(trans(s59, s32)), introduced(assumption)).
% 13.38/13.59 tff(5910,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s32) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s32)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s32) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s32)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(5911,plain,
% 13.38/13.59 (((~last(s59)) | (~trans(s59, s32)) | (~xuntil7(s59)) | until2p8(s32)) <=> (until2p8(s32) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s32)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(5912,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s32)) | (~xuntil7(s59)) | until2p8(s32))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s32) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s32))))),
% 13.38/13.59 inference(monotonicity,[status(thm)],[5911])).
% 13.38/13.59 tff(5913,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s32)) | (~xuntil7(s59)) | until2p8(s32))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s32) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s32)))),
% 13.38/13.59 inference(transitivity,[status(thm)],[5912, 5910])).
% 13.38/13.59 tff(5914,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s32)) | (~xuntil7(s59)) | until2p8(s32))),
% 13.38/13.59 inference(quant_inst,[status(thm)],[])).
% 13.38/13.59 tff(5915,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s32) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s32))),
% 13.38/13.59 inference(modus_ponens,[status(thm)],[5914, 5913])).
% 13.38/13.59 tff(5916,plain,
% 13.38/13.59 ($false),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[5915, 5178, 5909, 5766, 5908, 5767])).
% 13.38/13.59 tff(5917,plain,((~trans(s59, s32)) | until2p8(s32) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.59 tff(5918,plain,
% 13.38/13.59 (~trans(s59, s32)),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[5917, 5476, 5168])).
% 13.38/13.59 tff(5919,assumption,(~until2p8(s29)), introduced(assumption)).
% 13.38/13.59 tff(5920,assumption,(trans(s59, s29)), introduced(assumption)).
% 13.38/13.59 tff(5921,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s29) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s29)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s29) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s29)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(5922,plain,
% 13.38/13.59 (((~last(s59)) | (~trans(s59, s29)) | (~xuntil7(s59)) | until2p8(s29)) <=> (until2p8(s29) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s29)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(5923,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s29)) | (~xuntil7(s59)) | until2p8(s29))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s29) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s29))))),
% 13.38/13.59 inference(monotonicity,[status(thm)],[5922])).
% 13.38/13.59 tff(5924,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s29)) | (~xuntil7(s59)) | until2p8(s29))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s29) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s29)))),
% 13.38/13.59 inference(transitivity,[status(thm)],[5923, 5921])).
% 13.38/13.59 tff(5925,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s29)) | (~xuntil7(s59)) | until2p8(s29))),
% 13.38/13.59 inference(quant_inst,[status(thm)],[])).
% 13.38/13.59 tff(5926,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s29) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s29))),
% 13.38/13.59 inference(modus_ponens,[status(thm)],[5925, 5924])).
% 13.38/13.59 tff(5927,plain,
% 13.38/13.59 ($false),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[5926, 5178, 5920, 5766, 5919, 5767])).
% 13.38/13.59 tff(5928,plain,((~trans(s59, s29)) | until2p8(s29) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.59 tff(5929,plain,
% 13.38/13.59 (~trans(s59, s29)),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[5928, 5506, 5168])).
% 13.38/13.59 tff(5930,assumption,(~until2p8(s38)), introduced(assumption)).
% 13.38/13.59 tff(5931,assumption,(trans(s59, s38)), introduced(assumption)).
% 13.38/13.59 tff(5932,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s38) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s38)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s38) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s38)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(5933,plain,
% 13.38/13.59 (((~last(s59)) | (~trans(s59, s38)) | (~xuntil7(s59)) | until2p8(s38)) <=> (until2p8(s38) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s38)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(5934,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s38)) | (~xuntil7(s59)) | until2p8(s38))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s38) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s38))))),
% 13.38/13.59 inference(monotonicity,[status(thm)],[5933])).
% 13.38/13.59 tff(5935,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s38)) | (~xuntil7(s59)) | until2p8(s38))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s38) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s38)))),
% 13.38/13.59 inference(transitivity,[status(thm)],[5934, 5932])).
% 13.38/13.59 tff(5936,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s38)) | (~xuntil7(s59)) | until2p8(s38))),
% 13.38/13.59 inference(quant_inst,[status(thm)],[])).
% 13.38/13.59 tff(5937,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s38) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s38))),
% 13.38/13.59 inference(modus_ponens,[status(thm)],[5936, 5935])).
% 13.38/13.59 tff(5938,plain,
% 13.38/13.59 ($false),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[5937, 5178, 5931, 5766, 5930, 5767])).
% 13.38/13.59 tff(5939,plain,((~trans(s59, s38)) | until2p8(s38) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.59 tff(5940,plain,
% 13.38/13.59 (~trans(s59, s38)),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[5939, 5416, 5168])).
% 13.38/13.59 tff(5941,assumption,(~until2p8(s41)), introduced(assumption)).
% 13.38/13.59 tff(5942,assumption,(trans(s59, s41)), introduced(assumption)).
% 13.38/13.59 tff(5943,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s41) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s41)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s41) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s41)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(5944,plain,
% 13.38/13.59 (((~last(s59)) | (~trans(s59, s41)) | (~xuntil7(s59)) | until2p8(s41)) <=> (until2p8(s41) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s41)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(5945,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s41)) | (~xuntil7(s59)) | until2p8(s41))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s41) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s41))))),
% 13.38/13.59 inference(monotonicity,[status(thm)],[5944])).
% 13.38/13.59 tff(5946,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s41)) | (~xuntil7(s59)) | until2p8(s41))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s41) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s41)))),
% 13.38/13.59 inference(transitivity,[status(thm)],[5945, 5943])).
% 13.38/13.59 tff(5947,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s41)) | (~xuntil7(s59)) | until2p8(s41))),
% 13.38/13.59 inference(quant_inst,[status(thm)],[])).
% 13.38/13.59 tff(5948,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s41) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s41))),
% 13.38/13.59 inference(modus_ponens,[status(thm)],[5947, 5946])).
% 13.38/13.59 tff(5949,plain,
% 13.38/13.59 ($false),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[5948, 5178, 5942, 5766, 5941, 5767])).
% 13.38/13.59 tff(5950,plain,((~trans(s59, s41)) | until2p8(s41) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.59 tff(5951,plain,
% 13.38/13.59 (~trans(s59, s41)),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[5950, 5386, 5168])).
% 13.38/13.59 tff(5952,assumption,(~until2p8(s34)), introduced(assumption)).
% 13.38/13.59 tff(5953,assumption,(trans(s59, s34)), introduced(assumption)).
% 13.38/13.59 tff(5954,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s34) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s34)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s34) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s34)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(5955,plain,
% 13.38/13.59 (((~last(s59)) | (~trans(s59, s34)) | (~xuntil7(s59)) | until2p8(s34)) <=> (until2p8(s34) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s34)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(5956,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s34)) | (~xuntil7(s59)) | until2p8(s34))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s34) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s34))))),
% 13.38/13.59 inference(monotonicity,[status(thm)],[5955])).
% 13.38/13.59 tff(5957,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s34)) | (~xuntil7(s59)) | until2p8(s34))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s34) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s34)))),
% 13.38/13.59 inference(transitivity,[status(thm)],[5956, 5954])).
% 13.38/13.59 tff(5958,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s34)) | (~xuntil7(s59)) | until2p8(s34))),
% 13.38/13.59 inference(quant_inst,[status(thm)],[])).
% 13.38/13.59 tff(5959,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s34) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s34))),
% 13.38/13.59 inference(modus_ponens,[status(thm)],[5958, 5957])).
% 13.38/13.59 tff(5960,plain,
% 13.38/13.59 ($false),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[5959, 5178, 5953, 5766, 5952, 5767])).
% 13.38/13.59 tff(5961,plain,((~trans(s59, s34)) | until2p8(s34) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.59 tff(5962,plain,
% 13.38/13.59 (~trans(s59, s34)),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[5961, 5456, 5168])).
% 13.38/13.59 tff(5963,assumption,(~until2p8(s43)), introduced(assumption)).
% 13.38/13.59 tff(5964,assumption,(trans(s59, s43)), introduced(assumption)).
% 13.38/13.59 tff(5965,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s43) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s43)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s43) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s43)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(5966,plain,
% 13.38/13.59 (((~last(s59)) | (~trans(s59, s43)) | (~xuntil7(s59)) | until2p8(s43)) <=> (until2p8(s43) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s43)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(5967,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s43)) | (~xuntil7(s59)) | until2p8(s43))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s43) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s43))))),
% 13.38/13.59 inference(monotonicity,[status(thm)],[5966])).
% 13.38/13.59 tff(5968,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s43)) | (~xuntil7(s59)) | until2p8(s43))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s43) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s43)))),
% 13.38/13.59 inference(transitivity,[status(thm)],[5967, 5965])).
% 13.38/13.59 tff(5969,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s43)) | (~xuntil7(s59)) | until2p8(s43))),
% 13.38/13.59 inference(quant_inst,[status(thm)],[])).
% 13.38/13.59 tff(5970,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s43) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s43))),
% 13.38/13.59 inference(modus_ponens,[status(thm)],[5969, 5968])).
% 13.38/13.59 tff(5971,plain,
% 13.38/13.59 ($false),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[5970, 5178, 5964, 5766, 5963, 5767])).
% 13.38/13.59 tff(5972,plain,((~trans(s59, s43)) | until2p8(s43) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.59 tff(5973,plain,
% 13.38/13.59 (~trans(s59, s43)),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[5972, 5366, 5168])).
% 13.38/13.59 tff(5974,assumption,(~until2p8(s12)), introduced(assumption)).
% 13.38/13.59 tff(5975,assumption,(trans(s59, s12)), introduced(assumption)).
% 13.38/13.59 tff(5976,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s12) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s12)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s12) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s12)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(5977,plain,
% 13.38/13.59 (((~last(s59)) | (~trans(s59, s12)) | (~xuntil7(s59)) | until2p8(s12)) <=> (until2p8(s12) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s12)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(5978,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s12)) | (~xuntil7(s59)) | until2p8(s12))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s12) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s12))))),
% 13.38/13.59 inference(monotonicity,[status(thm)],[5977])).
% 13.38/13.59 tff(5979,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s12)) | (~xuntil7(s59)) | until2p8(s12))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s12) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s12)))),
% 13.38/13.59 inference(transitivity,[status(thm)],[5978, 5976])).
% 13.38/13.59 tff(5980,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s12)) | (~xuntil7(s59)) | until2p8(s12))),
% 13.38/13.59 inference(quant_inst,[status(thm)],[])).
% 13.38/13.59 tff(5981,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s12) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s12))),
% 13.38/13.59 inference(modus_ponens,[status(thm)],[5980, 5979])).
% 13.38/13.59 tff(5982,plain,
% 13.38/13.59 ($false),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[5981, 5178, 5975, 5766, 5974, 5767])).
% 13.38/13.59 tff(5983,plain,((~trans(s59, s12)) | until2p8(s12) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.59 tff(5984,plain,
% 13.38/13.59 (~trans(s59, s12)),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[5983, 5676, 5168])).
% 13.38/13.59 tff(5985,assumption,(~until2p8(s2)), introduced(assumption)).
% 13.38/13.59 tff(5986,assumption,(trans(s59, s2)), introduced(assumption)).
% 13.38/13.59 tff(5987,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s2) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s2)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s2) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s2)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(5988,plain,
% 13.38/13.59 (((~last(s59)) | (~trans(s59, s2)) | (~xuntil7(s59)) | until2p8(s2)) <=> (until2p8(s2) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s2)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(5989,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s2)) | (~xuntil7(s59)) | until2p8(s2))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s2) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s2))))),
% 13.38/13.59 inference(monotonicity,[status(thm)],[5988])).
% 13.38/13.59 tff(5990,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s2)) | (~xuntil7(s59)) | until2p8(s2))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s2) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s2)))),
% 13.38/13.59 inference(transitivity,[status(thm)],[5989, 5987])).
% 13.38/13.59 tff(5991,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s2)) | (~xuntil7(s59)) | until2p8(s2))),
% 13.38/13.59 inference(quant_inst,[status(thm)],[])).
% 13.38/13.59 tff(5992,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s2) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s2))),
% 13.38/13.59 inference(modus_ponens,[status(thm)],[5991, 5990])).
% 13.38/13.59 tff(5993,plain,
% 13.38/13.59 ($false),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[5992, 5178, 5986, 5766, 5985, 5767])).
% 13.38/13.59 tff(5994,plain,((~trans(s59, s2)) | until2p8(s2) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.59 tff(5995,plain,
% 13.38/13.59 (~trans(s59, s2)),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[5994, 5831, 5168])).
% 13.38/13.59 tff(5996,assumption,(~until2p8(s36)), introduced(assumption)).
% 13.38/13.59 tff(5997,assumption,(trans(s59, s36)), introduced(assumption)).
% 13.38/13.59 tff(5998,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s36) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s36)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s36) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s36)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(5999,plain,
% 13.38/13.59 (((~last(s59)) | (~trans(s59, s36)) | (~xuntil7(s59)) | until2p8(s36)) <=> (until2p8(s36) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s36)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(6000,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s36)) | (~xuntil7(s59)) | until2p8(s36))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s36) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s36))))),
% 13.38/13.59 inference(monotonicity,[status(thm)],[5999])).
% 13.38/13.59 tff(6001,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s36)) | (~xuntil7(s59)) | until2p8(s36))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s36) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s36)))),
% 13.38/13.59 inference(transitivity,[status(thm)],[6000, 5998])).
% 13.38/13.59 tff(6002,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s36)) | (~xuntil7(s59)) | until2p8(s36))),
% 13.38/13.59 inference(quant_inst,[status(thm)],[])).
% 13.38/13.59 tff(6003,plain,
% 13.38/13.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s36) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s36))),
% 13.38/13.59 inference(modus_ponens,[status(thm)],[6002, 6001])).
% 13.38/13.59 tff(6004,plain,
% 13.38/13.59 ($false),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[6003, 5178, 5997, 5766, 5996, 5767])).
% 13.38/13.59 tff(6005,plain,((~trans(s59, s36)) | until2p8(s36) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.59 tff(6006,plain,
% 13.38/13.59 (~trans(s59, s36)),
% 13.38/13.59 inference(unit_resolution,[status(thm)],[6005, 5436, 5168])).
% 13.38/13.59 tff(6007,assumption,(~until2p8(s44)), introduced(assumption)).
% 13.38/13.59 tff(6008,assumption,(trans(s59, s44)), introduced(assumption)).
% 13.38/13.59 tff(6009,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s44) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s44)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s44) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s44)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(6010,plain,
% 13.38/13.59 (((~last(s59)) | (~trans(s59, s44)) | (~xuntil7(s59)) | until2p8(s44)) <=> (until2p8(s44) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s44)))),
% 13.38/13.59 inference(rewrite,[status(thm)],[])).
% 13.38/13.59 tff(6011,plain,
% 13.38/13.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s44)) | (~xuntil7(s59)) | until2p8(s44))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s44) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s44))))),
% 13.38/13.60 inference(monotonicity,[status(thm)],[6010])).
% 13.38/13.60 tff(6012,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s44)) | (~xuntil7(s59)) | until2p8(s44))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s44) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s44)))),
% 13.38/13.60 inference(transitivity,[status(thm)],[6011, 6009])).
% 13.38/13.60 tff(6013,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s44)) | (~xuntil7(s59)) | until2p8(s44))),
% 13.38/13.60 inference(quant_inst,[status(thm)],[])).
% 13.38/13.60 tff(6014,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s44) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s44))),
% 13.38/13.60 inference(modus_ponens,[status(thm)],[6013, 6012])).
% 13.38/13.60 tff(6015,plain,
% 13.38/13.60 ($false),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6014, 5178, 6008, 5766, 6007, 5767])).
% 13.38/13.60 tff(6016,plain,((~trans(s59, s44)) | until2p8(s44) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.60 tff(6017,plain,
% 13.38/13.60 (~trans(s59, s44)),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6016, 5356, 5168])).
% 13.38/13.60 tff(6018,assumption,(~until2p8(s20)), introduced(assumption)).
% 13.38/13.60 tff(6019,assumption,(trans(s59, s20)), introduced(assumption)).
% 13.38/13.60 tff(6020,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s20) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s20)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s20) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s20)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6021,plain,
% 13.38/13.60 (((~last(s59)) | (~trans(s59, s20)) | (~xuntil7(s59)) | until2p8(s20)) <=> (until2p8(s20) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s20)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6022,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s20)) | (~xuntil7(s59)) | until2p8(s20))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s20) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s20))))),
% 13.38/13.60 inference(monotonicity,[status(thm)],[6021])).
% 13.38/13.60 tff(6023,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s20)) | (~xuntil7(s59)) | until2p8(s20))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s20) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s20)))),
% 13.38/13.60 inference(transitivity,[status(thm)],[6022, 6020])).
% 13.38/13.60 tff(6024,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s20)) | (~xuntil7(s59)) | until2p8(s20))),
% 13.38/13.60 inference(quant_inst,[status(thm)],[])).
% 13.38/13.60 tff(6025,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s20) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s20))),
% 13.38/13.60 inference(modus_ponens,[status(thm)],[6024, 6023])).
% 13.38/13.60 tff(6026,plain,
% 13.38/13.60 ($false),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6025, 5178, 6019, 5766, 6018, 5767])).
% 13.38/13.60 tff(6027,plain,((~trans(s59, s20)) | until2p8(s20) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.60 tff(6028,plain,
% 13.38/13.60 (~trans(s59, s20)),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6027, 5596, 5168])).
% 13.38/13.60 tff(6029,assumption,(~until2p8(s22)), introduced(assumption)).
% 13.38/13.60 tff(6030,assumption,(trans(s59, s22)), introduced(assumption)).
% 13.38/13.60 tff(6031,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s22) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s22)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s22) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s22)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6032,plain,
% 13.38/13.60 (((~last(s59)) | (~trans(s59, s22)) | (~xuntil7(s59)) | until2p8(s22)) <=> (until2p8(s22) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s22)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6033,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s22)) | (~xuntil7(s59)) | until2p8(s22))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s22) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s22))))),
% 13.38/13.60 inference(monotonicity,[status(thm)],[6032])).
% 13.38/13.60 tff(6034,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s22)) | (~xuntil7(s59)) | until2p8(s22))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s22) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s22)))),
% 13.38/13.60 inference(transitivity,[status(thm)],[6033, 6031])).
% 13.38/13.60 tff(6035,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s22)) | (~xuntil7(s59)) | until2p8(s22))),
% 13.38/13.60 inference(quant_inst,[status(thm)],[])).
% 13.38/13.60 tff(6036,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s22) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s22))),
% 13.38/13.60 inference(modus_ponens,[status(thm)],[6035, 6034])).
% 13.38/13.60 tff(6037,plain,
% 13.38/13.60 ($false),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6036, 5178, 6030, 5766, 6029, 5767])).
% 13.38/13.60 tff(6038,plain,((~trans(s59, s22)) | until2p8(s22) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.60 tff(6039,plain,
% 13.38/13.60 (~trans(s59, s22)),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6038, 5576, 5168])).
% 13.38/13.60 tff(6040,assumption,(~until2p8(s53)), introduced(assumption)).
% 13.38/13.60 tff(6041,assumption,(trans(s59, s53)), introduced(assumption)).
% 13.38/13.60 tff(6042,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s53) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s53)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s53) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s53)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6043,plain,
% 13.38/13.60 (((~last(s59)) | (~trans(s59, s53)) | (~xuntil7(s59)) | until2p8(s53)) <=> (until2p8(s53) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s53)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6044,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s53)) | (~xuntil7(s59)) | until2p8(s53))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s53) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s53))))),
% 13.38/13.60 inference(monotonicity,[status(thm)],[6043])).
% 13.38/13.60 tff(6045,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s53)) | (~xuntil7(s59)) | until2p8(s53))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s53) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s53)))),
% 13.38/13.60 inference(transitivity,[status(thm)],[6044, 6042])).
% 13.38/13.60 tff(6046,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s53)) | (~xuntil7(s59)) | until2p8(s53))),
% 13.38/13.60 inference(quant_inst,[status(thm)],[])).
% 13.38/13.60 tff(6047,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s53) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s53))),
% 13.38/13.60 inference(modus_ponens,[status(thm)],[6046, 6045])).
% 13.38/13.60 tff(6048,plain,
% 13.38/13.60 ($false),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6047, 5178, 6041, 5766, 6040, 5767])).
% 13.38/13.60 tff(6049,plain,((~trans(s59, s53)) | until2p8(s53) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.60 tff(6050,plain,
% 13.38/13.60 (~trans(s59, s53)),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6049, 5266, 5168])).
% 13.38/13.60 tff(6051,assumption,(~until2p8(s30)), introduced(assumption)).
% 13.38/13.60 tff(6052,assumption,(trans(s59, s30)), introduced(assumption)).
% 13.38/13.60 tff(6053,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s30) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s30)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s30) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s30)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6054,plain,
% 13.38/13.60 (((~last(s59)) | (~trans(s59, s30)) | (~xuntil7(s59)) | until2p8(s30)) <=> (until2p8(s30) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s30)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6055,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s30)) | (~xuntil7(s59)) | until2p8(s30))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s30) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s30))))),
% 13.38/13.60 inference(monotonicity,[status(thm)],[6054])).
% 13.38/13.60 tff(6056,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s30)) | (~xuntil7(s59)) | until2p8(s30))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s30) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s30)))),
% 13.38/13.60 inference(transitivity,[status(thm)],[6055, 6053])).
% 13.38/13.60 tff(6057,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s30)) | (~xuntil7(s59)) | until2p8(s30))),
% 13.38/13.60 inference(quant_inst,[status(thm)],[])).
% 13.38/13.60 tff(6058,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s30) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s30))),
% 13.38/13.60 inference(modus_ponens,[status(thm)],[6057, 6056])).
% 13.38/13.60 tff(6059,plain,
% 13.38/13.60 ($false),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6058, 5178, 6052, 5766, 6051, 5767])).
% 13.38/13.60 tff(6060,plain,((~trans(s59, s30)) | until2p8(s30) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.60 tff(6061,plain,
% 13.38/13.60 (~trans(s59, s30)),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6060, 5496, 5168])).
% 13.38/13.60 tff(6062,assumption,(~until2p8(s18)), introduced(assumption)).
% 13.38/13.60 tff(6063,assumption,(trans(s59, s18)), introduced(assumption)).
% 13.38/13.60 tff(6064,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s18) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s18)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s18) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s18)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6065,plain,
% 13.38/13.60 (((~last(s59)) | (~trans(s59, s18)) | (~xuntil7(s59)) | until2p8(s18)) <=> (until2p8(s18) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s18)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6066,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s18)) | (~xuntil7(s59)) | until2p8(s18))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s18) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s18))))),
% 13.38/13.60 inference(monotonicity,[status(thm)],[6065])).
% 13.38/13.60 tff(6067,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s18)) | (~xuntil7(s59)) | until2p8(s18))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s18) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s18)))),
% 13.38/13.60 inference(transitivity,[status(thm)],[6066, 6064])).
% 13.38/13.60 tff(6068,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s18)) | (~xuntil7(s59)) | until2p8(s18))),
% 13.38/13.60 inference(quant_inst,[status(thm)],[])).
% 13.38/13.60 tff(6069,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s18) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s18))),
% 13.38/13.60 inference(modus_ponens,[status(thm)],[6068, 6067])).
% 13.38/13.60 tff(6070,plain,
% 13.38/13.60 ($false),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6069, 5178, 6063, 5766, 6062, 5767])).
% 13.38/13.60 tff(6071,plain,((~trans(s59, s18)) | until2p8(s18) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.60 tff(6072,plain,
% 13.38/13.60 (~trans(s59, s18)),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6071, 5616, 5168])).
% 13.38/13.60 tff(6073,assumption,(~until2p8(s28)), introduced(assumption)).
% 13.38/13.60 tff(6074,assumption,(trans(s59, s28)), introduced(assumption)).
% 13.38/13.60 tff(6075,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s28) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s28)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s28) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s28)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6076,plain,
% 13.38/13.60 (((~last(s59)) | (~trans(s59, s28)) | (~xuntil7(s59)) | until2p8(s28)) <=> (until2p8(s28) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s28)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6077,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s28)) | (~xuntil7(s59)) | until2p8(s28))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s28) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s28))))),
% 13.38/13.60 inference(monotonicity,[status(thm)],[6076])).
% 13.38/13.60 tff(6078,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s28)) | (~xuntil7(s59)) | until2p8(s28))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s28) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s28)))),
% 13.38/13.60 inference(transitivity,[status(thm)],[6077, 6075])).
% 13.38/13.60 tff(6079,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s28)) | (~xuntil7(s59)) | until2p8(s28))),
% 13.38/13.60 inference(quant_inst,[status(thm)],[])).
% 13.38/13.60 tff(6080,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s28) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s28))),
% 13.38/13.60 inference(modus_ponens,[status(thm)],[6079, 6078])).
% 13.38/13.60 tff(6081,plain,
% 13.38/13.60 ($false),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6080, 5178, 6074, 5766, 6073, 5767])).
% 13.38/13.60 tff(6082,plain,((~trans(s59, s28)) | until2p8(s28) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.60 tff(6083,plain,
% 13.38/13.60 (~trans(s59, s28)),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6082, 5516, 5168])).
% 13.38/13.60 tff(6084,assumption,(~until2p8(s14)), introduced(assumption)).
% 13.38/13.60 tff(6085,assumption,(trans(s59, s14)), introduced(assumption)).
% 13.38/13.60 tff(6086,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s14) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s14)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s14) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s14)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6087,plain,
% 13.38/13.60 (((~last(s59)) | (~trans(s59, s14)) | (~xuntil7(s59)) | until2p8(s14)) <=> (until2p8(s14) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s14)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6088,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s14)) | (~xuntil7(s59)) | until2p8(s14))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s14) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s14))))),
% 13.38/13.60 inference(monotonicity,[status(thm)],[6087])).
% 13.38/13.60 tff(6089,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s14)) | (~xuntil7(s59)) | until2p8(s14))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s14) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s14)))),
% 13.38/13.60 inference(transitivity,[status(thm)],[6088, 6086])).
% 13.38/13.60 tff(6090,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s14)) | (~xuntil7(s59)) | until2p8(s14))),
% 13.38/13.60 inference(quant_inst,[status(thm)],[])).
% 13.38/13.60 tff(6091,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s14) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s14))),
% 13.38/13.60 inference(modus_ponens,[status(thm)],[6090, 6089])).
% 13.38/13.60 tff(6092,plain,
% 13.38/13.60 ($false),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6091, 5178, 6085, 5766, 6084, 5767])).
% 13.38/13.60 tff(6093,plain,((~trans(s59, s14)) | until2p8(s14) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.60 tff(6094,plain,
% 13.38/13.60 (~trans(s59, s14)),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6093, 5656, 5168])).
% 13.38/13.60 tff(6095,assumption,(~until2p8(s7)), introduced(assumption)).
% 13.38/13.60 tff(6096,assumption,(trans(s59, s7)), introduced(assumption)).
% 13.38/13.60 tff(6097,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s7) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s7)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s7) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s7)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6098,plain,
% 13.38/13.60 (((~last(s59)) | (~trans(s59, s7)) | (~xuntil7(s59)) | until2p8(s7)) <=> (until2p8(s7) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s7)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6099,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s7)) | (~xuntil7(s59)) | until2p8(s7))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s7) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s7))))),
% 13.38/13.60 inference(monotonicity,[status(thm)],[6098])).
% 13.38/13.60 tff(6100,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s7)) | (~xuntil7(s59)) | until2p8(s7))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s7) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s7)))),
% 13.38/13.60 inference(transitivity,[status(thm)],[6099, 6097])).
% 13.38/13.60 tff(6101,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s7)) | (~xuntil7(s59)) | until2p8(s7))),
% 13.38/13.60 inference(quant_inst,[status(thm)],[])).
% 13.38/13.60 tff(6102,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s7) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s7))),
% 13.38/13.60 inference(modus_ponens,[status(thm)],[6101, 6100])).
% 13.38/13.60 tff(6103,plain,
% 13.38/13.60 ($false),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6102, 5178, 6096, 5766, 6095, 5767])).
% 13.38/13.60 tff(6104,plain,((~trans(s59, s7)) | until2p8(s7) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.60 tff(6105,plain,
% 13.38/13.60 (~trans(s59, s7)),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6104, 5726, 5168])).
% 13.38/13.60 tff(6106,assumption,(~until2p8(s15)), introduced(assumption)).
% 13.38/13.60 tff(6107,assumption,(trans(s59, s15)), introduced(assumption)).
% 13.38/13.60 tff(6108,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s15) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s15)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s15) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s15)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6109,plain,
% 13.38/13.60 (((~last(s59)) | (~trans(s59, s15)) | (~xuntil7(s59)) | until2p8(s15)) <=> (until2p8(s15) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s15)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6110,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s15)) | (~xuntil7(s59)) | until2p8(s15))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s15) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s15))))),
% 13.38/13.60 inference(monotonicity,[status(thm)],[6109])).
% 13.38/13.60 tff(6111,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s15)) | (~xuntil7(s59)) | until2p8(s15))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s15) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s15)))),
% 13.38/13.60 inference(transitivity,[status(thm)],[6110, 6108])).
% 13.38/13.60 tff(6112,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s15)) | (~xuntil7(s59)) | until2p8(s15))),
% 13.38/13.60 inference(quant_inst,[status(thm)],[])).
% 13.38/13.60 tff(6113,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s15) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s15))),
% 13.38/13.60 inference(modus_ponens,[status(thm)],[6112, 6111])).
% 13.38/13.60 tff(6114,plain,
% 13.38/13.60 ($false),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6113, 5178, 6107, 5766, 6106, 5767])).
% 13.38/13.60 tff(6115,plain,((~trans(s59, s15)) | until2p8(s15) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.60 tff(6116,plain,
% 13.38/13.60 (~trans(s59, s15)),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6115, 5646, 5168])).
% 13.38/13.60 tff(6117,assumption,(~until2p8(s33)), introduced(assumption)).
% 13.38/13.60 tff(6118,assumption,(trans(s59, s33)), introduced(assumption)).
% 13.38/13.60 tff(6119,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s33) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s33)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s33) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s33)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6120,plain,
% 13.38/13.60 (((~last(s59)) | (~trans(s59, s33)) | (~xuntil7(s59)) | until2p8(s33)) <=> (until2p8(s33) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s33)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6121,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s33)) | (~xuntil7(s59)) | until2p8(s33))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s33) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s33))))),
% 13.38/13.60 inference(monotonicity,[status(thm)],[6120])).
% 13.38/13.60 tff(6122,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s33)) | (~xuntil7(s59)) | until2p8(s33))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s33) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s33)))),
% 13.38/13.60 inference(transitivity,[status(thm)],[6121, 6119])).
% 13.38/13.60 tff(6123,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s33)) | (~xuntil7(s59)) | until2p8(s33))),
% 13.38/13.60 inference(quant_inst,[status(thm)],[])).
% 13.38/13.60 tff(6124,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s33) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s33))),
% 13.38/13.60 inference(modus_ponens,[status(thm)],[6123, 6122])).
% 13.38/13.60 tff(6125,plain,
% 13.38/13.60 ($false),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6124, 5178, 6118, 5766, 6117, 5767])).
% 13.38/13.60 tff(6126,plain,((~trans(s59, s33)) | until2p8(s33) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.60 tff(6127,plain,
% 13.38/13.60 (~trans(s59, s33)),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6126, 5466, 5168])).
% 13.38/13.60 tff(6128,assumption,(~until2p8(s35)), introduced(assumption)).
% 13.38/13.60 tff(6129,assumption,(trans(s59, s35)), introduced(assumption)).
% 13.38/13.60 tff(6130,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s35) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s35)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s35) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s35)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6131,plain,
% 13.38/13.60 (((~last(s59)) | (~trans(s59, s35)) | (~xuntil7(s59)) | until2p8(s35)) <=> (until2p8(s35) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s35)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6132,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s35)) | (~xuntil7(s59)) | until2p8(s35))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s35) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s35))))),
% 13.38/13.60 inference(monotonicity,[status(thm)],[6131])).
% 13.38/13.60 tff(6133,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s35)) | (~xuntil7(s59)) | until2p8(s35))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s35) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s35)))),
% 13.38/13.60 inference(transitivity,[status(thm)],[6132, 6130])).
% 13.38/13.60 tff(6134,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s35)) | (~xuntil7(s59)) | until2p8(s35))),
% 13.38/13.60 inference(quant_inst,[status(thm)],[])).
% 13.38/13.60 tff(6135,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s35) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s35))),
% 13.38/13.60 inference(modus_ponens,[status(thm)],[6134, 6133])).
% 13.38/13.60 tff(6136,plain,
% 13.38/13.60 ($false),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6135, 5178, 6129, 5766, 6128, 5767])).
% 13.38/13.60 tff(6137,plain,((~trans(s59, s35)) | until2p8(s35) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.60 tff(6138,plain,
% 13.38/13.60 (~trans(s59, s35)),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6137, 5446, 5168])).
% 13.38/13.60 tff(6139,assumption,(~until2p8(s24)), introduced(assumption)).
% 13.38/13.60 tff(6140,assumption,(trans(s59, s24)), introduced(assumption)).
% 13.38/13.60 tff(6141,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s24) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s24)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s24) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s24)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6142,plain,
% 13.38/13.60 (((~last(s59)) | (~trans(s59, s24)) | (~xuntil7(s59)) | until2p8(s24)) <=> (until2p8(s24) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s24)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6143,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s24)) | (~xuntil7(s59)) | until2p8(s24))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s24) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s24))))),
% 13.38/13.60 inference(monotonicity,[status(thm)],[6142])).
% 13.38/13.60 tff(6144,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s24)) | (~xuntil7(s59)) | until2p8(s24))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s24) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s24)))),
% 13.38/13.60 inference(transitivity,[status(thm)],[6143, 6141])).
% 13.38/13.60 tff(6145,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s24)) | (~xuntil7(s59)) | until2p8(s24))),
% 13.38/13.60 inference(quant_inst,[status(thm)],[])).
% 13.38/13.60 tff(6146,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s24) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s24))),
% 13.38/13.60 inference(modus_ponens,[status(thm)],[6145, 6144])).
% 13.38/13.60 tff(6147,plain,
% 13.38/13.60 ($false),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6146, 5178, 6140, 5766, 6139, 5767])).
% 13.38/13.60 tff(6148,plain,((~trans(s59, s24)) | until2p8(s24) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.60 tff(6149,plain,
% 13.38/13.60 (~trans(s59, s24)),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6148, 5556, 5168])).
% 13.38/13.60 tff(6150,assumption,(~until2p8(s47)), introduced(assumption)).
% 13.38/13.60 tff(6151,assumption,(trans(s59, s47)), introduced(assumption)).
% 13.38/13.60 tff(6152,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s47) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s47)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s47) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s47)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6153,plain,
% 13.38/13.60 (((~last(s59)) | (~trans(s59, s47)) | (~xuntil7(s59)) | until2p8(s47)) <=> (until2p8(s47) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s47)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6154,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s47)) | (~xuntil7(s59)) | until2p8(s47))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s47) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s47))))),
% 13.38/13.60 inference(monotonicity,[status(thm)],[6153])).
% 13.38/13.60 tff(6155,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s47)) | (~xuntil7(s59)) | until2p8(s47))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s47) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s47)))),
% 13.38/13.60 inference(transitivity,[status(thm)],[6154, 6152])).
% 13.38/13.60 tff(6156,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s47)) | (~xuntil7(s59)) | until2p8(s47))),
% 13.38/13.60 inference(quant_inst,[status(thm)],[])).
% 13.38/13.60 tff(6157,plain,
% 13.38/13.60 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s47) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s47))),
% 13.38/13.60 inference(modus_ponens,[status(thm)],[6156, 6155])).
% 13.38/13.60 tff(6158,plain,
% 13.38/13.60 ($false),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6157, 5178, 6151, 5766, 6150, 5767])).
% 13.38/13.60 tff(6159,plain,((~trans(s59, s47)) | until2p8(s47) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.60 tff(6160,plain,
% 13.38/13.60 (~trans(s59, s47)),
% 13.38/13.60 inference(unit_resolution,[status(thm)],[6159, 5326, 5168])).
% 13.38/13.60 tff(6161,assumption,(~until2p8(s6)), introduced(assumption)).
% 13.38/13.60 tff(6162,assumption,(trans(s59, s6)), introduced(assumption)).
% 13.38/13.60 tff(6163,plain,
% 13.38/13.60 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s6) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s6)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s6) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s6)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6164,plain,
% 13.38/13.60 (((~last(s59)) | (~trans(s59, s6)) | (~xuntil7(s59)) | until2p8(s6)) <=> (until2p8(s6) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s6)))),
% 13.38/13.60 inference(rewrite,[status(thm)],[])).
% 13.38/13.60 tff(6165,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s6)) | (~xuntil7(s59)) | until2p8(s6))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s6) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s6))))),
% 13.38/13.61 inference(monotonicity,[status(thm)],[6164])).
% 13.38/13.61 tff(6166,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s6)) | (~xuntil7(s59)) | until2p8(s6))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s6) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s6)))),
% 13.38/13.61 inference(transitivity,[status(thm)],[6165, 6163])).
% 13.38/13.61 tff(6167,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s6)) | (~xuntil7(s59)) | until2p8(s6))),
% 13.38/13.61 inference(quant_inst,[status(thm)],[])).
% 13.38/13.61 tff(6168,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s6) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s6))),
% 13.38/13.61 inference(modus_ponens,[status(thm)],[6167, 6166])).
% 13.38/13.61 tff(6169,plain,
% 13.38/13.61 ($false),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6168, 5178, 6162, 5766, 6161, 5767])).
% 13.38/13.61 tff(6170,plain,((~trans(s59, s6)) | until2p8(s6) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.61 tff(6171,plain,
% 13.38/13.61 (~trans(s59, s6)),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6170, 5736, 5168])).
% 13.38/13.61 tff(6172,assumption,(~until2p8(s13)), introduced(assumption)).
% 13.38/13.61 tff(6173,assumption,(trans(s59, s13)), introduced(assumption)).
% 13.38/13.61 tff(6174,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s13) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s13)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s13) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s13)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6175,plain,
% 13.38/13.61 (((~last(s59)) | (~trans(s59, s13)) | (~xuntil7(s59)) | until2p8(s13)) <=> (until2p8(s13) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s13)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6176,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s13)) | (~xuntil7(s59)) | until2p8(s13))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s13) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s13))))),
% 13.38/13.61 inference(monotonicity,[status(thm)],[6175])).
% 13.38/13.61 tff(6177,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s13)) | (~xuntil7(s59)) | until2p8(s13))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s13) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s13)))),
% 13.38/13.61 inference(transitivity,[status(thm)],[6176, 6174])).
% 13.38/13.61 tff(6178,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s13)) | (~xuntil7(s59)) | until2p8(s13))),
% 13.38/13.61 inference(quant_inst,[status(thm)],[])).
% 13.38/13.61 tff(6179,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s13) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s13))),
% 13.38/13.61 inference(modus_ponens,[status(thm)],[6178, 6177])).
% 13.38/13.61 tff(6180,plain,
% 13.38/13.61 ($false),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6179, 5178, 6173, 5766, 6172, 5767])).
% 13.38/13.61 tff(6181,plain,((~trans(s59, s13)) | until2p8(s13) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.61 tff(6182,plain,
% 13.38/13.61 (~trans(s59, s13)),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6181, 5666, 5168])).
% 13.38/13.61 tff(6183,assumption,(~until2p8(s17)), introduced(assumption)).
% 13.38/13.61 tff(6184,assumption,(trans(s59, s17)), introduced(assumption)).
% 13.38/13.61 tff(6185,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s17) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s17)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s17) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s17)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6186,plain,
% 13.38/13.61 (((~last(s59)) | (~trans(s59, s17)) | (~xuntil7(s59)) | until2p8(s17)) <=> (until2p8(s17) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s17)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6187,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s17)) | (~xuntil7(s59)) | until2p8(s17))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s17) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s17))))),
% 13.38/13.61 inference(monotonicity,[status(thm)],[6186])).
% 13.38/13.61 tff(6188,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s17)) | (~xuntil7(s59)) | until2p8(s17))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s17) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s17)))),
% 13.38/13.61 inference(transitivity,[status(thm)],[6187, 6185])).
% 13.38/13.61 tff(6189,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s17)) | (~xuntil7(s59)) | until2p8(s17))),
% 13.38/13.61 inference(quant_inst,[status(thm)],[])).
% 13.38/13.61 tff(6190,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s17) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s17))),
% 13.38/13.61 inference(modus_ponens,[status(thm)],[6189, 6188])).
% 13.38/13.61 tff(6191,plain,
% 13.38/13.61 ($false),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6190, 5178, 6184, 5766, 6183, 5767])).
% 13.38/13.61 tff(6192,plain,((~trans(s59, s17)) | until2p8(s17) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.61 tff(6193,plain,
% 13.38/13.61 (~trans(s59, s17)),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6192, 5626, 5168])).
% 13.38/13.61 tff(6194,assumption,(~until2p8(s45)), introduced(assumption)).
% 13.38/13.61 tff(6195,assumption,(trans(s59, s45)), introduced(assumption)).
% 13.38/13.61 tff(6196,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s45) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s45)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s45) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s45)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6197,plain,
% 13.38/13.61 (((~last(s59)) | (~trans(s59, s45)) | (~xuntil7(s59)) | until2p8(s45)) <=> (until2p8(s45) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s45)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6198,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s45)) | (~xuntil7(s59)) | until2p8(s45))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s45) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s45))))),
% 13.38/13.61 inference(monotonicity,[status(thm)],[6197])).
% 13.38/13.61 tff(6199,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s45)) | (~xuntil7(s59)) | until2p8(s45))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s45) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s45)))),
% 13.38/13.61 inference(transitivity,[status(thm)],[6198, 6196])).
% 13.38/13.61 tff(6200,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s45)) | (~xuntil7(s59)) | until2p8(s45))),
% 13.38/13.61 inference(quant_inst,[status(thm)],[])).
% 13.38/13.61 tff(6201,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s45) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s45))),
% 13.38/13.61 inference(modus_ponens,[status(thm)],[6200, 6199])).
% 13.38/13.61 tff(6202,plain,
% 13.38/13.61 ($false),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6201, 5178, 6195, 5766, 6194, 5767])).
% 13.38/13.61 tff(6203,plain,((~trans(s59, s45)) | until2p8(s45) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.61 tff(6204,plain,
% 13.38/13.61 (~trans(s59, s45)),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6203, 5346, 5168])).
% 13.38/13.61 tff(6205,assumption,(~until2p8(s40)), introduced(assumption)).
% 13.38/13.61 tff(6206,assumption,(trans(s59, s40)), introduced(assumption)).
% 13.38/13.61 tff(6207,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s40) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s40)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s40) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s40)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6208,plain,
% 13.38/13.61 (((~last(s59)) | (~trans(s59, s40)) | (~xuntil7(s59)) | until2p8(s40)) <=> (until2p8(s40) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s40)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6209,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s40)) | (~xuntil7(s59)) | until2p8(s40))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s40) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s40))))),
% 13.38/13.61 inference(monotonicity,[status(thm)],[6208])).
% 13.38/13.61 tff(6210,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s40)) | (~xuntil7(s59)) | until2p8(s40))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s40) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s40)))),
% 13.38/13.61 inference(transitivity,[status(thm)],[6209, 6207])).
% 13.38/13.61 tff(6211,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s40)) | (~xuntil7(s59)) | until2p8(s40))),
% 13.38/13.61 inference(quant_inst,[status(thm)],[])).
% 13.38/13.61 tff(6212,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s40) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s40))),
% 13.38/13.61 inference(modus_ponens,[status(thm)],[6211, 6210])).
% 13.38/13.61 tff(6213,plain,
% 13.38/13.61 ($false),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6212, 5178, 6206, 5766, 6205, 5767])).
% 13.38/13.61 tff(6214,plain,((~trans(s59, s40)) | until2p8(s40) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.61 tff(6215,plain,
% 13.38/13.61 (~trans(s59, s40)),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6214, 5396, 5168])).
% 13.38/13.61 tff(6216,assumption,(~until2p8(s27)), introduced(assumption)).
% 13.38/13.61 tff(6217,assumption,(trans(s59, s27)), introduced(assumption)).
% 13.38/13.61 tff(6218,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s27) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s27)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s27) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s27)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6219,plain,
% 13.38/13.61 (((~last(s59)) | (~trans(s59, s27)) | (~xuntil7(s59)) | until2p8(s27)) <=> (until2p8(s27) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s27)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6220,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s27)) | (~xuntil7(s59)) | until2p8(s27))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s27) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s27))))),
% 13.38/13.61 inference(monotonicity,[status(thm)],[6219])).
% 13.38/13.61 tff(6221,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s27)) | (~xuntil7(s59)) | until2p8(s27))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s27) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s27)))),
% 13.38/13.61 inference(transitivity,[status(thm)],[6220, 6218])).
% 13.38/13.61 tff(6222,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s27)) | (~xuntil7(s59)) | until2p8(s27))),
% 13.38/13.61 inference(quant_inst,[status(thm)],[])).
% 13.38/13.61 tff(6223,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s27) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s27))),
% 13.38/13.61 inference(modus_ponens,[status(thm)],[6222, 6221])).
% 13.38/13.61 tff(6224,plain,
% 13.38/13.61 ($false),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6223, 5178, 6217, 5766, 6216, 5767])).
% 13.38/13.61 tff(6225,plain,((~trans(s59, s27)) | until2p8(s27) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.61 tff(6226,plain,
% 13.38/13.61 (~trans(s59, s27)),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6225, 5526, 5168])).
% 13.38/13.61 tff(6227,assumption,(~until2p8(s3)), introduced(assumption)).
% 13.38/13.61 tff(6228,assumption,(trans(s59, s3)), introduced(assumption)).
% 13.38/13.61 tff(6229,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s3) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s3)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s3) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s3)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6230,plain,
% 13.38/13.61 (((~last(s59)) | (~trans(s59, s3)) | (~xuntil7(s59)) | until2p8(s3)) <=> (until2p8(s3) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s3)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6231,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s3)) | (~xuntil7(s59)) | until2p8(s3))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s3) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s3))))),
% 13.38/13.61 inference(monotonicity,[status(thm)],[6230])).
% 13.38/13.61 tff(6232,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s3)) | (~xuntil7(s59)) | until2p8(s3))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s3) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s3)))),
% 13.38/13.61 inference(transitivity,[status(thm)],[6231, 6229])).
% 13.38/13.61 tff(6233,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s3)) | (~xuntil7(s59)) | until2p8(s3))),
% 13.38/13.61 inference(quant_inst,[status(thm)],[])).
% 13.38/13.61 tff(6234,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s3) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s3))),
% 13.38/13.61 inference(modus_ponens,[status(thm)],[6233, 6232])).
% 13.38/13.61 tff(6235,plain,
% 13.38/13.61 ($false),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6234, 5178, 6228, 5766, 6227, 5767])).
% 13.38/13.61 tff(6236,plain,((~trans(s59, s3)) | until2p8(s3) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.61 tff(6237,plain,
% 13.38/13.61 (~trans(s59, s3)),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6236, 5821, 5168])).
% 13.38/13.61 tff(6238,assumption,(~until2p8(s50)), introduced(assumption)).
% 13.38/13.61 tff(6239,assumption,(trans(s59, s50)), introduced(assumption)).
% 13.38/13.61 tff(6240,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s50) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s50)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s50) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s50)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6241,plain,
% 13.38/13.61 (((~last(s59)) | (~trans(s59, s50)) | (~xuntil7(s59)) | until2p8(s50)) <=> (until2p8(s50) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s50)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6242,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s50)) | (~xuntil7(s59)) | until2p8(s50))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s50) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s50))))),
% 13.38/13.61 inference(monotonicity,[status(thm)],[6241])).
% 13.38/13.61 tff(6243,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s50)) | (~xuntil7(s59)) | until2p8(s50))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s50) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s50)))),
% 13.38/13.61 inference(transitivity,[status(thm)],[6242, 6240])).
% 13.38/13.61 tff(6244,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s50)) | (~xuntil7(s59)) | until2p8(s50))),
% 13.38/13.61 inference(quant_inst,[status(thm)],[])).
% 13.38/13.61 tff(6245,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s50) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s50))),
% 13.38/13.61 inference(modus_ponens,[status(thm)],[6244, 6243])).
% 13.38/13.61 tff(6246,plain,
% 13.38/13.61 ($false),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6245, 5178, 6239, 5766, 6238, 5767])).
% 13.38/13.61 tff(6247,plain,((~trans(s59, s50)) | until2p8(s50) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.61 tff(6248,plain,
% 13.38/13.61 (~trans(s59, s50)),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6247, 5296, 5168])).
% 13.38/13.61 tff(6249,assumption,(~until2p8(s59)), introduced(assumption)).
% 13.38/13.61 tff(6250,assumption,(trans(s59, s59)), introduced(assumption)).
% 13.38/13.61 tff(6251,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s59) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s59)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s59) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s59)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6252,plain,
% 13.38/13.61 (((~last(s59)) | (~trans(s59, s59)) | (~xuntil7(s59)) | until2p8(s59)) <=> (until2p8(s59) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s59)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6253,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s59)) | (~xuntil7(s59)) | until2p8(s59))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s59) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s59))))),
% 13.38/13.61 inference(monotonicity,[status(thm)],[6252])).
% 13.38/13.61 tff(6254,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s59)) | (~xuntil7(s59)) | until2p8(s59))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s59) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s59)))),
% 13.38/13.61 inference(transitivity,[status(thm)],[6253, 6251])).
% 13.38/13.61 tff(6255,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s59)) | (~xuntil7(s59)) | until2p8(s59))),
% 13.38/13.61 inference(quant_inst,[status(thm)],[])).
% 13.38/13.61 tff(6256,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s59) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s59))),
% 13.38/13.61 inference(modus_ponens,[status(thm)],[6255, 6254])).
% 13.38/13.61 tff(6257,plain,
% 13.38/13.61 ($false),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6256, 5178, 6250, 5766, 6249, 5767])).
% 13.38/13.61 tff(6258,plain,((~trans(s59, s59)) | until2p8(s59) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.61 tff(6259,plain,
% 13.38/13.61 (~trans(s59, s59)),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6258, 5197, 5168])).
% 13.38/13.61 tff(6260,assumption,(~until2p8(s8)), introduced(assumption)).
% 13.38/13.61 tff(6261,assumption,(trans(s59, s8)), introduced(assumption)).
% 13.38/13.61 tff(6262,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s8) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s8)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s8) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s8)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6263,plain,
% 13.38/13.61 (((~last(s59)) | (~trans(s59, s8)) | (~xuntil7(s59)) | until2p8(s8)) <=> (until2p8(s8) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s8)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6264,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s8)) | (~xuntil7(s59)) | until2p8(s8))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s8) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s8))))),
% 13.38/13.61 inference(monotonicity,[status(thm)],[6263])).
% 13.38/13.61 tff(6265,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s8)) | (~xuntil7(s59)) | until2p8(s8))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s8) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s8)))),
% 13.38/13.61 inference(transitivity,[status(thm)],[6264, 6262])).
% 13.38/13.61 tff(6266,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s8)) | (~xuntil7(s59)) | until2p8(s8))),
% 13.38/13.61 inference(quant_inst,[status(thm)],[])).
% 13.38/13.61 tff(6267,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s8) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s8))),
% 13.38/13.61 inference(modus_ponens,[status(thm)],[6266, 6265])).
% 13.38/13.61 tff(6268,plain,
% 13.38/13.61 ($false),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6267, 5178, 6261, 5766, 6260, 5767])).
% 13.38/13.61 tff(6269,plain,((~trans(s59, s8)) | until2p8(s8) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.61 tff(6270,plain,
% 13.38/13.61 (~trans(s59, s8)),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6269, 5716, 5168])).
% 13.38/13.61 tff(6271,assumption,(~until2p8(s31)), introduced(assumption)).
% 13.38/13.61 tff(6272,assumption,(trans(s59, s31)), introduced(assumption)).
% 13.38/13.61 tff(6273,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s31) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s31)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s31) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s31)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6274,plain,
% 13.38/13.61 (((~last(s59)) | (~trans(s59, s31)) | (~xuntil7(s59)) | until2p8(s31)) <=> (until2p8(s31) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s31)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6275,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s31)) | (~xuntil7(s59)) | until2p8(s31))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s31) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s31))))),
% 13.38/13.61 inference(monotonicity,[status(thm)],[6274])).
% 13.38/13.61 tff(6276,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s31)) | (~xuntil7(s59)) | until2p8(s31))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s31) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s31)))),
% 13.38/13.61 inference(transitivity,[status(thm)],[6275, 6273])).
% 13.38/13.61 tff(6277,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s31)) | (~xuntil7(s59)) | until2p8(s31))),
% 13.38/13.61 inference(quant_inst,[status(thm)],[])).
% 13.38/13.61 tff(6278,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s31) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s31))),
% 13.38/13.61 inference(modus_ponens,[status(thm)],[6277, 6276])).
% 13.38/13.61 tff(6279,plain,
% 13.38/13.61 ($false),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6278, 5178, 6272, 5766, 6271, 5767])).
% 13.38/13.61 tff(6280,plain,((~trans(s59, s31)) | until2p8(s31) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.61 tff(6281,plain,
% 13.38/13.61 (~trans(s59, s31)),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6280, 5486, 5168])).
% 13.38/13.61 tff(6282,assumption,(~until2p8(s39)), introduced(assumption)).
% 13.38/13.61 tff(6283,assumption,(trans(s59, s39)), introduced(assumption)).
% 13.38/13.61 tff(6284,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s39) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s39)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s39) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s39)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6285,plain,
% 13.38/13.61 (((~last(s59)) | (~trans(s59, s39)) | (~xuntil7(s59)) | until2p8(s39)) <=> (until2p8(s39) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s39)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6286,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s39)) | (~xuntil7(s59)) | until2p8(s39))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s39) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s39))))),
% 13.38/13.61 inference(monotonicity,[status(thm)],[6285])).
% 13.38/13.61 tff(6287,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s39)) | (~xuntil7(s59)) | until2p8(s39))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s39) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s39)))),
% 13.38/13.61 inference(transitivity,[status(thm)],[6286, 6284])).
% 13.38/13.61 tff(6288,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s39)) | (~xuntil7(s59)) | until2p8(s39))),
% 13.38/13.61 inference(quant_inst,[status(thm)],[])).
% 13.38/13.61 tff(6289,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s39) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s39))),
% 13.38/13.61 inference(modus_ponens,[status(thm)],[6288, 6287])).
% 13.38/13.61 tff(6290,plain,
% 13.38/13.61 ($false),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6289, 5178, 6283, 5766, 6282, 5767])).
% 13.38/13.61 tff(6291,plain,((~trans(s59, s39)) | until2p8(s39) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.61 tff(6292,plain,
% 13.38/13.61 (~trans(s59, s39)),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6291, 5406, 5168])).
% 13.38/13.61 tff(6293,assumption,(~until2p8(s52)), introduced(assumption)).
% 13.38/13.61 tff(6294,assumption,(trans(s59, s52)), introduced(assumption)).
% 13.38/13.61 tff(6295,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s52) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s52)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s52) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s52)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6296,plain,
% 13.38/13.61 (((~last(s59)) | (~trans(s59, s52)) | (~xuntil7(s59)) | until2p8(s52)) <=> (until2p8(s52) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s52)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6297,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s52)) | (~xuntil7(s59)) | until2p8(s52))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s52) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s52))))),
% 13.38/13.61 inference(monotonicity,[status(thm)],[6296])).
% 13.38/13.61 tff(6298,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s52)) | (~xuntil7(s59)) | until2p8(s52))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s52) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s52)))),
% 13.38/13.61 inference(transitivity,[status(thm)],[6297, 6295])).
% 13.38/13.61 tff(6299,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s52)) | (~xuntil7(s59)) | until2p8(s52))),
% 13.38/13.61 inference(quant_inst,[status(thm)],[])).
% 13.38/13.61 tff(6300,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s52) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s52))),
% 13.38/13.61 inference(modus_ponens,[status(thm)],[6299, 6298])).
% 13.38/13.61 tff(6301,plain,
% 13.38/13.61 ($false),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6300, 5178, 6294, 5766, 6293, 5767])).
% 13.38/13.61 tff(6302,plain,((~trans(s59, s52)) | until2p8(s52) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.61 tff(6303,plain,
% 13.38/13.61 (~trans(s59, s52)),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6302, 5276, 5168])).
% 13.38/13.61 tff(6304,assumption,(~until2p8(s46)), introduced(assumption)).
% 13.38/13.61 tff(6305,assumption,(trans(s59, s46)), introduced(assumption)).
% 13.38/13.61 tff(6306,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s46) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s46)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s46) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s46)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6307,plain,
% 13.38/13.61 (((~last(s59)) | (~trans(s59, s46)) | (~xuntil7(s59)) | until2p8(s46)) <=> (until2p8(s46) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s46)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6308,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s46)) | (~xuntil7(s59)) | until2p8(s46))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s46) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s46))))),
% 13.38/13.61 inference(monotonicity,[status(thm)],[6307])).
% 13.38/13.61 tff(6309,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s46)) | (~xuntil7(s59)) | until2p8(s46))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s46) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s46)))),
% 13.38/13.61 inference(transitivity,[status(thm)],[6308, 6306])).
% 13.38/13.61 tff(6310,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s46)) | (~xuntil7(s59)) | until2p8(s46))),
% 13.38/13.61 inference(quant_inst,[status(thm)],[])).
% 13.38/13.61 tff(6311,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s46) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s46))),
% 13.38/13.61 inference(modus_ponens,[status(thm)],[6310, 6309])).
% 13.38/13.61 tff(6312,plain,
% 13.38/13.61 ($false),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6311, 5178, 6305, 5766, 6304, 5767])).
% 13.38/13.61 tff(6313,plain,((~trans(s59, s46)) | until2p8(s46) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.61 tff(6314,plain,
% 13.38/13.61 (~trans(s59, s46)),
% 13.38/13.61 inference(unit_resolution,[status(thm)],[6313, 5336, 5168])).
% 13.38/13.61 tff(6315,assumption,(~until2p8(s49)), introduced(assumption)).
% 13.38/13.61 tff(6316,assumption,(trans(s59, s49)), introduced(assumption)).
% 13.38/13.61 tff(6317,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s49) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s49)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s49) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s49)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6318,plain,
% 13.38/13.61 (((~last(s59)) | (~trans(s59, s49)) | (~xuntil7(s59)) | until2p8(s49)) <=> (until2p8(s49) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s49)))),
% 13.38/13.61 inference(rewrite,[status(thm)],[])).
% 13.38/13.61 tff(6319,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s49)) | (~xuntil7(s59)) | until2p8(s49))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s49) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s49))))),
% 13.38/13.61 inference(monotonicity,[status(thm)],[6318])).
% 13.38/13.61 tff(6320,plain,
% 13.38/13.61 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s49)) | (~xuntil7(s59)) | until2p8(s49))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s49) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s49)))),
% 13.38/13.61 inference(transitivity,[status(thm)],[6319, 6317])).
% 13.38/13.61 tff(6321,plain,
% 13.38/13.61 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s49)) | (~xuntil7(s59)) | until2p8(s49))),
% 13.38/13.61 inference(quant_inst,[status(thm)],[])).
% 13.38/13.62 tff(6322,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s49) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s49))),
% 13.38/13.62 inference(modus_ponens,[status(thm)],[6321, 6320])).
% 13.38/13.62 tff(6323,plain,
% 13.38/13.62 ($false),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6322, 5178, 6316, 5766, 6315, 5767])).
% 13.38/13.62 tff(6324,plain,((~trans(s59, s49)) | until2p8(s49) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.62 tff(6325,plain,
% 13.38/13.62 (~trans(s59, s49)),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6324, 5306, 5168])).
% 13.38/13.62 tff(6326,assumption,(~until2p8(s19)), introduced(assumption)).
% 13.38/13.62 tff(6327,assumption,(trans(s59, s19)), introduced(assumption)).
% 13.38/13.62 tff(6328,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s19) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s19)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s19) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s19)))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6329,plain,
% 13.38/13.62 (((~last(s59)) | (~trans(s59, s19)) | (~xuntil7(s59)) | until2p8(s19)) <=> (until2p8(s19) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s19)))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6330,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s19)) | (~xuntil7(s59)) | until2p8(s19))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s19) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s19))))),
% 13.38/13.62 inference(monotonicity,[status(thm)],[6329])).
% 13.38/13.62 tff(6331,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s19)) | (~xuntil7(s59)) | until2p8(s19))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s19) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s19)))),
% 13.38/13.62 inference(transitivity,[status(thm)],[6330, 6328])).
% 13.38/13.62 tff(6332,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s19)) | (~xuntil7(s59)) | until2p8(s19))),
% 13.38/13.62 inference(quant_inst,[status(thm)],[])).
% 13.38/13.62 tff(6333,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s19) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s19))),
% 13.38/13.62 inference(modus_ponens,[status(thm)],[6332, 6331])).
% 13.38/13.62 tff(6334,plain,
% 13.38/13.62 ($false),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6333, 5178, 6327, 5766, 6326, 5767])).
% 13.38/13.62 tff(6335,plain,((~trans(s59, s19)) | until2p8(s19) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.62 tff(6336,plain,
% 13.38/13.62 (~trans(s59, s19)),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6335, 5606, 5168])).
% 13.38/13.62 tff(6337,assumption,(~until2p8(s58)), introduced(assumption)).
% 13.38/13.62 tff(6338,assumption,(trans(s59, s58)), introduced(assumption)).
% 13.38/13.62 tff(6339,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s58) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s58)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s58) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s58)))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6340,plain,
% 13.38/13.62 (((~last(s59)) | (~trans(s59, s58)) | (~xuntil7(s59)) | until2p8(s58)) <=> (until2p8(s58) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s58)))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6341,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s58)) | (~xuntil7(s59)) | until2p8(s58))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s58) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s58))))),
% 13.38/13.62 inference(monotonicity,[status(thm)],[6340])).
% 13.38/13.62 tff(6342,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s58)) | (~xuntil7(s59)) | until2p8(s58))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s58) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s58)))),
% 13.38/13.62 inference(transitivity,[status(thm)],[6341, 6339])).
% 13.38/13.62 tff(6343,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s58)) | (~xuntil7(s59)) | until2p8(s58))),
% 13.38/13.62 inference(quant_inst,[status(thm)],[])).
% 13.38/13.62 tff(6344,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s58) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s58))),
% 13.38/13.62 inference(modus_ponens,[status(thm)],[6343, 6342])).
% 13.38/13.62 tff(6345,plain,
% 13.38/13.62 ($false),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6344, 5178, 6338, 5766, 6337, 5767])).
% 13.38/13.62 tff(6346,plain,((~trans(s59, s58)) | until2p8(s58) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.62 tff(6347,plain,
% 13.38/13.62 (~trans(s59, s58)),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6346, 5216, 5168])).
% 13.38/13.62 tff(6348,assumption,(~until2p8(s21)), introduced(assumption)).
% 13.38/13.62 tff(6349,assumption,(trans(s59, s21)), introduced(assumption)).
% 13.38/13.62 tff(6350,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s21) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s21)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s21) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s21)))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6351,plain,
% 13.38/13.62 (((~last(s59)) | (~trans(s59, s21)) | (~xuntil7(s59)) | until2p8(s21)) <=> (until2p8(s21) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s21)))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6352,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s21)) | (~xuntil7(s59)) | until2p8(s21))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s21) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s21))))),
% 13.38/13.62 inference(monotonicity,[status(thm)],[6351])).
% 13.38/13.62 tff(6353,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s21)) | (~xuntil7(s59)) | until2p8(s21))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s21) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s21)))),
% 13.38/13.62 inference(transitivity,[status(thm)],[6352, 6350])).
% 13.38/13.62 tff(6354,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s21)) | (~xuntil7(s59)) | until2p8(s21))),
% 13.38/13.62 inference(quant_inst,[status(thm)],[])).
% 13.38/13.62 tff(6355,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s21) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s21))),
% 13.38/13.62 inference(modus_ponens,[status(thm)],[6354, 6353])).
% 13.38/13.62 tff(6356,plain,
% 13.38/13.62 ($false),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6355, 5178, 6349, 5766, 6348, 5767])).
% 13.38/13.62 tff(6357,plain,((~trans(s59, s21)) | until2p8(s21) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.62 tff(6358,plain,
% 13.38/13.62 (~trans(s59, s21)),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6357, 5586, 5168])).
% 13.38/13.62 tff(6359,assumption,(~until2p8(s23)), introduced(assumption)).
% 13.38/13.62 tff(6360,assumption,(trans(s59, s23)), introduced(assumption)).
% 13.38/13.62 tff(6361,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s23) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s23)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s23) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s23)))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6362,plain,
% 13.38/13.62 (((~last(s59)) | (~trans(s59, s23)) | (~xuntil7(s59)) | until2p8(s23)) <=> (until2p8(s23) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s23)))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6363,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s23)) | (~xuntil7(s59)) | until2p8(s23))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s23) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s23))))),
% 13.38/13.62 inference(monotonicity,[status(thm)],[6362])).
% 13.38/13.62 tff(6364,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s23)) | (~xuntil7(s59)) | until2p8(s23))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s23) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s23)))),
% 13.38/13.62 inference(transitivity,[status(thm)],[6363, 6361])).
% 13.38/13.62 tff(6365,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s23)) | (~xuntil7(s59)) | until2p8(s23))),
% 13.38/13.62 inference(quant_inst,[status(thm)],[])).
% 13.38/13.62 tff(6366,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s23) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s23))),
% 13.38/13.62 inference(modus_ponens,[status(thm)],[6365, 6364])).
% 13.38/13.62 tff(6367,plain,
% 13.38/13.62 ($false),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6366, 5178, 6360, 5766, 6359, 5767])).
% 13.38/13.62 tff(6368,plain,((~trans(s59, s23)) | until2p8(s23) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.62 tff(6369,plain,
% 13.38/13.62 (~trans(s59, s23)),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6368, 5566, 5168])).
% 13.38/13.62 tff(6370,assumption,(~until2p8(s16)), introduced(assumption)).
% 13.38/13.62 tff(6371,assumption,(trans(s59, s16)), introduced(assumption)).
% 13.38/13.62 tff(6372,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s16) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s16)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s16) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s16)))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6373,plain,
% 13.38/13.62 (((~last(s59)) | (~trans(s59, s16)) | (~xuntil7(s59)) | until2p8(s16)) <=> (until2p8(s16) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s16)))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6374,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s16)) | (~xuntil7(s59)) | until2p8(s16))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s16) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s16))))),
% 13.38/13.62 inference(monotonicity,[status(thm)],[6373])).
% 13.38/13.62 tff(6375,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s16)) | (~xuntil7(s59)) | until2p8(s16))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s16) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s16)))),
% 13.38/13.62 inference(transitivity,[status(thm)],[6374, 6372])).
% 13.38/13.62 tff(6376,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s16)) | (~xuntil7(s59)) | until2p8(s16))),
% 13.38/13.62 inference(quant_inst,[status(thm)],[])).
% 13.38/13.62 tff(6377,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s16) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s16))),
% 13.38/13.62 inference(modus_ponens,[status(thm)],[6376, 6375])).
% 13.38/13.62 tff(6378,plain,
% 13.38/13.62 ($false),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6377, 5178, 6371, 5766, 6370, 5767])).
% 13.38/13.62 tff(6379,plain,((~trans(s59, s16)) | until2p8(s16) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.62 tff(6380,plain,
% 13.38/13.62 (~trans(s59, s16)),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6379, 5636, 5168])).
% 13.38/13.62 tff(6381,assumption,(~until2p8(s42)), introduced(assumption)).
% 13.38/13.62 tff(6382,assumption,(trans(s59, s42)), introduced(assumption)).
% 13.38/13.62 tff(6383,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s42) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s42)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s42) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s42)))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6384,plain,
% 13.38/13.62 (((~last(s59)) | (~trans(s59, s42)) | (~xuntil7(s59)) | until2p8(s42)) <=> (until2p8(s42) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s42)))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6385,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s42)) | (~xuntil7(s59)) | until2p8(s42))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s42) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s42))))),
% 13.38/13.62 inference(monotonicity,[status(thm)],[6384])).
% 13.38/13.62 tff(6386,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s42)) | (~xuntil7(s59)) | until2p8(s42))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s42) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s42)))),
% 13.38/13.62 inference(transitivity,[status(thm)],[6385, 6383])).
% 13.38/13.62 tff(6387,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s42)) | (~xuntil7(s59)) | until2p8(s42))),
% 13.38/13.62 inference(quant_inst,[status(thm)],[])).
% 13.38/13.62 tff(6388,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s42) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s42))),
% 13.38/13.62 inference(modus_ponens,[status(thm)],[6387, 6386])).
% 13.38/13.62 tff(6389,plain,
% 13.38/13.62 ($false),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6388, 5178, 6382, 5766, 6381, 5767])).
% 13.38/13.62 tff(6390,plain,((~trans(s59, s42)) | until2p8(s42) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.62 tff(6391,plain,
% 13.38/13.62 (~trans(s59, s42)),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6390, 5376, 5168])).
% 13.38/13.62 tff(6392,assumption,(~until2p8(s11)), introduced(assumption)).
% 13.38/13.62 tff(6393,assumption,(trans(s59, s11)), introduced(assumption)).
% 13.38/13.62 tff(6394,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s11) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s11)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s11) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s11)))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6395,plain,
% 13.38/13.62 (((~last(s59)) | (~trans(s59, s11)) | (~xuntil7(s59)) | until2p8(s11)) <=> (until2p8(s11) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s11)))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6396,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s11)) | (~xuntil7(s59)) | until2p8(s11))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s11) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s11))))),
% 13.38/13.62 inference(monotonicity,[status(thm)],[6395])).
% 13.38/13.62 tff(6397,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s11)) | (~xuntil7(s59)) | until2p8(s11))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s11) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s11)))),
% 13.38/13.62 inference(transitivity,[status(thm)],[6396, 6394])).
% 13.38/13.62 tff(6398,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s11)) | (~xuntil7(s59)) | until2p8(s11))),
% 13.38/13.62 inference(quant_inst,[status(thm)],[])).
% 13.38/13.62 tff(6399,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s11) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s11))),
% 13.38/13.62 inference(modus_ponens,[status(thm)],[6398, 6397])).
% 13.38/13.62 tff(6400,plain,
% 13.38/13.62 ($false),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6399, 5178, 6393, 5766, 6392, 5767])).
% 13.38/13.62 tff(6401,plain,((~trans(s59, s11)) | until2p8(s11) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.62 tff(6402,plain,
% 13.38/13.62 (~trans(s59, s11)),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6401, 5686, 5168])).
% 13.38/13.62 tff(6403,assumption,(~until2p8(s54)), introduced(assumption)).
% 13.38/13.62 tff(6404,assumption,(trans(s59, s54)), introduced(assumption)).
% 13.38/13.62 tff(6405,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s54) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s54)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s54) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s54)))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6406,plain,
% 13.38/13.62 (((~last(s59)) | (~trans(s59, s54)) | (~xuntil7(s59)) | until2p8(s54)) <=> (until2p8(s54) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s54)))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6407,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s54)) | (~xuntil7(s59)) | until2p8(s54))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s54) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s54))))),
% 13.38/13.62 inference(monotonicity,[status(thm)],[6406])).
% 13.38/13.62 tff(6408,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s54)) | (~xuntil7(s59)) | until2p8(s54))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s54) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s54)))),
% 13.38/13.62 inference(transitivity,[status(thm)],[6407, 6405])).
% 13.38/13.62 tff(6409,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s54)) | (~xuntil7(s59)) | until2p8(s54))),
% 13.38/13.62 inference(quant_inst,[status(thm)],[])).
% 13.38/13.62 tff(6410,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s54) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s54))),
% 13.38/13.62 inference(modus_ponens,[status(thm)],[6409, 6408])).
% 13.38/13.62 tff(6411,plain,
% 13.38/13.62 ($false),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6410, 5178, 6404, 5766, 6403, 5767])).
% 13.38/13.62 tff(6412,plain,((~trans(s59, s54)) | until2p8(s54) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.62 tff(6413,plain,
% 13.38/13.62 (~trans(s59, s54)),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6412, 5256, 5168])).
% 13.38/13.62 tff(6414,assumption,(~until2p8(s57)), introduced(assumption)).
% 13.38/13.62 tff(6415,assumption,(trans(s59, s57)), introduced(assumption)).
% 13.38/13.62 tff(6416,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s57) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s57)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s57) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s57)))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6417,plain,
% 13.38/13.62 (((~last(s59)) | (~trans(s59, s57)) | (~xuntil7(s59)) | until2p8(s57)) <=> (until2p8(s57) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s57)))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6418,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s57)) | (~xuntil7(s59)) | until2p8(s57))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s57) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s57))))),
% 13.38/13.62 inference(monotonicity,[status(thm)],[6417])).
% 13.38/13.62 tff(6419,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s57)) | (~xuntil7(s59)) | until2p8(s57))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s57) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s57)))),
% 13.38/13.62 inference(transitivity,[status(thm)],[6418, 6416])).
% 13.38/13.62 tff(6420,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s57)) | (~xuntil7(s59)) | until2p8(s57))),
% 13.38/13.62 inference(quant_inst,[status(thm)],[])).
% 13.38/13.62 tff(6421,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s57) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s57))),
% 13.38/13.62 inference(modus_ponens,[status(thm)],[6420, 6419])).
% 13.38/13.62 tff(6422,plain,
% 13.38/13.62 ($false),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6421, 5178, 6415, 5766, 6414, 5767])).
% 13.38/13.62 tff(6423,plain,((~trans(s59, s57)) | until2p8(s57) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 13.38/13.62 tff(6424,plain,
% 13.38/13.62 (~trans(s59, s57)),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6423, 5226, 5168])).
% 13.38/13.62 tff(6425,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s0, s1)) | until2p8(s1) | (~xuntil2p9(s0)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s0, s1)) | until2p8(s1) | (~xuntil2p9(s0)))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6426,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s0, s1)) | until2p8(s1) | (~xuntil2p9(s0)))),
% 13.38/13.62 inference(quant_inst,[status(thm)],[])).
% 13.38/13.62 tff(6427,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s0, s1)) | until2p8(s1) | (~xuntil2p9(s0))),
% 13.38/13.62 inference(modus_ponens,[status(thm)],[6426, 6425])).
% 13.38/13.62 tff(6428,plain,
% 13.38/13.62 (until2p8(s1) | (~xuntil2p9(s0))),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6427, 48, 5207])).
% 13.38/13.62 tff(6429,plain,
% 13.38/13.62 (~xuntil2p9(s0)),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6428, 5841])).
% 13.38/13.62 tff(6430,plain,
% 13.38/13.62 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s0) | xuntil2p9(s0) | (~until2p8(s0)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s0) | xuntil2p9(s0) | (~until2p8(s0)))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6431,plain,
% 13.38/13.62 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s0) | xuntil2p9(s0) | (~until2p8(s0)))),
% 13.38/13.62 inference(quant_inst,[status(thm)],[])).
% 13.38/13.62 tff(6432,plain,
% 13.38/13.62 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s0) | xuntil2p9(s0) | (~until2p8(s0))),
% 13.38/13.62 inference(modus_ponens,[status(thm)],[6431, 6430])).
% 13.38/13.62 tff(6433,plain,
% 13.38/13.62 (xuntil2p9(s0) | (~until2p8(s0))),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6432, 5192, 4362])).
% 13.38/13.62 tff(6434,plain,
% 13.38/13.62 (~until2p8(s0)),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6433, 6429])).
% 13.38/13.62 tff(6435,assumption,(~until2p8(s0)), introduced(assumption)).
% 13.38/13.62 tff(6436,assumption,(trans(s59, s0)), introduced(assumption)).
% 13.38/13.62 tff(6437,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s0)) | until2p8(s0))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s0)) | until2p8(s0))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6438,plain,
% 13.38/13.62 (((~last(s59)) | (~trans(s59, s0)) | (~xuntil7(s59)) | until2p8(s0)) <=> ((~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s0)) | until2p8(s0))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6439,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s0)) | (~xuntil7(s59)) | until2p8(s0))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s0)) | until2p8(s0)))),
% 13.38/13.62 inference(monotonicity,[status(thm)],[6438])).
% 13.38/13.62 tff(6440,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s0)) | (~xuntil7(s59)) | until2p8(s0))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s0)) | until2p8(s0))),
% 13.38/13.62 inference(transitivity,[status(thm)],[6439, 6437])).
% 13.38/13.62 tff(6441,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s0)) | (~xuntil7(s59)) | until2p8(s0))),
% 13.38/13.62 inference(quant_inst,[status(thm)],[])).
% 13.38/13.62 tff(6442,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s0)) | until2p8(s0)),
% 13.38/13.62 inference(modus_ponens,[status(thm)],[6441, 6440])).
% 13.38/13.62 tff(6443,plain,
% 13.38/13.62 ($false),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6442, 5178, 6436, 5766, 5767, 6435])).
% 13.38/13.62 tff(6444,plain,((~trans(s59, s0)) | (~xuntil7(s59)) | until2p8(s0)), inference(lemma,lemma(discharge,[]))).
% 13.38/13.62 tff(6445,plain,
% 13.38/13.62 (~trans(s59, s0)),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6444, 5168, 6434])).
% 13.38/13.62 tff(6446,assumption,(~until2p8(s5)), introduced(assumption)).
% 13.38/13.62 tff(6447,assumption,(trans(s59, s5)), introduced(assumption)).
% 13.38/13.62 tff(6448,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s5) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s5)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s5) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s5)))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6449,plain,
% 13.38/13.62 (((~last(s59)) | (~trans(s59, s5)) | (~xuntil7(s59)) | until2p8(s5)) <=> (until2p8(s5) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s5)))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6450,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s5)) | (~xuntil7(s59)) | until2p8(s5))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s5) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s5))))),
% 13.38/13.62 inference(monotonicity,[status(thm)],[6449])).
% 13.38/13.62 tff(6451,plain,
% 13.38/13.62 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s5)) | (~xuntil7(s59)) | until2p8(s5))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s5) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s5)))),
% 13.38/13.62 inference(transitivity,[status(thm)],[6450, 6448])).
% 13.38/13.62 tff(6452,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s5)) | (~xuntil7(s59)) | until2p8(s5))),
% 13.38/13.62 inference(quant_inst,[status(thm)],[])).
% 13.38/13.62 tff(6453,plain,
% 13.38/13.62 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s5) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s5))),
% 13.38/13.62 inference(modus_ponens,[status(thm)],[6452, 6451])).
% 13.38/13.62 tff(6454,plain,
% 13.38/13.62 ($false),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6453, 5178, 6447, 5766, 6446, 5767])).
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% 13.38/13.62 tff(6456,plain,
% 13.38/13.62 (~trans(s59, s5)),
% 13.38/13.62 inference(unit_resolution,[status(thm)],[6455, 5746, 5168])).
% 13.38/13.62 tff(6457,assumption,(~loop), introduced(assumption)).
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% 13.38/13.62 (^[X: $i] : refl((loop | (~last(X)) | (~xuntil7(X))) <=> (loop | (~last(X)) | (~xuntil7(X))))),
% 13.38/13.62 inference(bind,[status(th)],[])).
% 13.38/13.62 tff(6459,plain,
% 13.38/13.62 (![X: $i] : (loop | (~last(X)) | (~xuntil7(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 13.38/13.62 inference(quant_intro,[status(thm)],[6458])).
% 13.38/13.62 tff(6460,plain,
% 13.38/13.62 (![X: $i] : (loop | (~last(X)) | (~xuntil7(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 13.38/13.62 inference(rewrite,[status(thm)],[])).
% 13.38/13.62 tff(6461,plain,
% 13.38/13.62 (^[X: $i] : rewrite(((loop | (~last(X))) | (~xuntil7(X))) <=> (loop | (~last(X)) | (~xuntil7(X))))),
% 13.38/13.62 inference(bind,[status(th)],[])).
% 13.38/13.62 tff(6462,plain,
% 13.38/13.62 (![X: $i] : ((loop | (~last(X))) | (~xuntil7(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 13.38/13.62 inference(quant_intro,[status(thm)],[6461])).
% 13.38/13.62 tff(6463,axiom,(![X: $i] : ((loop | (~last(X))) | (~xuntil7(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty6')).
% 13.38/13.62 tff(6464,plain,
% 13.38/13.62 (![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 13.38/13.62 inference(modus_ponens,[status(thm)],[6463, 6462])).
% 13.38/13.62 tff(6465,plain,
% 13.38/13.62 (![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 13.38/13.62 inference(modus_ponens,[status(thm)],[6464, 6460])).
% 13.38/13.62 tff(6466,plain,(
% 13.38/13.62 ![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 13.48/13.62 inference(skolemize,[status(sab)],[6465])).
% 13.48/13.62 tff(6467,plain,
% 13.48/13.62 (![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 13.48/13.62 inference(modus_ponens,[status(thm)],[6466, 6459])).
% 13.48/13.62 tff(6468,plain,
% 13.48/13.62 (((~![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))) | (loop | (~last(s59)) | (~xuntil7(s59)))) <=> ((~![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))) | loop | (~last(s59)) | (~xuntil7(s59)))),
% 13.48/13.62 inference(rewrite,[status(thm)],[])).
% 13.48/13.62 tff(6469,plain,
% 13.48/13.62 ((~![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))) | (loop | (~last(s59)) | (~xuntil7(s59)))),
% 13.48/13.62 inference(quant_inst,[status(thm)],[])).
% 13.48/13.62 tff(6470,plain,
% 13.48/13.62 ((~![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))) | loop | (~last(s59)) | (~xuntil7(s59))),
% 13.48/13.62 inference(modus_ponens,[status(thm)],[6469, 6468])).
% 13.48/13.62 tff(6471,plain,
% 13.48/13.62 (loop | (~xuntil7(s59))),
% 13.48/13.62 inference(unit_resolution,[status(thm)],[6470, 5178, 6467])).
% 13.48/13.62 tff(6472,plain,
% 13.48/13.62 (~xuntil7(s59)),
% 13.48/13.62 inference(unit_resolution,[status(thm)],[6471, 6457])).
% 13.48/13.62 tff(6473,plain,
% 13.48/13.62 (^[X: $i] : refl((loop | (~always5(X)) | (~last(X))) <=> (loop | (~always5(X)) | (~last(X))))),
% 13.48/13.62 inference(bind,[status(th)],[])).
% 13.48/13.62 tff(6474,plain,
% 13.48/13.62 (![X: $i] : (loop | (~always5(X)) | (~last(X))) <=> ![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 13.48/13.62 inference(quant_intro,[status(thm)],[6473])).
% 13.48/13.62 tff(6475,plain,
% 13.48/13.62 (![X: $i] : (loop | (~always5(X)) | (~last(X))) <=> ![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 13.48/13.62 inference(rewrite,[status(thm)],[])).
% 13.48/13.62 tff(6476,plain,
% 13.48/13.62 (^[X: $i] : rewrite(((loop | (~always5(X))) | (~last(X))) <=> (loop | (~always5(X)) | (~last(X))))),
% 13.48/13.62 inference(bind,[status(th)],[])).
% 13.48/13.62 tff(6477,plain,
% 13.48/13.62 (![X: $i] : ((loop | (~always5(X))) | (~last(X))) <=> ![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 13.48/13.62 inference(quant_intro,[status(thm)],[6476])).
% 13.48/13.62 tff(6478,axiom,(![X: $i] : ((loop | (~always5(X))) | (~last(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty3')).
% 13.48/13.62 tff(6479,plain,
% 13.48/13.62 (![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 13.48/13.62 inference(modus_ponens,[status(thm)],[6478, 6477])).
% 13.48/13.62 tff(6480,plain,
% 13.48/13.62 (![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 13.48/13.62 inference(modus_ponens,[status(thm)],[6479, 6475])).
% 13.48/13.62 tff(6481,plain,(
% 13.48/13.62 ![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 13.48/13.62 inference(skolemize,[status(sab)],[6480])).
% 13.48/13.62 tff(6482,plain,
% 13.48/13.62 (![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 13.48/13.62 inference(modus_ponens,[status(thm)],[6481, 6474])).
% 13.48/13.62 tff(6483,plain,
% 13.48/13.62 (((~![X: $i] : (loop | (~always5(X)) | (~last(X)))) | (loop | (~always5(s59)) | (~last(s59)))) <=> ((~![X: $i] : (loop | (~always5(X)) | (~last(X)))) | loop | (~always5(s59)) | (~last(s59)))),
% 13.48/13.62 inference(rewrite,[status(thm)],[])).
% 13.48/13.62 tff(6484,plain,
% 13.48/13.62 ((~![X: $i] : (loop | (~always5(X)) | (~last(X)))) | (loop | (~always5(s59)) | (~last(s59)))),
% 13.48/13.62 inference(quant_inst,[status(thm)],[])).
% 13.48/13.62 tff(6485,plain,
% 13.48/13.62 ((~![X: $i] : (loop | (~always5(X)) | (~last(X)))) | loop | (~always5(s59)) | (~last(s59))),
% 13.48/13.62 inference(modus_ponens,[status(thm)],[6484, 6483])).
% 13.48/13.62 tff(6486,plain,
% 13.48/13.62 (loop | (~always5(s59))),
% 13.48/13.62 inference(unit_resolution,[status(thm)],[6485, 5178, 6482])).
% 13.48/13.62 tff(6487,plain,
% 13.48/13.62 (~always5(s59)),
% 13.48/13.62 inference(unit_resolution,[status(thm)],[6486, 6457])).
% 13.48/13.62 tff(6488,plain,
% 13.48/13.62 (~until6(s59)),
% 13.48/13.62 inference(unit_resolution,[status(thm)],[5167, 4375, 6487, 6472])).
% 13.48/13.62 tff(6489,plain,
% 13.48/13.62 (~xuntil7(s58)),
% 13.48/13.62 inference(unit_resolution,[status(thm)],[5160, 6488])).
% 13.48/13.62 tff(6490,plain,
% 13.48/13.62 (~always5(s58)),
% 13.48/13.62 inference(unit_resolution,[status(thm)],[3897, 6487])).
% 13.48/13.62 tff(6491,plain,
% 13.48/13.62 (xuntil7(s58) | (~until6(s58))),
% 13.48/13.62 inference(unit_resolution,[status(thm)],[5154, 4375, 6490])).
% 13.48/13.62 tff(6492,plain,
% 13.48/13.62 (~until6(s58)),
% 13.48/13.62 inference(unit_resolution,[status(thm)],[6491, 6489])).
% 13.48/13.62 tff(6493,plain,
% 13.48/13.62 (~xuntil7(s57)),
% 13.48/13.62 inference(unit_resolution,[status(thm)],[5147, 6492])).
% 13.48/13.62 tff(6494,plain,
% 13.48/13.62 (~always5(s57)),
% 13.48/13.62 inference(unit_resolution,[status(thm)],[3905, 6490])).
% 13.48/13.62 tff(6495,plain,
% 13.48/13.62 (xuntil7(s57) | (~until6(s57))),
% 13.48/13.62 inference(unit_resolution,[status(thm)],[5141, 4375, 6494])).
% 13.48/13.62 tff(6496,plain,
% 13.48/13.62 (~until6(s57)),
% 13.48/13.62 inference(unit_resolution,[status(thm)],[6495, 6493])).
% 13.48/13.63 tff(6497,plain,
% 13.48/13.63 (~xuntil7(s56)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[5134, 6496])).
% 13.48/13.63 tff(6498,plain,
% 13.48/13.63 (~always5(s56)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[3913, 6494])).
% 13.48/13.63 tff(6499,plain,
% 13.48/13.63 (xuntil7(s56) | (~until6(s56))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[5128, 4375, 6498])).
% 13.48/13.63 tff(6500,plain,
% 13.48/13.63 (~until6(s56)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6499, 6497])).
% 13.48/13.63 tff(6501,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[5121, 6500])).
% 13.48/13.63 tff(6502,plain,
% 13.48/13.63 (~always5(s55)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[3921, 6498])).
% 13.48/13.63 tff(6503,plain,
% 13.48/13.63 (xuntil7(s55) | (~until6(s55))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[5115, 4375, 6502])).
% 13.48/13.63 tff(6504,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[6503, 6501])).
% 13.48/13.63 tff(6505,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[5108, 6504])).
% 13.48/13.63 tff(6506,plain,
% 13.48/13.63 (~always5(s54)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[3929, 6502])).
% 13.48/13.63 tff(6507,plain,
% 13.48/13.63 (xuntil7(s54) | (~until6(s54))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[5102, 4375, 6506])).
% 13.48/13.63 tff(6508,plain,
% 13.48/13.63 (~until6(s54)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6507, 6505])).
% 13.48/13.63 tff(6509,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[5095, 6508])).
% 13.48/13.63 tff(6510,plain,
% 13.48/13.63 (~always5(s53)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[3937, 6506])).
% 13.48/13.63 tff(6511,plain,
% 13.48/13.63 (xuntil7(s53) | (~until6(s53))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[5089, 4375, 6510])).
% 13.48/13.63 tff(6512,plain,
% 13.48/13.63 (~until6(s53)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6511, 6509])).
% 13.48/13.63 tff(6513,plain,
% 13.48/13.63 (~xuntil7(s52)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[5082, 6512])).
% 13.48/13.63 tff(6514,plain,
% 13.48/13.63 (~always5(s52)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[3945, 6510])).
% 13.48/13.63 tff(6515,plain,
% 13.48/13.63 (xuntil7(s52) | (~until6(s52))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[5076, 4375, 6514])).
% 13.48/13.63 tff(6516,plain,
% 13.48/13.63 (~until6(s52)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6515, 6513])).
% 13.48/13.63 tff(6517,plain,
% 13.48/13.63 (~xuntil7(s51)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[5069, 6516])).
% 13.48/13.63 tff(6518,plain,
% 13.48/13.63 (~always5(s51)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[3953, 6514])).
% 13.48/13.63 tff(6519,plain,
% 13.48/13.63 (xuntil7(s51) | (~until6(s51))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[5063, 4375, 6518])).
% 13.48/13.63 tff(6520,plain,
% 13.48/13.63 (~until6(s51)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6519, 6517])).
% 13.48/13.63 tff(6521,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[5056, 6520])).
% 13.48/13.63 tff(6522,plain,
% 13.48/13.63 (~always5(s50)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[3961, 6518])).
% 13.48/13.63 tff(6523,plain,
% 13.48/13.63 (xuntil7(s50) | (~until6(s50))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[5050, 4375, 6522])).
% 13.48/13.63 tff(6524,plain,
% 13.48/13.63 (~until6(s50)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6523, 6521])).
% 13.48/13.63 tff(6525,plain,
% 13.48/13.63 (~xuntil7(s49)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[5043, 6524])).
% 13.48/13.63 tff(6526,plain,
% 13.48/13.63 (~always5(s49)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[3969, 6522])).
% 13.48/13.63 tff(6527,plain,
% 13.48/13.63 (xuntil7(s49) | (~until6(s49))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[5037, 4375, 6526])).
% 13.48/13.63 tff(6528,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[6527, 6525])).
% 13.48/13.63 tff(6529,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[5030, 6528])).
% 13.48/13.63 tff(6530,plain,
% 13.48/13.63 (~always5(s48)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[3977, 6526])).
% 13.48/13.63 tff(6531,plain,
% 13.48/13.63 (xuntil7(s48) | (~until6(s48))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[5024, 4375, 6530])).
% 13.48/13.63 tff(6532,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[6531, 6529])).
% 13.48/13.63 tff(6533,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[5017, 6532])).
% 13.48/13.63 tff(6534,plain,
% 13.48/13.63 (~always5(s47)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[3985, 6530])).
% 13.48/13.63 tff(6535,plain,
% 13.48/13.63 (xuntil7(s47) | (~until6(s47))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[5011, 4375, 6534])).
% 13.48/13.63 tff(6536,plain,
% 13.48/13.63 (~until6(s47)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6535, 6533])).
% 13.48/13.63 tff(6537,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[5004, 6536])).
% 13.48/13.63 tff(6538,plain,
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% 13.48/13.63 tff(6539,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4998, 4375, 6538])).
% 13.48/13.63 tff(6540,plain,
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% 13.48/13.63 tff(6541,plain,
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% 13.48/13.63 tff(6548,plain,
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% 13.48/13.63 tff(6549,plain,
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% 13.48/13.63 tff(6550,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4017, 6546])).
% 13.48/13.63 tff(6551,plain,
% 13.48/13.63 (xuntil7(s43) | (~until6(s43))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4959, 4375, 6550])).
% 13.48/13.63 tff(6552,plain,
% 13.48/13.63 (~until6(s43)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6551, 6549])).
% 13.48/13.63 tff(6553,plain,
% 13.48/13.63 (~xuntil7(s42)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4952, 6552])).
% 13.48/13.63 tff(6554,plain,
% 13.48/13.63 (~always5(s42)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4025, 6550])).
% 13.48/13.63 tff(6555,plain,
% 13.48/13.63 (xuntil7(s42) | (~until6(s42))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4946, 4375, 6554])).
% 13.48/13.63 tff(6556,plain,
% 13.48/13.63 (~until6(s42)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6555, 6553])).
% 13.48/13.63 tff(6557,plain,
% 13.48/13.63 (~xuntil7(s41)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4939, 6556])).
% 13.48/13.63 tff(6558,plain,
% 13.48/13.63 (~always5(s41)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4033, 6554])).
% 13.48/13.63 tff(6559,plain,
% 13.48/13.63 (xuntil7(s41) | (~until6(s41))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4933, 4375, 6558])).
% 13.48/13.63 tff(6560,plain,
% 13.48/13.63 (~until6(s41)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6559, 6557])).
% 13.48/13.63 tff(6561,plain,
% 13.48/13.63 (~xuntil7(s40)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4926, 6560])).
% 13.48/13.63 tff(6562,plain,
% 13.48/13.63 (~always5(s40)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4041, 6558])).
% 13.48/13.63 tff(6563,plain,
% 13.48/13.63 (xuntil7(s40) | (~until6(s40))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4920, 4375, 6562])).
% 13.48/13.63 tff(6564,plain,
% 13.48/13.63 (~until6(s40)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6563, 6561])).
% 13.48/13.63 tff(6565,plain,
% 13.48/13.63 (~xuntil7(s39)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4913, 6564])).
% 13.48/13.63 tff(6566,plain,
% 13.48/13.63 (~always5(s39)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4049, 6562])).
% 13.48/13.63 tff(6567,plain,
% 13.48/13.63 (xuntil7(s39) | (~until6(s39))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4907, 4375, 6566])).
% 13.48/13.63 tff(6568,plain,
% 13.48/13.63 (~until6(s39)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6567, 6565])).
% 13.48/13.63 tff(6569,plain,
% 13.48/13.63 (~xuntil7(s38)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4900, 6568])).
% 13.48/13.63 tff(6570,plain,
% 13.48/13.63 (~always5(s38)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4057, 6566])).
% 13.48/13.63 tff(6571,plain,
% 13.48/13.63 (xuntil7(s38) | (~until6(s38))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4894, 4375, 6570])).
% 13.48/13.63 tff(6572,plain,
% 13.48/13.63 (~until6(s38)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6571, 6569])).
% 13.48/13.63 tff(6573,plain,
% 13.48/13.63 (~xuntil7(s37)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4887, 6572])).
% 13.48/13.63 tff(6574,plain,
% 13.48/13.63 (~always5(s37)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4065, 6570])).
% 13.48/13.63 tff(6575,plain,
% 13.48/13.63 (xuntil7(s37) | (~until6(s37))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4881, 4375, 6574])).
% 13.48/13.63 tff(6576,plain,
% 13.48/13.63 (~until6(s37)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6575, 6573])).
% 13.48/13.63 tff(6577,plain,
% 13.48/13.63 (~xuntil7(s36)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4874, 6576])).
% 13.48/13.63 tff(6578,plain,
% 13.48/13.63 (~always5(s36)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4073, 6574])).
% 13.48/13.63 tff(6579,plain,
% 13.48/13.63 (xuntil7(s36) | (~until6(s36))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4868, 4375, 6578])).
% 13.48/13.63 tff(6580,plain,
% 13.48/13.63 (~until6(s36)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6579, 6577])).
% 13.48/13.63 tff(6581,plain,
% 13.48/13.63 (~xuntil7(s35)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4861, 6580])).
% 13.48/13.63 tff(6582,plain,
% 13.48/13.63 (~always5(s35)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4081, 6578])).
% 13.48/13.63 tff(6583,plain,
% 13.48/13.63 (xuntil7(s35) | (~until6(s35))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4855, 4375, 6582])).
% 13.48/13.63 tff(6584,plain,
% 13.48/13.63 (~until6(s35)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6583, 6581])).
% 13.48/13.63 tff(6585,plain,
% 13.48/13.63 (~xuntil7(s34)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4848, 6584])).
% 13.48/13.63 tff(6586,plain,
% 13.48/13.63 (~always5(s34)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4089, 6582])).
% 13.48/13.63 tff(6587,plain,
% 13.48/13.63 (xuntil7(s34) | (~until6(s34))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4842, 4375, 6586])).
% 13.48/13.63 tff(6588,plain,
% 13.48/13.63 (~until6(s34)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6587, 6585])).
% 13.48/13.63 tff(6589,plain,
% 13.48/13.63 (~xuntil7(s33)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4835, 6588])).
% 13.48/13.63 tff(6590,plain,
% 13.48/13.63 (~always5(s33)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4097, 6586])).
% 13.48/13.63 tff(6591,plain,
% 13.48/13.63 (xuntil7(s33) | (~until6(s33))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4829, 4375, 6590])).
% 13.48/13.63 tff(6592,plain,
% 13.48/13.63 (~until6(s33)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6591, 6589])).
% 13.48/13.63 tff(6593,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4822, 6592])).
% 13.48/13.63 tff(6594,plain,
% 13.48/13.63 (~always5(s32)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4105, 6590])).
% 13.48/13.63 tff(6595,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4816, 4375, 6594])).
% 13.48/13.63 tff(6596,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[6595, 6593])).
% 13.48/13.63 tff(6597,plain,
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% 13.48/13.63 tff(6598,plain,
% 13.48/13.63 (~always5(s31)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4113, 6594])).
% 13.48/13.63 tff(6599,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4803, 4375, 6598])).
% 13.48/13.63 tff(6600,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[6599, 6597])).
% 13.48/13.63 tff(6601,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4796, 6600])).
% 13.48/13.63 tff(6602,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4121, 6598])).
% 13.48/13.63 tff(6603,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4129, 6602])).
% 13.48/13.63 tff(6604,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4137, 6603])).
% 13.48/13.63 tff(6605,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4145, 6604])).
% 13.48/13.63 tff(6606,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4153, 6605])).
% 13.48/13.63 tff(6607,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4161, 6606])).
% 13.48/13.63 tff(6608,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4169, 6607])).
% 13.48/13.63 tff(6609,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4177, 6608])).
% 13.48/13.63 tff(6610,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4185, 6609])).
% 13.48/13.63 tff(6611,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4193, 6610])).
% 13.48/13.63 tff(6612,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4201, 6611])).
% 13.48/13.63 tff(6613,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4209, 6612])).
% 13.48/13.63 tff(6614,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4217, 6613])).
% 13.48/13.63 tff(6615,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4225, 6614])).
% 13.48/13.63 tff(6616,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4233, 6615])).
% 13.48/13.63 tff(6617,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4241, 6616])).
% 13.48/13.63 tff(6618,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4249, 6617])).
% 13.48/13.63 tff(6619,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4257, 6618])).
% 13.48/13.63 tff(6620,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4265, 6619])).
% 13.48/13.63 tff(6621,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4273, 6620])).
% 13.48/13.63 tff(6622,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4281, 6621])).
% 13.48/13.63 tff(6623,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4289, 6622])).
% 13.48/13.63 tff(6624,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4297, 6623])).
% 13.48/13.63 tff(6625,plain,
% 13.48/13.63 (~always5(s7)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4305, 6624])).
% 13.48/13.63 tff(6626,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4313, 6625])).
% 13.48/13.63 tff(6627,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4321, 6626])).
% 13.48/13.63 tff(6628,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4329, 6627])).
% 13.48/13.63 tff(6629,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4337, 6628])).
% 13.48/13.63 tff(6630,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4345, 6629])).
% 13.48/13.63 tff(6631,plain,
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% 13.48/13.63 inference(unit_resolution,[status(thm)],[4353, 6630])).
% 13.48/13.63 tff(6632,plain,
% 13.48/13.63 (~always5(s0)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4361, 6631])).
% 13.48/13.63 tff(6633,plain,
% 13.48/13.63 (xuntil7(s0)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4382, 6632])).
% 13.48/13.63 tff(6634,plain,
% 13.48/13.63 (until6(s1)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4397, 6633])).
% 13.48/13.63 tff(6635,plain,
% 13.48/13.63 (xuntil7(s1)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4404, 4375, 6634, 6631])).
% 13.48/13.63 tff(6636,plain,
% 13.48/13.63 (until6(s2)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4409, 6635])).
% 13.48/13.63 tff(6637,plain,
% 13.48/13.63 (xuntil7(s2) | (~until6(s2))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4416, 4375, 6630])).
% 13.48/13.63 tff(6638,plain,
% 13.48/13.63 (xuntil7(s2)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6637, 6636])).
% 13.48/13.63 tff(6639,plain,
% 13.48/13.63 (until6(s3)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4422, 6638])).
% 13.48/13.63 tff(6640,plain,
% 13.48/13.63 (xuntil7(s3) | (~until6(s3))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4429, 4375, 6629])).
% 13.48/13.63 tff(6641,plain,
% 13.48/13.63 (xuntil7(s3)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6640, 6639])).
% 13.48/13.63 tff(6642,plain,
% 13.48/13.63 (until6(s4)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4435, 6641])).
% 13.48/13.63 tff(6643,plain,
% 13.48/13.63 (xuntil7(s4) | (~until6(s4))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4442, 4375, 6628])).
% 13.48/13.63 tff(6644,plain,
% 13.48/13.63 (xuntil7(s4)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6643, 6642])).
% 13.48/13.63 tff(6645,plain,
% 13.48/13.63 (until6(s5)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4448, 6644])).
% 13.48/13.63 tff(6646,plain,
% 13.48/13.63 (xuntil7(s5) | (~until6(s5))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4455, 4375, 6627])).
% 13.48/13.63 tff(6647,plain,
% 13.48/13.63 (xuntil7(s5)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6646, 6645])).
% 13.48/13.63 tff(6648,plain,
% 13.48/13.63 (until6(s6)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4461, 6647])).
% 13.48/13.63 tff(6649,plain,
% 13.48/13.63 (xuntil7(s6) | (~until6(s6))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4468, 4375, 6626])).
% 13.48/13.63 tff(6650,plain,
% 13.48/13.63 (xuntil7(s6)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6649, 6648])).
% 13.48/13.63 tff(6651,plain,
% 13.48/13.63 (until6(s7)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4474, 6650])).
% 13.48/13.63 tff(6652,plain,
% 13.48/13.63 (xuntil7(s7) | (~until6(s7))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4481, 4375, 6625])).
% 13.48/13.63 tff(6653,plain,
% 13.48/13.63 (xuntil7(s7)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6652, 6651])).
% 13.48/13.63 tff(6654,plain,
% 13.48/13.63 (until6(s8)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4487, 6653])).
% 13.48/13.63 tff(6655,plain,
% 13.48/13.63 (xuntil7(s8) | (~until6(s8))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4550, 4375, 6624])).
% 13.48/13.63 tff(6656,plain,
% 13.48/13.63 (xuntil7(s8)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6655, 6654])).
% 13.48/13.63 tff(6657,plain,
% 13.48/13.63 (until6(s9)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4556, 6656])).
% 13.48/13.63 tff(6658,plain,
% 13.48/13.63 (xuntil7(s9) | (~until6(s9))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4563, 4375, 6623])).
% 13.48/13.63 tff(6659,plain,
% 13.48/13.63 (xuntil7(s9)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6658, 6657])).
% 13.48/13.63 tff(6660,plain,
% 13.48/13.63 (until6(s10)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4568, 6659])).
% 13.48/13.63 tff(6661,plain,
% 13.48/13.63 (xuntil7(s10) | (~until6(s10))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4575, 4375, 6622])).
% 13.48/13.63 tff(6662,plain,
% 13.48/13.63 (xuntil7(s10)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6661, 6660])).
% 13.48/13.63 tff(6663,plain,
% 13.48/13.63 (until6(s11)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4581, 6662])).
% 13.48/13.63 tff(6664,plain,
% 13.48/13.63 (xuntil7(s11) | (~until6(s11))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4588, 4375, 6621])).
% 13.48/13.63 tff(6665,plain,
% 13.48/13.63 (xuntil7(s11)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6664, 6663])).
% 13.48/13.63 tff(6666,plain,
% 13.48/13.63 (until6(s12)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4594, 6665])).
% 13.48/13.63 tff(6667,plain,
% 13.48/13.63 (xuntil7(s12) | (~until6(s12))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4537, 4375, 6620])).
% 13.48/13.63 tff(6668,plain,
% 13.48/13.63 (xuntil7(s12)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6667, 6666])).
% 13.48/13.63 tff(6669,plain,
% 13.48/13.63 (until6(s13)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4529, 6668])).
% 13.48/13.63 tff(6670,plain,
% 13.48/13.63 (xuntil7(s13) | (~until6(s13))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4523, 4375, 6619])).
% 13.48/13.63 tff(6671,plain,
% 13.48/13.63 (xuntil7(s13)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6670, 6669])).
% 13.48/13.63 tff(6672,plain,
% 13.48/13.63 (until6(s14)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4515, 6671])).
% 13.48/13.63 tff(6673,plain,
% 13.48/13.63 (xuntil7(s14) | (~until6(s14))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4510, 4375, 6618])).
% 13.48/13.63 tff(6674,plain,
% 13.48/13.63 (xuntil7(s14)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6673, 6672])).
% 13.48/13.63 tff(6675,plain,
% 13.48/13.63 (until6(s15)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4503, 6674])).
% 13.48/13.63 tff(6676,plain,
% 13.48/13.63 (xuntil7(s15) | (~until6(s15))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4497, 4375, 6617])).
% 13.48/13.63 tff(6677,plain,
% 13.48/13.63 (xuntil7(s15)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6676, 6675])).
% 13.48/13.63 tff(6678,plain,
% 13.48/13.63 (until6(s16)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4601, 6677])).
% 13.48/13.63 tff(6679,plain,
% 13.48/13.63 (xuntil7(s16) | (~until6(s16))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4608, 4375, 6616])).
% 13.48/13.63 tff(6680,plain,
% 13.48/13.63 (xuntil7(s16)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6679, 6678])).
% 13.48/13.63 tff(6681,plain,
% 13.48/13.63 (until6(s17)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4614, 6680])).
% 13.48/13.63 tff(6682,plain,
% 13.48/13.63 (xuntil7(s17) | (~until6(s17))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4621, 4375, 6615])).
% 13.48/13.63 tff(6683,plain,
% 13.48/13.63 (xuntil7(s17)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6682, 6681])).
% 13.48/13.63 tff(6684,plain,
% 13.48/13.63 (until6(s18)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4627, 6683])).
% 13.48/13.63 tff(6685,plain,
% 13.48/13.63 (xuntil7(s18) | (~until6(s18))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4634, 4375, 6614])).
% 13.48/13.63 tff(6686,plain,
% 13.48/13.63 (xuntil7(s18)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6685, 6684])).
% 13.48/13.63 tff(6687,plain,
% 13.48/13.63 (until6(s19)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4640, 6686])).
% 13.48/13.63 tff(6688,plain,
% 13.48/13.63 (xuntil7(s19) | (~until6(s19))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4647, 4375, 6613])).
% 13.48/13.63 tff(6689,plain,
% 13.48/13.63 (xuntil7(s19)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6688, 6687])).
% 13.48/13.63 tff(6690,plain,
% 13.48/13.63 (until6(s20)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4653, 6689])).
% 13.48/13.63 tff(6691,plain,
% 13.48/13.63 (xuntil7(s20) | (~until6(s20))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4660, 4375, 6612])).
% 13.48/13.63 tff(6692,plain,
% 13.48/13.63 (xuntil7(s20)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6691, 6690])).
% 13.48/13.63 tff(6693,plain,
% 13.48/13.63 (until6(s21)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4666, 6692])).
% 13.48/13.63 tff(6694,plain,
% 13.48/13.63 (xuntil7(s21) | (~until6(s21))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4673, 4375, 6611])).
% 13.48/13.63 tff(6695,plain,
% 13.48/13.63 (xuntil7(s21)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6694, 6693])).
% 13.48/13.63 tff(6696,plain,
% 13.48/13.63 (until6(s22)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4679, 6695])).
% 13.48/13.63 tff(6697,plain,
% 13.48/13.63 (xuntil7(s22) | (~until6(s22))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4686, 4375, 6610])).
% 13.48/13.63 tff(6698,plain,
% 13.48/13.63 (xuntil7(s22)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6697, 6696])).
% 13.48/13.63 tff(6699,plain,
% 13.48/13.63 (until6(s23)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4692, 6698])).
% 13.48/13.63 tff(6700,plain,
% 13.48/13.63 (xuntil7(s23) | (~until6(s23))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4699, 4375, 6609])).
% 13.48/13.63 tff(6701,plain,
% 13.48/13.63 (xuntil7(s23)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6700, 6699])).
% 13.48/13.63 tff(6702,plain,
% 13.48/13.63 (until6(s24)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4705, 6701])).
% 13.48/13.63 tff(6703,plain,
% 13.48/13.63 (xuntil7(s24) | (~until6(s24))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4712, 4375, 6608])).
% 13.48/13.63 tff(6704,plain,
% 13.48/13.63 (xuntil7(s24)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6703, 6702])).
% 13.48/13.63 tff(6705,plain,
% 13.48/13.63 (until6(s25)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4718, 6704])).
% 13.48/13.63 tff(6706,plain,
% 13.48/13.63 (xuntil7(s25) | (~until6(s25))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4725, 4375, 6607])).
% 13.48/13.63 tff(6707,plain,
% 13.48/13.63 (xuntil7(s25)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6706, 6705])).
% 13.48/13.63 tff(6708,plain,
% 13.48/13.63 (until6(s26)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4731, 6707])).
% 13.48/13.63 tff(6709,plain,
% 13.48/13.63 (xuntil7(s26) | (~until6(s26))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4738, 4375, 6606])).
% 13.48/13.63 tff(6710,plain,
% 13.48/13.63 (xuntil7(s26)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6709, 6708])).
% 13.48/13.63 tff(6711,plain,
% 13.48/13.63 (until6(s27)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4744, 6710])).
% 13.48/13.63 tff(6712,plain,
% 13.48/13.63 (xuntil7(s27) | (~until6(s27))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4751, 4375, 6605])).
% 13.48/13.63 tff(6713,plain,
% 13.48/13.63 (xuntil7(s27)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6712, 6711])).
% 13.48/13.63 tff(6714,plain,
% 13.48/13.63 (until6(s28)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4757, 6713])).
% 13.48/13.63 tff(6715,plain,
% 13.48/13.63 (xuntil7(s28) | (~until6(s28))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4764, 4375, 6604])).
% 13.48/13.63 tff(6716,plain,
% 13.48/13.63 (xuntil7(s28)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6715, 6714])).
% 13.48/13.63 tff(6717,plain,
% 13.48/13.63 (until6(s29)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4770, 6716])).
% 13.48/13.63 tff(6718,plain,
% 13.48/13.63 (xuntil7(s29) | (~until6(s29))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4777, 4375, 6603])).
% 13.48/13.63 tff(6719,plain,
% 13.48/13.63 (xuntil7(s29)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6718, 6717])).
% 13.48/13.63 tff(6720,plain,
% 13.48/13.63 (until6(s30)),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4783, 6719])).
% 13.48/13.63 tff(6721,plain,
% 13.48/13.63 (xuntil7(s30) | (~until6(s30))),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[4790, 4375, 6602])).
% 13.48/13.63 tff(6722,plain,
% 13.48/13.63 ($false),
% 13.48/13.63 inference(unit_resolution,[status(thm)],[6721, 6720, 6601])).
% 13.48/13.63 tff(6723,plain,(loop), inference(lemma,lemma(discharge,[]))).
% 13.48/13.63 tff(6724,plain,
% 13.48/13.63 (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58) | trans(s59, s59)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58) | trans(s59, s59))),
% 13.48/13.63 inference(rewrite,[status(thm)],[])).
% 13.48/13.63 tff(6725,plain,
% 13.48/13.63 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58)) | trans(s59, s59)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58) | trans(s59, s59))),
% 13.48/13.63 inference(rewrite,[status(thm)],[])).
% 13.48/13.63 tff(6726,plain,
% 13.48/13.63 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57)) | trans(s59, s58)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58))),
% 13.48/13.64 inference(rewrite,[status(thm)],[])).
% 13.48/13.64 tff(6727,plain,
% 13.48/13.64 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56)) | trans(s59, s57)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57))),
% 13.48/13.64 inference(rewrite,[status(thm)],[])).
% 13.48/13.64 tff(6728,plain,
% 13.48/13.64 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55)) | trans(s59, s56)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56))),
% 13.48/13.64 inference(rewrite,[status(thm)],[])).
% 13.48/13.64 tff(6729,plain,
% 13.48/13.64 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54)) | trans(s59, s55)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55))),
% 13.48/13.64 inference(rewrite,[status(thm)],[])).
% 13.48/13.64 tff(6730,plain,
% 13.48/13.64 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53)) | trans(s59, s54)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54))),
% 13.48/13.64 inference(rewrite,[status(thm)],[])).
% 13.48/13.64 tff(6731,plain,
% 13.48/13.64 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52)) | trans(s59, s53)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53))),
% 13.48/13.64 inference(rewrite,[status(thm)],[])).
% 13.48/13.64 tff(6732,plain,
% 13.48/13.64 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51)) | trans(s59, s52)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52))),
% 13.48/13.65 inference(rewrite,[status(thm)],[])).
% 13.48/13.65 tff(6733,plain,
% 13.48/13.65 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50)) | trans(s59, s51)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51))),
% 13.48/13.65 inference(rewrite,[status(thm)],[])).
% 13.48/13.65 tff(6734,plain,
% 13.48/13.65 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49)) | trans(s59, s50)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50))),
% 13.48/13.65 inference(rewrite,[status(thm)],[])).
% 13.48/13.65 tff(6735,plain,
% 13.48/13.65 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48)) | trans(s59, s49)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49))),
% 13.48/13.65 inference(rewrite,[status(thm)],[])).
% 13.48/13.65 tff(6736,plain,
% 13.48/13.65 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47)) | trans(s59, s48)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48))),
% 13.48/13.65 inference(rewrite,[status(thm)],[])).
% 13.48/13.65 tff(6737,plain,
% 13.48/13.65 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46)) | trans(s59, s47)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47))),
% 13.48/13.65 inference(rewrite,[status(thm)],[])).
% 13.48/13.65 tff(6738,plain,
% 13.48/13.65 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45)) | trans(s59, s46)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46))),
% 13.48/13.65 inference(rewrite,[status(thm)],[])).
% 13.48/13.65 tff(6739,plain,
% 13.48/13.65 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44)) | trans(s59, s45)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45))),
% 13.48/13.65 inference(rewrite,[status(thm)],[])).
% 13.48/13.65 tff(6740,plain,
% 13.48/13.65 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43)) | trans(s59, s44)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44))),
% 13.48/13.65 inference(rewrite,[status(thm)],[])).
% 13.48/13.65 tff(6741,plain,
% 13.48/13.65 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42)) | trans(s59, s43)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43))),
% 13.48/13.66 inference(rewrite,[status(thm)],[])).
% 13.48/13.66 tff(6742,plain,
% 13.48/13.66 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41)) | trans(s59, s42)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42))),
% 13.48/13.66 inference(rewrite,[status(thm)],[])).
% 13.48/13.66 tff(6743,plain,
% 13.48/13.66 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40)) | trans(s59, s41)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41))),
% 13.48/13.66 inference(rewrite,[status(thm)],[])).
% 13.48/13.66 tff(6744,plain,
% 13.48/13.66 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39)) | trans(s59, s40)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40))),
% 13.48/13.66 inference(rewrite,[status(thm)],[])).
% 13.48/13.66 tff(6745,plain,
% 13.48/13.66 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38)) | trans(s59, s39)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39))),
% 13.48/13.66 inference(rewrite,[status(thm)],[])).
% 13.48/13.66 tff(6746,plain,
% 13.48/13.66 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37)) | trans(s59, s38)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38))),
% 13.48/13.66 inference(rewrite,[status(thm)],[])).
% 13.48/13.66 tff(6747,plain,
% 13.48/13.66 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36)) | trans(s59, s37)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37))),
% 13.48/13.66 inference(rewrite,[status(thm)],[])).
% 13.48/13.66 tff(6748,plain,
% 13.48/13.66 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35)) | trans(s59, s36)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36))),
% 13.48/13.66 inference(rewrite,[status(thm)],[])).
% 13.48/13.66 tff(6749,plain,
% 13.48/13.66 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34)) | trans(s59, s35)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35))),
% 13.48/13.67 inference(rewrite,[status(thm)],[])).
% 13.48/13.67 tff(6750,plain,
% 13.48/13.67 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33)) | trans(s59, s34)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34))),
% 13.48/13.67 inference(rewrite,[status(thm)],[])).
% 13.48/13.67 tff(6751,plain,
% 13.48/13.67 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32)) | trans(s59, s33)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33))),
% 13.48/13.67 inference(rewrite,[status(thm)],[])).
% 13.48/13.67 tff(6752,plain,
% 13.48/13.67 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31)) | trans(s59, s32)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32))),
% 13.48/13.67 inference(rewrite,[status(thm)],[])).
% 13.48/13.67 tff(6753,plain,
% 13.48/13.67 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30)) | trans(s59, s31)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31))),
% 13.48/13.67 inference(rewrite,[status(thm)],[])).
% 13.48/13.67 tff(6754,plain,
% 13.48/13.67 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29)) | trans(s59, s30)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30))),
% 13.48/13.67 inference(rewrite,[status(thm)],[])).
% 13.48/13.67 tff(6755,plain,
% 13.48/13.67 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28)) | trans(s59, s29)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29))),
% 13.48/13.67 inference(rewrite,[status(thm)],[])).
% 13.48/13.67 tff(6756,plain,
% 13.48/13.67 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27)) | trans(s59, s28)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28))),
% 13.48/13.67 inference(rewrite,[status(thm)],[])).
% 13.48/13.67 tff(6757,plain,
% 13.48/13.67 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26)) | trans(s59, s27)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27))),
% 13.48/13.67 inference(rewrite,[status(thm)],[])).
% 13.48/13.67 tff(6758,plain,
% 13.48/13.67 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25)) | trans(s59, s26)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26))),
% 13.48/13.67 inference(rewrite,[status(thm)],[])).
% 13.48/13.67 tff(6759,plain,
% 13.48/13.67 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24)) | trans(s59, s25)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6760,plain,
% 13.48/13.68 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23)) | trans(s59, s24)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6761,plain,
% 13.48/13.68 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22)) | trans(s59, s23)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6762,plain,
% 13.48/13.68 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21)) | trans(s59, s22)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6763,plain,
% 13.48/13.68 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20)) | trans(s59, s21)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6764,plain,
% 13.48/13.68 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19)) | trans(s59, s20)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6765,plain,
% 13.48/13.68 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18)) | trans(s59, s19)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6766,plain,
% 13.48/13.68 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17)) | trans(s59, s18)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6767,plain,
% 13.48/13.68 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16)) | trans(s59, s17)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6768,plain,
% 13.48/13.68 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15)) | trans(s59, s16)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6769,plain,
% 13.48/13.68 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14)) | trans(s59, s15)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6770,plain,
% 13.48/13.68 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13)) | trans(s59, s14)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6771,plain,
% 13.48/13.68 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12)) | trans(s59, s13)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6772,plain,
% 13.48/13.68 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11)) | trans(s59, s12)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6773,plain,
% 13.48/13.68 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10)) | trans(s59, s11)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6774,plain,
% 13.48/13.68 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9)) | trans(s59, s10)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6775,plain,
% 13.48/13.68 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8)) | trans(s59, s9)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6776,plain,
% 13.48/13.68 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7)) | trans(s59, s8)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6777,plain,
% 13.48/13.68 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6)) | trans(s59, s7)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6778,plain,
% 13.48/13.68 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5)) | trans(s59, s6)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6779,plain,
% 13.48/13.68 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4)) | trans(s59, s5)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6780,plain,
% 13.48/13.68 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3)) | trans(s59, s4)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6781,plain,
% 13.48/13.68 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2)) | trans(s59, s3)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6782,plain,
% 13.48/13.68 ((((~loop) | trans(s59, s0) | trans(s59, s1)) | trans(s59, s2)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6783,plain,
% 13.48/13.68 ((((~loop) | trans(s59, s0)) | trans(s59, s1)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1))),
% 13.48/13.68 inference(rewrite,[status(thm)],[])).
% 13.48/13.68 tff(6784,plain,
% 13.48/13.68 (((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1)) | trans(s59, s2))),
% 13.48/13.68 inference(monotonicity,[status(thm)],[6783])).
% 13.48/13.68 tff(6785,plain,
% 13.48/13.68 (((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2))),
% 13.48/13.68 inference(transitivity,[status(thm)],[6784, 6782])).
% 13.48/13.68 tff(6786,plain,
% 13.48/13.68 ((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2)) | trans(s59, s3))),
% 13.48/13.68 inference(monotonicity,[status(thm)],[6785])).
% 13.48/13.68 tff(6787,plain,
% 13.48/13.68 ((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3))),
% 13.48/13.68 inference(transitivity,[status(thm)],[6786, 6781])).
% 13.48/13.68 tff(6788,plain,
% 13.48/13.68 (((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3)) | trans(s59, s4))),
% 13.48/13.68 inference(monotonicity,[status(thm)],[6787])).
% 13.48/13.68 tff(6789,plain,
% 13.48/13.68 (((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4))),
% 13.48/13.68 inference(transitivity,[status(thm)],[6788, 6780])).
% 13.48/13.68 tff(6790,plain,
% 13.48/13.68 ((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4)) | trans(s59, s5))),
% 13.48/13.68 inference(monotonicity,[status(thm)],[6789])).
% 13.48/13.68 tff(6791,plain,
% 13.48/13.68 ((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5))),
% 13.48/13.68 inference(transitivity,[status(thm)],[6790, 6779])).
% 13.48/13.68 tff(6792,plain,
% 13.48/13.68 (((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5)) | trans(s59, s6))),
% 13.48/13.68 inference(monotonicity,[status(thm)],[6791])).
% 13.48/13.68 tff(6793,plain,
% 13.48/13.68 (((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6))),
% 13.48/13.68 inference(transitivity,[status(thm)],[6792, 6778])).
% 13.48/13.68 tff(6794,plain,
% 13.48/13.68 ((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6)) | trans(s59, s7))),
% 13.48/13.69 inference(monotonicity,[status(thm)],[6793])).
% 13.48/13.69 tff(6795,plain,
% 13.48/13.69 ((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7))),
% 13.48/13.69 inference(transitivity,[status(thm)],[6794, 6777])).
% 13.48/13.69 tff(6796,plain,
% 13.48/13.69 (((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7)) | trans(s59, s8))),
% 13.48/13.69 inference(monotonicity,[status(thm)],[6795])).
% 13.48/13.69 tff(6797,plain,
% 13.48/13.69 (((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8))),
% 13.48/13.69 inference(transitivity,[status(thm)],[6796, 6776])).
% 13.48/13.69 tff(6798,plain,
% 13.48/13.69 ((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8)) | trans(s59, s9))),
% 13.48/13.69 inference(monotonicity,[status(thm)],[6797])).
% 13.48/13.69 tff(6799,plain,
% 13.48/13.69 ((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9))),
% 13.48/13.69 inference(transitivity,[status(thm)],[6798, 6775])).
% 13.48/13.69 tff(6800,plain,
% 13.48/13.69 (((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9)) | trans(s59, s10))),
% 13.48/13.69 inference(monotonicity,[status(thm)],[6799])).
% 13.48/13.69 tff(6801,plain,
% 13.48/13.69 (((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10))),
% 13.48/13.69 inference(transitivity,[status(thm)],[6800, 6774])).
% 13.48/13.69 tff(6802,plain,
% 13.48/13.69 ((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10)) | trans(s59, s11))),
% 13.48/13.69 inference(monotonicity,[status(thm)],[6801])).
% 13.48/13.69 tff(6803,plain,
% 13.48/13.69 ((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11))),
% 13.48/13.69 inference(transitivity,[status(thm)],[6802, 6773])).
% 13.48/13.69 tff(6804,plain,
% 13.48/13.69 (((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11)) | trans(s59, s12))),
% 13.48/13.69 inference(monotonicity,[status(thm)],[6803])).
% 13.48/13.69 tff(6805,plain,
% 13.48/13.69 (((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12))),
% 13.48/13.69 inference(transitivity,[status(thm)],[6804, 6772])).
% 13.48/13.69 tff(6806,plain,
% 13.48/13.69 ((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12)) | trans(s59, s13))),
% 13.48/13.69 inference(monotonicity,[status(thm)],[6805])).
% 13.48/13.69 tff(6807,plain,
% 13.48/13.69 ((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13))),
% 13.48/13.69 inference(transitivity,[status(thm)],[6806, 6771])).
% 13.48/13.69 tff(6808,plain,
% 13.48/13.69 (((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13)) | trans(s59, s14))),
% 13.48/13.69 inference(monotonicity,[status(thm)],[6807])).
% 13.48/13.69 tff(6809,plain,
% 13.48/13.69 (((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14))),
% 13.48/13.69 inference(transitivity,[status(thm)],[6808, 6770])).
% 13.55/13.69 tff(6810,plain,
% 13.55/13.69 ((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14)) | trans(s59, s15))),
% 13.55/13.69 inference(monotonicity,[status(thm)],[6809])).
% 13.55/13.69 tff(6811,plain,
% 13.55/13.69 ((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15))),
% 13.55/13.69 inference(transitivity,[status(thm)],[6810, 6769])).
% 13.55/13.69 tff(6812,plain,
% 13.55/13.69 (((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15)) | trans(s59, s16))),
% 13.55/13.69 inference(monotonicity,[status(thm)],[6811])).
% 13.55/13.69 tff(6813,plain,
% 13.55/13.69 (((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16))),
% 13.55/13.69 inference(transitivity,[status(thm)],[6812, 6768])).
% 13.55/13.69 tff(6814,plain,
% 13.55/13.69 ((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16)) | trans(s59, s17))),
% 13.55/13.69 inference(monotonicity,[status(thm)],[6813])).
% 13.55/13.69 tff(6815,plain,
% 13.55/13.69 ((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17))),
% 13.55/13.70 inference(transitivity,[status(thm)],[6814, 6767])).
% 13.55/13.70 tff(6816,plain,
% 13.55/13.70 (((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17)) | trans(s59, s18))),
% 13.55/13.70 inference(monotonicity,[status(thm)],[6815])).
% 13.55/13.70 tff(6817,plain,
% 13.55/13.70 (((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18))),
% 13.55/13.70 inference(transitivity,[status(thm)],[6816, 6766])).
% 13.55/13.70 tff(6818,plain,
% 13.55/13.70 ((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18)) | trans(s59, s19))),
% 13.55/13.70 inference(monotonicity,[status(thm)],[6817])).
% 13.55/13.70 tff(6819,plain,
% 13.55/13.70 ((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19))),
% 13.55/13.70 inference(transitivity,[status(thm)],[6818, 6765])).
% 13.55/13.70 tff(6820,plain,
% 13.55/13.70 (((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19)) | trans(s59, s20))),
% 13.55/13.70 inference(monotonicity,[status(thm)],[6819])).
% 13.55/13.70 tff(6821,plain,
% 13.55/13.70 (((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20))),
% 13.55/13.70 inference(transitivity,[status(thm)],[6820, 6764])).
% 13.55/13.70 tff(6822,plain,
% 13.55/13.70 ((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20)) | trans(s59, s21))),
% 13.55/13.70 inference(monotonicity,[status(thm)],[6821])).
% 13.55/13.70 tff(6823,plain,
% 13.55/13.70 ((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21))),
% 13.55/13.70 inference(transitivity,[status(thm)],[6822, 6763])).
% 13.55/13.70 tff(6824,plain,
% 13.55/13.70 (((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21)) | trans(s59, s22))),
% 13.55/13.70 inference(monotonicity,[status(thm)],[6823])).
% 13.55/13.70 tff(6825,plain,
% 13.55/13.70 (((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22))),
% 13.55/13.70 inference(transitivity,[status(thm)],[6824, 6762])).
% 13.55/13.70 tff(6826,plain,
% 13.55/13.70 ((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22)) | trans(s59, s23))),
% 13.55/13.70 inference(monotonicity,[status(thm)],[6825])).
% 13.55/13.70 tff(6827,plain,
% 13.55/13.70 ((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23))),
% 13.55/13.70 inference(transitivity,[status(thm)],[6826, 6761])).
% 13.55/13.70 tff(6828,plain,
% 13.55/13.70 (((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23)) | trans(s59, s24))),
% 13.55/13.70 inference(monotonicity,[status(thm)],[6827])).
% 13.55/13.70 tff(6829,plain,
% 13.55/13.70 (((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24))),
% 13.55/13.70 inference(transitivity,[status(thm)],[6828, 6760])).
% 13.55/13.70 tff(6830,plain,
% 13.55/13.70 ((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24)) | trans(s59, s25))),
% 13.55/13.70 inference(monotonicity,[status(thm)],[6829])).
% 13.55/13.70 tff(6831,plain,
% 13.55/13.70 ((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25))),
% 13.55/13.70 inference(transitivity,[status(thm)],[6830, 6759])).
% 13.55/13.70 tff(6832,plain,
% 13.55/13.70 (((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25)) | trans(s59, s26))),
% 13.55/13.70 inference(monotonicity,[status(thm)],[6831])).
% 13.55/13.70 tff(6833,plain,
% 13.55/13.70 (((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26))),
% 13.55/13.71 inference(transitivity,[status(thm)],[6832, 6758])).
% 13.55/13.71 tff(6834,plain,
% 13.55/13.71 ((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26)) | trans(s59, s27))),
% 13.55/13.71 inference(monotonicity,[status(thm)],[6833])).
% 13.55/13.71 tff(6835,plain,
% 13.55/13.71 ((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27))),
% 13.55/13.71 inference(transitivity,[status(thm)],[6834, 6757])).
% 13.55/13.71 tff(6836,plain,
% 13.55/13.71 (((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27)) | trans(s59, s28))),
% 13.55/13.71 inference(monotonicity,[status(thm)],[6835])).
% 13.55/13.71 tff(6837,plain,
% 13.55/13.71 (((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28))),
% 13.55/13.71 inference(transitivity,[status(thm)],[6836, 6756])).
% 13.55/13.71 tff(6838,plain,
% 13.55/13.71 ((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28)) | trans(s59, s29))),
% 13.55/13.71 inference(monotonicity,[status(thm)],[6837])).
% 13.55/13.71 tff(6839,plain,
% 13.55/13.71 ((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29))),
% 13.55/13.71 inference(transitivity,[status(thm)],[6838, 6755])).
% 13.55/13.71 tff(6840,plain,
% 13.55/13.71 (((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29)) | trans(s59, s30))),
% 13.55/13.71 inference(monotonicity,[status(thm)],[6839])).
% 13.55/13.71 tff(6841,plain,
% 13.55/13.71 (((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30))),
% 13.55/13.71 inference(transitivity,[status(thm)],[6840, 6754])).
% 13.55/13.71 tff(6842,plain,
% 13.55/13.71 ((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30)) | trans(s59, s31))),
% 13.55/13.71 inference(monotonicity,[status(thm)],[6841])).
% 13.55/13.71 tff(6843,plain,
% 13.55/13.71 ((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31))),
% 13.55/13.72 inference(transitivity,[status(thm)],[6842, 6753])).
% 13.55/13.72 tff(6844,plain,
% 13.55/13.72 (((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31)) | trans(s59, s32))),
% 13.55/13.72 inference(monotonicity,[status(thm)],[6843])).
% 13.55/13.72 tff(6845,plain,
% 13.55/13.72 (((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32))),
% 13.55/13.72 inference(transitivity,[status(thm)],[6844, 6752])).
% 13.55/13.72 tff(6846,plain,
% 13.55/13.72 ((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32)) | trans(s59, s33))),
% 13.55/13.72 inference(monotonicity,[status(thm)],[6845])).
% 13.55/13.72 tff(6847,plain,
% 13.55/13.72 ((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33))),
% 13.55/13.72 inference(transitivity,[status(thm)],[6846, 6751])).
% 13.55/13.72 tff(6848,plain,
% 13.55/13.72 (((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33)) | trans(s59, s34))),
% 13.55/13.72 inference(monotonicity,[status(thm)],[6847])).
% 13.55/13.72 tff(6849,plain,
% 13.55/13.72 (((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34))),
% 13.55/13.72 inference(transitivity,[status(thm)],[6848, 6750])).
% 13.55/13.72 tff(6850,plain,
% 13.55/13.72 ((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34)) | trans(s59, s35))),
% 13.55/13.72 inference(monotonicity,[status(thm)],[6849])).
% 13.55/13.72 tff(6851,plain,
% 13.55/13.72 ((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35))),
% 13.55/13.72 inference(transitivity,[status(thm)],[6850, 6749])).
% 13.55/13.72 tff(6852,plain,
% 13.55/13.72 (((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35)) | trans(s59, s36))),
% 13.55/13.73 inference(monotonicity,[status(thm)],[6851])).
% 13.55/13.73 tff(6853,plain,
% 13.55/13.73 (((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36))),
% 13.55/13.73 inference(transitivity,[status(thm)],[6852, 6748])).
% 13.55/13.73 tff(6854,plain,
% 13.55/13.73 ((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36)) | trans(s59, s37))),
% 13.55/13.73 inference(monotonicity,[status(thm)],[6853])).
% 13.55/13.73 tff(6855,plain,
% 13.55/13.73 ((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37))),
% 13.55/13.73 inference(transitivity,[status(thm)],[6854, 6747])).
% 13.55/13.73 tff(6856,plain,
% 13.55/13.73 (((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37)) | trans(s59, s38))),
% 13.55/13.73 inference(monotonicity,[status(thm)],[6855])).
% 13.55/13.73 tff(6857,plain,
% 13.55/13.73 (((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38))),
% 13.55/13.73 inference(transitivity,[status(thm)],[6856, 6746])).
% 13.55/13.73 tff(6858,plain,
% 13.55/13.73 ((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38)) | trans(s59, s39))),
% 13.55/13.73 inference(monotonicity,[status(thm)],[6857])).
% 13.55/13.73 tff(6859,plain,
% 13.55/13.73 ((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39))),
% 13.55/13.73 inference(transitivity,[status(thm)],[6858, 6745])).
% 13.55/13.73 tff(6860,plain,
% 13.55/13.73 (((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39)) | trans(s59, s40))),
% 13.55/13.73 inference(monotonicity,[status(thm)],[6859])).
% 13.55/13.73 tff(6861,plain,
% 13.55/13.73 (((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40))),
% 13.55/13.73 inference(transitivity,[status(thm)],[6860, 6744])).
% 13.55/13.73 tff(6862,plain,
% 13.55/13.73 ((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40)) | trans(s59, s41))),
% 13.55/13.74 inference(monotonicity,[status(thm)],[6861])).
% 13.55/13.74 tff(6863,plain,
% 13.55/13.74 ((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41))),
% 13.55/13.74 inference(transitivity,[status(thm)],[6862, 6743])).
% 13.55/13.74 tff(6864,plain,
% 13.55/13.74 (((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41)) | trans(s59, s42))),
% 13.55/13.74 inference(monotonicity,[status(thm)],[6863])).
% 13.55/13.74 tff(6865,plain,
% 13.55/13.74 (((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42))),
% 13.55/13.74 inference(transitivity,[status(thm)],[6864, 6742])).
% 13.55/13.74 tff(6866,plain,
% 13.55/13.74 ((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42)) | trans(s59, s43))),
% 13.55/13.74 inference(monotonicity,[status(thm)],[6865])).
% 13.55/13.74 tff(6867,plain,
% 13.55/13.74 ((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43))),
% 13.55/13.74 inference(transitivity,[status(thm)],[6866, 6741])).
% 13.55/13.74 tff(6868,plain,
% 13.55/13.74 (((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43)) | trans(s59, s44))),
% 13.55/13.74 inference(monotonicity,[status(thm)],[6867])).
% 13.55/13.74 tff(6869,plain,
% 13.55/13.74 (((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44))),
% 13.55/13.75 inference(transitivity,[status(thm)],[6868, 6740])).
% 13.55/13.75 tff(6870,plain,
% 13.55/13.75 ((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44)) | trans(s59, s45))),
% 13.55/13.75 inference(monotonicity,[status(thm)],[6869])).
% 13.55/13.75 tff(6871,plain,
% 13.55/13.75 ((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45))),
% 13.55/13.75 inference(transitivity,[status(thm)],[6870, 6739])).
% 13.55/13.75 tff(6872,plain,
% 13.55/13.75 (((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45)) | trans(s59, s46))),
% 13.55/13.75 inference(monotonicity,[status(thm)],[6871])).
% 13.55/13.75 tff(6873,plain,
% 13.55/13.75 (((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46))),
% 13.55/13.75 inference(transitivity,[status(thm)],[6872, 6738])).
% 13.55/13.75 tff(6874,plain,
% 13.55/13.75 ((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46)) | trans(s59, s47))),
% 13.55/13.75 inference(monotonicity,[status(thm)],[6873])).
% 13.55/13.75 tff(6875,plain,
% 13.55/13.75 ((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47))),
% 13.55/13.75 inference(transitivity,[status(thm)],[6874, 6737])).
% 13.55/13.75 tff(6876,plain,
% 13.55/13.75 (((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47)) | trans(s59, s48))),
% 13.55/13.76 inference(monotonicity,[status(thm)],[6875])).
% 13.55/13.76 tff(6877,plain,
% 13.55/13.76 (((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48))),
% 13.55/13.76 inference(transitivity,[status(thm)],[6876, 6736])).
% 13.55/13.76 tff(6878,plain,
% 13.55/13.76 ((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48)) | trans(s59, s49))),
% 13.55/13.76 inference(monotonicity,[status(thm)],[6877])).
% 13.55/13.76 tff(6879,plain,
% 13.55/13.76 ((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49))),
% 13.55/13.76 inference(transitivity,[status(thm)],[6878, 6735])).
% 13.55/13.76 tff(6880,plain,
% 13.55/13.76 (((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49)) | trans(s59, s50))),
% 13.55/13.76 inference(monotonicity,[status(thm)],[6879])).
% 13.55/13.76 tff(6881,plain,
% 13.55/13.76 (((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50))),
% 13.55/13.76 inference(transitivity,[status(thm)],[6880, 6734])).
% 13.55/13.76 tff(6882,plain,
% 13.55/13.76 ((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50)) | trans(s59, s51))),
% 13.62/13.76 inference(monotonicity,[status(thm)],[6881])).
% 13.62/13.76 tff(6883,plain,
% 13.62/13.76 ((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51))),
% 13.62/13.76 inference(transitivity,[status(thm)],[6882, 6733])).
% 13.62/13.76 tff(6884,plain,
% 13.62/13.76 (((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51)) | trans(s59, s52))),
% 13.62/13.77 inference(monotonicity,[status(thm)],[6883])).
% 13.62/13.77 tff(6885,plain,
% 13.62/13.77 (((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52))),
% 13.62/13.77 inference(transitivity,[status(thm)],[6884, 6732])).
% 13.62/13.77 tff(6886,plain,
% 13.62/13.77 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52)) | trans(s59, s53))),
% 13.62/13.77 inference(monotonicity,[status(thm)],[6885])).
% 13.62/13.77 tff(6887,plain,
% 13.62/13.77 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53))),
% 13.62/13.77 inference(transitivity,[status(thm)],[6886, 6731])).
% 13.62/13.77 tff(6888,plain,
% 13.62/13.77 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53)) | trans(s59, s54))),
% 13.62/13.77 inference(monotonicity,[status(thm)],[6887])).
% 13.62/13.77 tff(6889,plain,
% 13.62/13.77 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54))),
% 13.62/13.77 inference(transitivity,[status(thm)],[6888, 6730])).
% 13.62/13.77 tff(6890,plain,
% 13.62/13.77 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) | trans(s59, s55)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54)) | trans(s59, s55))),
% 13.62/13.78 inference(monotonicity,[status(thm)],[6889])).
% 13.62/13.78 tff(6891,plain,
% 13.62/13.78 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) | trans(s59, s55)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55))),
% 13.62/13.78 inference(transitivity,[status(thm)],[6890, 6729])).
% 13.62/13.78 tff(6892,plain,
% 13.62/13.78 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) | trans(s59, s55)) | trans(s59, s56)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55)) | trans(s59, s56))),
% 13.62/13.78 inference(monotonicity,[status(thm)],[6891])).
% 13.62/13.78 tff(6893,plain,
% 13.62/13.78 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) | trans(s59, s55)) | trans(s59, s56)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56))),
% 13.62/13.78 inference(transitivity,[status(thm)],[6892, 6728])).
% 13.62/13.78 tff(6894,plain,
% 13.62/13.78 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) | trans(s59, s55)) | trans(s59, s56)) | trans(s59, s57)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56)) | trans(s59, s57))),
% 13.62/13.78 inference(monotonicity,[status(thm)],[6893])).
% 13.62/13.78 tff(6895,plain,
% 13.62/13.78 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) | trans(s59, s55)) | trans(s59, s56)) | trans(s59, s57)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57))),
% 13.62/13.79 inference(transitivity,[status(thm)],[6894, 6727])).
% 13.62/13.79 tff(6896,plain,
% 13.62/13.79 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) | trans(s59, s55)) | trans(s59, s56)) | trans(s59, s57)) | trans(s59, s58)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57)) | trans(s59, s58))),
% 13.62/13.79 inference(monotonicity,[status(thm)],[6895])).
% 13.62/13.79 tff(6897,plain,
% 13.62/13.79 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) | trans(s59, s55)) | trans(s59, s56)) | trans(s59, s57)) | trans(s59, s58)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58))),
% 13.62/13.79 inference(transitivity,[status(thm)],[6896, 6726])).
% 13.62/13.79 tff(6898,plain,
% 13.62/13.79 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) | trans(s59, s55)) | trans(s59, s56)) | trans(s59, s57)) | trans(s59, s58)) | trans(s59, s59)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58)) | trans(s59, s59))),
% 13.62/13.79 inference(monotonicity,[status(thm)],[6897])).
% 13.62/13.79 tff(6899,plain,
% 13.62/13.79 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) | trans(s59, s55)) | trans(s59, s56)) | trans(s59, s57)) | trans(s59, s58)) | trans(s59, s59)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58) | trans(s59, s59))),
% 13.62/13.79 inference(transitivity,[status(thm)],[6898, 6725])).
% 13.62/13.79 tff(6900,axiom,(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) | trans(s59, s55)) | trans(s59, s56)) | trans(s59, s57)) | trans(s59, s58)) | trans(s59, s59)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound62')).
% 13.62/13.79 tff(6901,plain,
% 13.62/13.79 ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58) | trans(s59, s59)),
% 13.62/13.79 inference(modus_ponens,[status(thm)],[6900, 6899])).
% 13.62/13.79 tff(6902,plain,
% 13.62/13.79 ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58) | trans(s59, s59)),
% 13.62/13.79 inference(modus_ponens,[status(thm)],[6901, 6724])).
% 13.62/13.79 tff(6903,plain,
% 13.62/13.79 ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58) | trans(s59, s59)),
% 13.62/13.79 inference(modus_ponens,[status(thm)],[6902, 6724])).
% 13.62/13.79 tff(6904,plain,
% 13.62/13.79 ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58) | trans(s59, s59)),
% 13.62/13.79 inference(modus_ponens,[status(thm)],[6903, 6724])).
% 13.62/13.79 tff(6905,plain,
% 13.62/13.79 ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58) | trans(s59, s59)),
% 13.62/13.80 inference(modus_ponens,[status(thm)],[6904, 6724])).
% 13.62/13.80 tff(6906,plain,
% 13.62/13.80 (trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58) | trans(s59, s59)),
% 13.62/13.80 inference(unit_resolution,[status(thm)],[6905, 6723])).
% 13.62/13.80 tff(6907,plain,
% 13.62/13.80 (trans(s59, s4)),
% 13.62/13.80 inference(unit_resolution,[status(thm)],[6906, 6456, 6445, 6424, 6413, 6402, 6391, 6380, 6369, 6358, 6347, 6336, 6325, 6314, 6303, 6292, 6281, 6270, 6259, 6248, 6237, 6226, 6215, 6204, 6193, 6182, 6171, 6160, 6149, 6138, 6127, 6116, 6105, 6094, 6083, 6072, 6061, 6050, 6039, 6028, 6017, 6006, 5995, 5984, 5973, 5962, 5951, 5940, 5929, 5918, 5907, 5896, 5885, 5874, 5863, 5852, 5811, 5800, 5789, 5778])).
% 13.62/13.80 tff(6908,plain,
% 13.62/13.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s4) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s4)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s4) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s4)))),
% 13.62/13.80 inference(rewrite,[status(thm)],[])).
% 13.62/13.80 tff(6909,plain,
% 13.62/13.80 (((~last(s59)) | (~trans(s59, s4)) | (~xuntil7(s59)) | until2p8(s4)) <=> (until2p8(s4) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s4)))),
% 13.62/13.80 inference(rewrite,[status(thm)],[])).
% 13.62/13.80 tff(6910,plain,
% 13.62/13.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s4)) | (~xuntil7(s59)) | until2p8(s4))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s4) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s4))))),
% 13.62/13.80 inference(monotonicity,[status(thm)],[6909])).
% 13.62/13.80 tff(6911,plain,
% 13.62/13.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s4)) | (~xuntil7(s59)) | until2p8(s4))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s4) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s4)))),
% 13.62/13.80 inference(transitivity,[status(thm)],[6910, 6908])).
% 13.62/13.80 tff(6912,plain,
% 13.62/13.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s4)) | (~xuntil7(s59)) | until2p8(s4))),
% 13.62/13.80 inference(quant_inst,[status(thm)],[])).
% 13.62/13.80 tff(6913,plain,
% 13.62/13.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s4) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s4))),
% 13.62/13.80 inference(modus_ponens,[status(thm)],[6912, 6911])).
% 13.62/13.80 tff(6914,plain,
% 13.62/13.80 ($false),
% 13.62/13.80 inference(unit_resolution,[status(thm)],[6913, 5178, 6907, 5766, 5756, 5168])).
% 13.62/13.80 tff(6915,plain,(always5(s59)), inference(lemma,lemma(discharge,[]))).
% 13.62/13.80 tff(6916,plain,
% 13.62/13.80 (^[X: $i] : refl(((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X))) <=> ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X))))),
% 13.62/13.80 inference(bind,[status(th)],[])).
% 13.62/13.80 tff(6917,plain,
% 13.62/13.80 (![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X))) <=> ![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))),
% 13.62/13.80 inference(quant_intro,[status(thm)],[6916])).
% 13.62/13.80 tff(6918,plain,
% 13.62/13.80 (![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X))) <=> ![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))),
% 13.62/13.80 inference(rewrite,[status(thm)],[])).
% 13.62/13.80 tff(6919,plain,
% 13.62/13.80 (^[X: $i] : rewrite(((~m_counter_cell_v_carry_out(c_bit2, X)) | (~always5(X))) <=> ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X))))),
% 13.62/13.80 inference(bind,[status(th)],[])).
% 13.62/13.80 tff(6920,plain,
% 13.62/13.80 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit2, X)) | (~always5(X))) <=> ![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))),
% 13.62/13.80 inference(quant_intro,[status(thm)],[6919])).
% 13.62/13.80 tff(6921,axiom,(![X: $i] : ((~m_counter_cell_v_carry_out(c_bit2, X)) | (~always5(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty1')).
% 13.62/13.80 tff(6922,plain,
% 13.62/13.80 (![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))),
% 13.62/13.80 inference(modus_ponens,[status(thm)],[6921, 6920])).
% 13.62/13.80 tff(6923,plain,
% 13.62/13.80 (![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))),
% 13.62/13.80 inference(modus_ponens,[status(thm)],[6922, 6918])).
% 13.62/13.80 tff(6924,plain,(
% 13.62/13.80 ![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))),
% 13.62/13.80 inference(skolemize,[status(sab)],[6923])).
% 13.62/13.80 tff(6925,plain,
% 13.62/13.80 (![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))),
% 13.62/13.80 inference(modus_ponens,[status(thm)],[6924, 6917])).
% 13.62/13.80 tff(6926,plain,
% 13.62/13.80 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s59)) | (~m_counter_cell_v_carry_out(c_bit2, s59)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s59)) | (~m_counter_cell_v_carry_out(c_bit2, s59)))),
% 13.62/13.80 inference(rewrite,[status(thm)],[])).
% 13.62/13.80 tff(6927,plain,
% 13.62/13.80 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s59)) | (~m_counter_cell_v_carry_out(c_bit2, s59)))),
% 13.62/13.80 inference(quant_inst,[status(thm)],[])).
% 13.62/13.80 tff(6928,plain,
% 13.62/13.80 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s59)) | (~m_counter_cell_v_carry_out(c_bit2, s59))),
% 13.62/13.80 inference(modus_ponens,[status(thm)],[6927, 6926])).
% 13.62/13.80 tff(6929,plain,
% 13.62/13.80 (~m_counter_cell_v_carry_out(c_bit2, s59)),
% 13.62/13.80 inference(unit_resolution,[status(thm)],[6928, 6925, 6915])).
% 13.62/13.80 tff(6930,plain,
% 13.62/13.80 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s59)) | (~m_counter_cell_v_value(c_bit2, s59)) | m_counter_cell_v_carry_out(c_bit2, s59))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s59)) | (~m_counter_cell_v_value(c_bit2, s59)) | m_counter_cell_v_carry_out(c_bit2, s59))),
% 13.62/13.80 inference(rewrite,[status(thm)],[])).
% 13.62/13.80 tff(6931,plain,
% 13.62/13.80 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s59)) | (~m_counter_cell_v_value(c_bit2, s59)) | m_counter_cell_v_carry_out(c_bit2, s59))),
% 13.62/13.80 inference(quant_inst,[status(thm)],[])).
% 13.62/13.80 tff(6932,plain,
% 13.62/13.80 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s59)) | (~m_counter_cell_v_value(c_bit2, s59)) | m_counter_cell_v_carry_out(c_bit2, s59)),
% 13.62/13.80 inference(modus_ponens,[status(thm)],[6931, 6930])).
% 13.62/13.80 tff(6933,plain,
% 13.62/13.80 ((~m_counter_cell_v_carry_in(c_bit2, s59)) | (~m_counter_cell_v_value(c_bit2, s59))),
% 13.62/13.80 inference(unit_resolution,[status(thm)],[6932, 1390, 6929])).
% 13.62/13.80 tff(6934,plain,
% 13.62/13.80 (~m_counter_cell_v_value(c_bit2, s59)),
% 13.62/13.80 inference(unit_resolution,[status(thm)],[6933, 3879])).
% 13.62/13.80 tff(6935,plain,
% 13.62/13.80 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s58, s59)) | node3(c_bit2, s58, s59))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s58, s59)) | node3(c_bit2, s58, s59))),
% 13.62/13.80 inference(rewrite,[status(thm)],[])).
% 13.62/13.80 tff(6936,plain,
% 13.62/13.80 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s58, s59)) | node3(c_bit2, s58, s59))),
% 13.62/13.80 inference(quant_inst,[status(thm)],[])).
% 13.62/13.80 tff(6937,plain,
% 13.62/13.80 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s58, s59)) | node3(c_bit2, s58, s59)),
% 13.62/13.80 inference(modus_ponens,[status(thm)],[6936, 6935])).
% 13.62/13.80 tff(6938,plain,
% 13.62/13.80 (node3(c_bit2, s58, s59)),
% 13.62/13.80 inference(unit_resolution,[status(thm)],[6937, 59, 3817])).
% 13.62/13.80 tff(6939,plain,
% 13.62/13.80 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s59) | node1(c_bit2, s58) | (~node3(c_bit2, s58, s59)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s59) | node1(c_bit2, s58) | (~node3(c_bit2, s58, s59)))),
% 13.62/13.80 inference(rewrite,[status(thm)],[])).
% 13.62/13.80 tff(6940,plain,
% 13.62/13.80 ((node1(c_bit2, s58) | (~node3(c_bit2, s58, s59)) | m_counter_cell_v_value(c_bit2, s59)) <=> (m_counter_cell_v_value(c_bit2, s59) | node1(c_bit2, s58) | (~node3(c_bit2, s58, s59)))),
% 13.62/13.80 inference(rewrite,[status(thm)],[])).
% 13.62/13.80 tff(6941,plain,
% 13.62/13.80 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s58) | (~node3(c_bit2, s58, s59)) | m_counter_cell_v_value(c_bit2, s59))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s59) | node1(c_bit2, s58) | (~node3(c_bit2, s58, s59))))),
% 13.62/13.80 inference(monotonicity,[status(thm)],[6940])).
% 13.62/13.80 tff(6942,plain,
% 13.62/13.80 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s58) | (~node3(c_bit2, s58, s59)) | m_counter_cell_v_value(c_bit2, s59))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s59) | node1(c_bit2, s58) | (~node3(c_bit2, s58, s59)))),
% 13.62/13.80 inference(transitivity,[status(thm)],[6941, 6939])).
% 13.62/13.80 tff(6943,plain,
% 13.62/13.80 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s58) | (~node3(c_bit2, s58, s59)) | m_counter_cell_v_value(c_bit2, s59))),
% 13.62/13.80 inference(quant_inst,[status(thm)],[])).
% 13.62/13.80 tff(6944,plain,
% 13.62/13.80 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s59) | node1(c_bit2, s58) | (~node3(c_bit2, s58, s59))),
% 13.62/13.80 inference(modus_ponens,[status(thm)],[6943, 6942])).
% 13.62/13.80 tff(6945,plain,
% 13.62/13.80 (m_counter_cell_v_value(c_bit2, s59) | node1(c_bit2, s58)),
% 13.62/13.80 inference(unit_resolution,[status(thm)],[6944, 73, 6938])).
% 13.62/13.80 tff(6946,plain,
% 13.62/13.80 (node1(c_bit2, s58)),
% 13.62/13.80 inference(unit_resolution,[status(thm)],[6945, 6934])).
% 13.62/13.80 tff(6947,plain,
% 13.62/13.80 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s58)) | m_counter_cell_v_carry_out(c_bit1, s58))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s58)) | m_counter_cell_v_carry_out(c_bit1, s58))),
% 13.62/13.80 inference(rewrite,[status(thm)],[])).
% 13.62/13.80 tff(6948,plain,
% 13.62/13.80 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s58)) | m_counter_cell_v_carry_out(c_bit1, s58))),
% 13.62/13.80 inference(quant_inst,[status(thm)],[])).
% 13.62/13.80 tff(6949,plain,
% 13.62/13.80 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s58)) | m_counter_cell_v_carry_out(c_bit1, s58)),
% 13.62/13.80 inference(modus_ponens,[status(thm)],[6948, 6947])).
% 13.62/13.80 tff(6950,plain,
% 13.62/13.80 (~m_counter_cell_v_carry_in(c_bit2, s58)),
% 13.62/13.80 inference(unit_resolution,[status(thm)],[6949, 3675, 3790])).
% 13.62/13.80 tff(6951,plain,
% 13.62/13.80 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s58) | (~m_counter_cell_v_value(c_bit2, s58)) | (~node1(c_bit2, s58)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s58) | (~m_counter_cell_v_value(c_bit2, s58)) | (~node1(c_bit2, s58)))),
% 13.62/13.80 inference(rewrite,[status(thm)],[])).
% 13.62/13.80 tff(6952,plain,
% 13.62/13.80 (((~node1(c_bit2, s58)) | m_counter_cell_v_carry_in(c_bit2, s58) | (~m_counter_cell_v_value(c_bit2, s58))) <=> (m_counter_cell_v_carry_in(c_bit2, s58) | (~m_counter_cell_v_value(c_bit2, s58)) | (~node1(c_bit2, s58)))),
% 13.62/13.80 inference(rewrite,[status(thm)],[])).
% 13.62/13.80 tff(6953,plain,
% 13.62/13.80 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s58)) | m_counter_cell_v_carry_in(c_bit2, s58) | (~m_counter_cell_v_value(c_bit2, s58)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s58) | (~m_counter_cell_v_value(c_bit2, s58)) | (~node1(c_bit2, s58))))),
% 13.62/13.80 inference(monotonicity,[status(thm)],[6952])).
% 13.62/13.80 tff(6954,plain,
% 13.62/13.80 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s58)) | m_counter_cell_v_carry_in(c_bit2, s58) | (~m_counter_cell_v_value(c_bit2, s58)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s58) | (~m_counter_cell_v_value(c_bit2, s58)) | (~node1(c_bit2, s58)))),
% 13.62/13.80 inference(transitivity,[status(thm)],[6953, 6951])).
% 13.62/13.80 tff(6955,plain,
% 13.62/13.80 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s58)) | m_counter_cell_v_carry_in(c_bit2, s58) | (~m_counter_cell_v_value(c_bit2, s58)))),
% 13.62/13.80 inference(quant_inst,[status(thm)],[])).
% 13.62/13.80 tff(6956,plain,
% 13.62/13.80 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s58) | (~m_counter_cell_v_value(c_bit2, s58)) | (~node1(c_bit2, s58))),
% 13.62/13.80 inference(modus_ponens,[status(thm)],[6955, 6954])).
% 13.62/13.80 tff(6957,plain,
% 13.62/13.80 ((~m_counter_cell_v_value(c_bit2, s58)) | (~node1(c_bit2, s58))),
% 13.62/13.80 inference(unit_resolution,[status(thm)],[6956, 1569, 6950])).
% 13.62/13.80 tff(6958,plain,
% 13.62/13.80 (~m_counter_cell_v_value(c_bit2, s58)),
% 13.62/13.80 inference(unit_resolution,[status(thm)],[6957, 6946])).
% 13.62/13.80 tff(6959,plain,
% 13.62/13.80 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s57, s58)) | node3(c_bit2, s57, s58))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s57, s58)) | node3(c_bit2, s57, s58))),
% 13.62/13.80 inference(rewrite,[status(thm)],[])).
% 13.62/13.80 tff(6960,plain,
% 13.62/13.80 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s57, s58)) | node3(c_bit2, s57, s58))),
% 13.62/13.80 inference(quant_inst,[status(thm)],[])).
% 13.62/13.80 tff(6961,plain,
% 13.62/13.80 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s57, s58)) | node3(c_bit2, s57, s58)),
% 13.62/13.80 inference(modus_ponens,[status(thm)],[6960, 6959])).
% 13.62/13.80 tff(6962,plain,
% 13.62/13.80 (node3(c_bit2, s57, s58)),
% 13.62/13.80 inference(unit_resolution,[status(thm)],[6961, 59, 3733])).
% 13.62/13.80 tff(6963,plain,
% 13.62/13.80 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s58) | node1(c_bit2, s57) | (~node3(c_bit2, s57, s58)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s58) | node1(c_bit2, s57) | (~node3(c_bit2, s57, s58)))),
% 13.62/13.80 inference(rewrite,[status(thm)],[])).
% 13.62/13.80 tff(6964,plain,
% 13.62/13.80 ((node1(c_bit2, s57) | (~node3(c_bit2, s57, s58)) | m_counter_cell_v_value(c_bit2, s58)) <=> (m_counter_cell_v_value(c_bit2, s58) | node1(c_bit2, s57) | (~node3(c_bit2, s57, s58)))),
% 13.62/13.80 inference(rewrite,[status(thm)],[])).
% 13.62/13.80 tff(6965,plain,
% 13.62/13.80 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s57) | (~node3(c_bit2, s57, s58)) | m_counter_cell_v_value(c_bit2, s58))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s58) | node1(c_bit2, s57) | (~node3(c_bit2, s57, s58))))),
% 13.62/13.80 inference(monotonicity,[status(thm)],[6964])).
% 13.62/13.80 tff(6966,plain,
% 13.62/13.80 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s57) | (~node3(c_bit2, s57, s58)) | m_counter_cell_v_value(c_bit2, s58))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s58) | node1(c_bit2, s57) | (~node3(c_bit2, s57, s58)))),
% 13.62/13.80 inference(transitivity,[status(thm)],[6965, 6963])).
% 13.62/13.80 tff(6967,plain,
% 13.62/13.80 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s57) | (~node3(c_bit2, s57, s58)) | m_counter_cell_v_value(c_bit2, s58))),
% 13.62/13.80 inference(quant_inst,[status(thm)],[])).
% 13.62/13.80 tff(6968,plain,
% 13.62/13.80 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s58) | node1(c_bit2, s57) | (~node3(c_bit2, s57, s58))),
% 13.62/13.80 inference(modus_ponens,[status(thm)],[6967, 6966])).
% 13.62/13.80 tff(6969,plain,
% 13.62/13.80 (m_counter_cell_v_value(c_bit2, s58) | node1(c_bit2, s57)),
% 13.62/13.80 inference(unit_resolution,[status(thm)],[6968, 73, 6962])).
% 13.62/13.80 tff(6970,plain,
% 13.62/13.80 (node1(c_bit2, s57)),
% 13.62/13.80 inference(unit_resolution,[status(thm)],[6969, 6958])).
% 13.62/13.80 tff(6971,plain,
% 13.62/13.80 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s57) | (~m_counter_cell_v_value(c_bit2, s57)) | (~node1(c_bit2, s57)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s57) | (~m_counter_cell_v_value(c_bit2, s57)) | (~node1(c_bit2, s57)))),
% 13.62/13.80 inference(rewrite,[status(thm)],[])).
% 13.62/13.80 tff(6972,plain,
% 13.62/13.80 (((~node1(c_bit2, s57)) | m_counter_cell_v_carry_in(c_bit2, s57) | (~m_counter_cell_v_value(c_bit2, s57))) <=> (m_counter_cell_v_carry_in(c_bit2, s57) | (~m_counter_cell_v_value(c_bit2, s57)) | (~node1(c_bit2, s57)))),
% 13.62/13.80 inference(rewrite,[status(thm)],[])).
% 13.62/13.80 tff(6973,plain,
% 13.62/13.80 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s57)) | m_counter_cell_v_carry_in(c_bit2, s57) | (~m_counter_cell_v_value(c_bit2, s57)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s57) | (~m_counter_cell_v_value(c_bit2, s57)) | (~node1(c_bit2, s57))))),
% 13.62/13.80 inference(monotonicity,[status(thm)],[6972])).
% 13.62/13.80 tff(6974,plain,
% 13.62/13.80 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s57)) | m_counter_cell_v_carry_in(c_bit2, s57) | (~m_counter_cell_v_value(c_bit2, s57)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s57) | (~m_counter_cell_v_value(c_bit2, s57)) | (~node1(c_bit2, s57)))),
% 13.62/13.80 inference(transitivity,[status(thm)],[6973, 6971])).
% 13.62/13.80 tff(6975,plain,
% 13.62/13.80 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s57)) | m_counter_cell_v_carry_in(c_bit2, s57) | (~m_counter_cell_v_value(c_bit2, s57)))),
% 13.62/13.80 inference(quant_inst,[status(thm)],[])).
% 13.62/13.80 tff(6976,plain,
% 13.62/13.80 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s57) | (~m_counter_cell_v_value(c_bit2, s57)) | (~node1(c_bit2, s57))),
% 13.62/13.80 inference(modus_ponens,[status(thm)],[6975, 6974])).
% 13.62/13.80 tff(6977,plain,
% 13.62/13.80 (m_counter_cell_v_carry_in(c_bit2, s57) | (~m_counter_cell_v_value(c_bit2, s57))),
% 13.62/13.80 inference(unit_resolution,[status(thm)],[6976, 1569, 6970])).
% 13.62/13.80 tff(6978,plain,
% 13.62/13.80 (~m_counter_cell_v_value(c_bit2, s57)),
% 13.62/13.80 inference(unit_resolution,[status(thm)],[6977, 3681])).
% 13.62/13.80 tff(6979,plain,
% 13.62/13.80 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s56, s57)) | node3(c_bit2, s56, s57))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s56, s57)) | node3(c_bit2, s56, s57))),
% 13.62/13.80 inference(rewrite,[status(thm)],[])).
% 13.62/13.80 tff(6980,plain,
% 13.62/13.80 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s56, s57)) | node3(c_bit2, s56, s57))),
% 13.62/13.80 inference(quant_inst,[status(thm)],[])).
% 13.62/13.80 tff(6981,plain,
% 13.62/13.80 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s56, s57)) | node3(c_bit2, s56, s57)),
% 13.62/13.80 inference(modus_ponens,[status(thm)],[6980, 6979])).
% 13.62/13.80 tff(6982,plain,
% 13.62/13.80 (node3(c_bit2, s56, s57)),
% 13.62/13.80 inference(unit_resolution,[status(thm)],[6981, 59, 3642])).
% 13.62/13.80 tff(6983,plain,
% 13.62/13.80 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s57) | node1(c_bit2, s56) | (~node3(c_bit2, s56, s57)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s57) | node1(c_bit2, s56) | (~node3(c_bit2, s56, s57)))),
% 13.62/13.80 inference(rewrite,[status(thm)],[])).
% 13.62/13.80 tff(6984,plain,
% 13.62/13.80 ((node1(c_bit2, s56) | (~node3(c_bit2, s56, s57)) | m_counter_cell_v_value(c_bit2, s57)) <=> (m_counter_cell_v_value(c_bit2, s57) | node1(c_bit2, s56) | (~node3(c_bit2, s56, s57)))),
% 13.62/13.80 inference(rewrite,[status(thm)],[])).
% 13.62/13.80 tff(6985,plain,
% 13.62/13.80 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s56) | (~node3(c_bit2, s56, s57)) | m_counter_cell_v_value(c_bit2, s57))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s57) | node1(c_bit2, s56) | (~node3(c_bit2, s56, s57))))),
% 13.62/13.80 inference(monotonicity,[status(thm)],[6984])).
% 13.62/13.80 tff(6986,plain,
% 13.62/13.80 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s56) | (~node3(c_bit2, s56, s57)) | m_counter_cell_v_value(c_bit2, s57))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s57) | node1(c_bit2, s56) | (~node3(c_bit2, s56, s57)))),
% 13.62/13.80 inference(transitivity,[status(thm)],[6985, 6983])).
% 13.62/13.80 tff(6987,plain,
% 13.62/13.80 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s56) | (~node3(c_bit2, s56, s57)) | m_counter_cell_v_value(c_bit2, s57))),
% 13.62/13.80 inference(quant_inst,[status(thm)],[])).
% 13.62/13.80 tff(6988,plain,
% 13.62/13.80 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s57) | node1(c_bit2, s56) | (~node3(c_bit2, s56, s57))),
% 13.62/13.80 inference(modus_ponens,[status(thm)],[6987, 6986])).
% 13.62/13.80 tff(6989,plain,
% 13.62/13.80 (m_counter_cell_v_value(c_bit2, s57) | node1(c_bit2, s56)),
% 13.62/13.80 inference(unit_resolution,[status(thm)],[6988, 73, 6982])).
% 13.62/13.80 tff(6990,plain,
% 13.62/13.80 (node1(c_bit2, s56)),
% 13.62/13.80 inference(unit_resolution,[status(thm)],[6989, 6978])).
% 13.62/13.80 tff(6991,assumption,(m_counter_cell_v_value(c_bit2, s56)), introduced(assumption)).
% 13.62/13.80 tff(6992,plain,
% 13.62/13.80 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s56) | (~m_counter_cell_v_value(c_bit2, s56)) | (~node1(c_bit2, s56)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s56) | (~m_counter_cell_v_value(c_bit2, s56)) | (~node1(c_bit2, s56)))),
% 13.62/13.80 inference(rewrite,[status(thm)],[])).
% 13.62/13.80 tff(6993,plain,
% 13.62/13.80 (((~node1(c_bit2, s56)) | m_counter_cell_v_carry_in(c_bit2, s56) | (~m_counter_cell_v_value(c_bit2, s56))) <=> (m_counter_cell_v_carry_in(c_bit2, s56) | (~m_counter_cell_v_value(c_bit2, s56)) | (~node1(c_bit2, s56)))),
% 13.62/13.80 inference(rewrite,[status(thm)],[])).
% 13.62/13.80 tff(6994,plain,
% 13.62/13.80 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s56)) | m_counter_cell_v_carry_in(c_bit2, s56) | (~m_counter_cell_v_value(c_bit2, s56)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s56) | (~m_counter_cell_v_value(c_bit2, s56)) | (~node1(c_bit2, s56))))),
% 13.62/13.80 inference(monotonicity,[status(thm)],[6993])).
% 13.62/13.80 tff(6995,plain,
% 13.62/13.80 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s56)) | m_counter_cell_v_carry_in(c_bit2, s56) | (~m_counter_cell_v_value(c_bit2, s56)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s56) | (~m_counter_cell_v_value(c_bit2, s56)) | (~node1(c_bit2, s56)))),
% 13.62/13.80 inference(transitivity,[status(thm)],[6994, 6992])).
% 13.62/13.80 tff(6996,plain,
% 13.62/13.80 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s56)) | m_counter_cell_v_carry_in(c_bit2, s56) | (~m_counter_cell_v_value(c_bit2, s56)))),
% 13.62/13.80 inference(quant_inst,[status(thm)],[])).
% 13.62/13.80 tff(6997,plain,
% 13.62/13.80 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s56) | (~m_counter_cell_v_value(c_bit2, s56)) | (~node1(c_bit2, s56))),
% 13.62/13.80 inference(modus_ponens,[status(thm)],[6996, 6995])).
% 13.62/13.80 tff(6998,plain,
% 13.62/13.80 (m_counter_cell_v_carry_in(c_bit2, s56) | (~node1(c_bit2, s56))),
% 13.62/13.80 inference(unit_resolution,[status(thm)],[6997, 1569, 6991])).
% 13.62/13.80 tff(6999,plain,
% 13.62/13.80 (m_counter_cell_v_carry_in(c_bit2, s56)),
% 13.62/13.80 inference(unit_resolution,[status(thm)],[6998, 6990])).
% 13.62/13.80 tff(7000,plain,
% 13.62/13.80 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s56)) | m_counter_cell_v_carry_out(c_bit1, s56))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s56)) | m_counter_cell_v_carry_out(c_bit1, s56))),
% 13.62/13.80 inference(rewrite,[status(thm)],[])).
% 13.62/13.80 tff(7001,plain,
% 13.62/13.80 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s56)) | m_counter_cell_v_carry_out(c_bit1, s56))),
% 13.62/13.80 inference(quant_inst,[status(thm)],[])).
% 13.62/13.80 tff(7002,plain,
% 13.62/13.80 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s56)) | m_counter_cell_v_carry_out(c_bit1, s56)),
% 13.62/13.80 inference(modus_ponens,[status(thm)],[7001, 7000])).
% 13.62/13.80 tff(7003,plain,
% 13.62/13.80 ($false),
% 13.62/13.80 inference(unit_resolution,[status(thm)],[7002, 3675, 6999, 3597])).
% 13.62/13.80 tff(7004,plain,(m_counter_cell_v_value(c_bit1, s56) | (~m_counter_cell_v_value(c_bit2, s56))), inference(lemma,lemma(discharge,[]))).
% 13.62/13.80 tff(7005,plain,
% 13.62/13.80 (~m_counter_cell_v_value(c_bit2, s56)),
% 13.62/13.80 inference(unit_resolution,[status(thm)],[7004, 3588])).
% 13.62/13.81 tff(7006,plain,
% 13.62/13.81 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s55, s56)) | node3(c_bit2, s55, s56))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s55, s56)) | node3(c_bit2, s55, s56))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7007,plain,
% 13.62/13.81 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s55, s56)) | node3(c_bit2, s55, s56))),
% 13.62/13.81 inference(quant_inst,[status(thm)],[])).
% 13.62/13.81 tff(7008,plain,
% 13.62/13.81 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s55, s56)) | node3(c_bit2, s55, s56)),
% 13.62/13.81 inference(modus_ponens,[status(thm)],[7007, 7006])).
% 13.62/13.81 tff(7009,plain,
% 13.62/13.81 (node3(c_bit2, s55, s56)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7008, 59, 3576])).
% 13.62/13.81 tff(7010,plain,
% 13.62/13.81 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s56) | node1(c_bit2, s55) | (~node3(c_bit2, s55, s56)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s56) | node1(c_bit2, s55) | (~node3(c_bit2, s55, s56)))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7011,plain,
% 13.62/13.81 ((node1(c_bit2, s55) | (~node3(c_bit2, s55, s56)) | m_counter_cell_v_value(c_bit2, s56)) <=> (m_counter_cell_v_value(c_bit2, s56) | node1(c_bit2, s55) | (~node3(c_bit2, s55, s56)))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7012,plain,
% 13.62/13.81 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s55) | (~node3(c_bit2, s55, s56)) | m_counter_cell_v_value(c_bit2, s56))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s56) | node1(c_bit2, s55) | (~node3(c_bit2, s55, s56))))),
% 13.62/13.81 inference(monotonicity,[status(thm)],[7011])).
% 13.62/13.81 tff(7013,plain,
% 13.62/13.81 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s55) | (~node3(c_bit2, s55, s56)) | m_counter_cell_v_value(c_bit2, s56))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s56) | node1(c_bit2, s55) | (~node3(c_bit2, s55, s56)))),
% 13.62/13.81 inference(transitivity,[status(thm)],[7012, 7010])).
% 13.62/13.81 tff(7014,plain,
% 13.62/13.81 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s55) | (~node3(c_bit2, s55, s56)) | m_counter_cell_v_value(c_bit2, s56))),
% 13.62/13.81 inference(quant_inst,[status(thm)],[])).
% 13.62/13.81 tff(7015,plain,
% 13.62/13.81 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s56) | node1(c_bit2, s55) | (~node3(c_bit2, s55, s56))),
% 13.62/13.81 inference(modus_ponens,[status(thm)],[7014, 7013])).
% 13.62/13.81 tff(7016,plain,
% 13.62/13.81 (m_counter_cell_v_value(c_bit2, s56) | node1(c_bit2, s55)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7015, 73, 7009])).
% 13.62/13.81 tff(7017,plain,
% 13.62/13.81 (node1(c_bit2, s55)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7016, 7005])).
% 13.62/13.81 tff(7018,plain,
% 13.62/13.81 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s52) | (~node4(c_bit1, s52)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s52) | (~node4(c_bit1, s52)))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7019,plain,
% 13.62/13.81 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s52) | (~node4(c_bit1, s52)))),
% 13.62/13.81 inference(quant_inst,[status(thm)],[])).
% 13.62/13.81 tff(7020,plain,
% 13.62/13.81 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s52) | (~node4(c_bit1, s52))),
% 13.62/13.81 inference(modus_ponens,[status(thm)],[7019, 7018])).
% 13.62/13.81 tff(7021,plain,
% 13.62/13.81 (~node4(c_bit1, s52)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7020, 1344, 3337])).
% 13.62/13.81 tff(7022,plain,
% 13.62/13.81 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s52)) | node4(c_bit1, s52))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s52)) | node4(c_bit1, s52))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7023,plain,
% 13.62/13.81 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s52)) | node4(c_bit1, s52))),
% 13.62/13.81 inference(quant_inst,[status(thm)],[])).
% 13.62/13.81 tff(7024,plain,
% 13.62/13.81 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s52)) | node4(c_bit1, s52)),
% 13.62/13.81 inference(modus_ponens,[status(thm)],[7023, 7022])).
% 13.62/13.81 tff(7025,plain,
% 13.62/13.81 (~m_counter_cell_v_carry_out(c_bit1, s52)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7024, 1359, 7021])).
% 13.62/13.81 tff(7026,plain,
% 13.62/13.81 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s52)) | m_counter_cell_v_carry_out(c_bit1, s52))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s52)) | m_counter_cell_v_carry_out(c_bit1, s52))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7027,plain,
% 13.62/13.81 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s52)) | m_counter_cell_v_carry_out(c_bit1, s52))),
% 13.62/13.81 inference(quant_inst,[status(thm)],[])).
% 13.62/13.81 tff(7028,plain,
% 13.62/13.81 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s52)) | m_counter_cell_v_carry_out(c_bit1, s52)),
% 13.62/13.81 inference(modus_ponens,[status(thm)],[7027, 7026])).
% 13.62/13.81 tff(7029,plain,
% 13.62/13.81 (~m_counter_cell_v_carry_in(c_bit2, s52)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7028, 3675, 7025])).
% 13.62/13.81 tff(7030,assumption,(m_counter_cell_v_carry_in(c_bit2, s51)), introduced(assumption)).
% 13.62/13.81 tff(7031,assumption,(always5(s51)), introduced(assumption)).
% 13.62/13.81 tff(7032,plain,
% 13.62/13.81 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s51)) | (~m_counter_cell_v_carry_out(c_bit2, s51)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s51)) | (~m_counter_cell_v_carry_out(c_bit2, s51)))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7033,plain,
% 13.62/13.81 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s51)) | (~m_counter_cell_v_carry_out(c_bit2, s51)))),
% 13.62/13.81 inference(quant_inst,[status(thm)],[])).
% 13.62/13.81 tff(7034,plain,
% 13.62/13.81 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s51)) | (~m_counter_cell_v_carry_out(c_bit2, s51))),
% 13.62/13.81 inference(modus_ponens,[status(thm)],[7033, 7032])).
% 13.62/13.81 tff(7035,plain,
% 13.62/13.81 (~m_counter_cell_v_carry_out(c_bit2, s51)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7034, 6925, 7031])).
% 13.62/13.81 tff(7036,plain,
% 13.62/13.81 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s51)) | (~m_counter_cell_v_value(c_bit2, s51)) | m_counter_cell_v_carry_out(c_bit2, s51))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s51)) | (~m_counter_cell_v_value(c_bit2, s51)) | m_counter_cell_v_carry_out(c_bit2, s51))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7037,plain,
% 13.62/13.81 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s51)) | (~m_counter_cell_v_value(c_bit2, s51)) | m_counter_cell_v_carry_out(c_bit2, s51))),
% 13.62/13.81 inference(quant_inst,[status(thm)],[])).
% 13.62/13.81 tff(7038,plain,
% 13.62/13.81 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s51)) | (~m_counter_cell_v_value(c_bit2, s51)) | m_counter_cell_v_carry_out(c_bit2, s51)),
% 13.62/13.81 inference(modus_ponens,[status(thm)],[7037, 7036])).
% 13.62/13.81 tff(7039,plain,
% 13.62/13.81 (~m_counter_cell_v_value(c_bit2, s51)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7038, 1390, 7030, 7035])).
% 13.62/13.81 tff(7040,plain,
% 13.62/13.81 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s51)) | m_counter_cell_v_value(c_bit2, s51) | (~node1(c_bit2, s51)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s51)) | m_counter_cell_v_value(c_bit2, s51) | (~node1(c_bit2, s51)))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7041,plain,
% 13.62/13.81 (((~node1(c_bit2, s51)) | (~m_counter_cell_v_carry_in(c_bit2, s51)) | m_counter_cell_v_value(c_bit2, s51)) <=> ((~m_counter_cell_v_carry_in(c_bit2, s51)) | m_counter_cell_v_value(c_bit2, s51) | (~node1(c_bit2, s51)))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7042,plain,
% 13.62/13.81 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s51)) | (~m_counter_cell_v_carry_in(c_bit2, s51)) | m_counter_cell_v_value(c_bit2, s51))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s51)) | m_counter_cell_v_value(c_bit2, s51) | (~node1(c_bit2, s51))))),
% 13.62/13.81 inference(monotonicity,[status(thm)],[7041])).
% 13.62/13.81 tff(7043,plain,
% 13.62/13.81 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s51)) | (~m_counter_cell_v_carry_in(c_bit2, s51)) | m_counter_cell_v_value(c_bit2, s51))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s51)) | m_counter_cell_v_value(c_bit2, s51) | (~node1(c_bit2, s51)))),
% 13.62/13.81 inference(transitivity,[status(thm)],[7042, 7040])).
% 13.62/13.81 tff(7044,plain,
% 13.62/13.81 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s51)) | (~m_counter_cell_v_carry_in(c_bit2, s51)) | m_counter_cell_v_value(c_bit2, s51))),
% 13.62/13.81 inference(quant_inst,[status(thm)],[])).
% 13.62/13.81 tff(7045,plain,
% 13.62/13.81 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s51)) | m_counter_cell_v_value(c_bit2, s51) | (~node1(c_bit2, s51))),
% 13.62/13.81 inference(modus_ponens,[status(thm)],[7044, 7043])).
% 13.62/13.81 tff(7046,plain,
% 13.62/13.81 (~node1(c_bit2, s51)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7045, 30, 7039, 7030])).
% 13.62/13.81 tff(7047,plain,
% 13.62/13.81 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s51, s52)) | node3(c_bit2, s51, s52))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s51, s52)) | node3(c_bit2, s51, s52))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7048,plain,
% 13.62/13.81 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s51, s52)) | node3(c_bit2, s51, s52))),
% 13.62/13.81 inference(quant_inst,[status(thm)],[])).
% 13.62/13.81 tff(7049,plain,
% 13.62/13.81 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s51, s52)) | node3(c_bit2, s51, s52)),
% 13.62/13.81 inference(modus_ponens,[status(thm)],[7048, 7047])).
% 13.62/13.81 tff(7050,plain,
% 13.62/13.81 (node3(c_bit2, s51, s52)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7049, 59, 3325])).
% 13.62/13.81 tff(7051,plain,
% 13.62/13.81 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s52) | node1(c_bit2, s51) | (~node3(c_bit2, s51, s52)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s52) | node1(c_bit2, s51) | (~node3(c_bit2, s51, s52)))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7052,plain,
% 13.62/13.81 ((node1(c_bit2, s51) | (~node3(c_bit2, s51, s52)) | m_counter_cell_v_value(c_bit2, s52)) <=> (m_counter_cell_v_value(c_bit2, s52) | node1(c_bit2, s51) | (~node3(c_bit2, s51, s52)))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7053,plain,
% 13.62/13.81 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s51) | (~node3(c_bit2, s51, s52)) | m_counter_cell_v_value(c_bit2, s52))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s52) | node1(c_bit2, s51) | (~node3(c_bit2, s51, s52))))),
% 13.62/13.81 inference(monotonicity,[status(thm)],[7052])).
% 13.62/13.81 tff(7054,plain,
% 13.62/13.81 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s51) | (~node3(c_bit2, s51, s52)) | m_counter_cell_v_value(c_bit2, s52))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s52) | node1(c_bit2, s51) | (~node3(c_bit2, s51, s52)))),
% 13.62/13.81 inference(transitivity,[status(thm)],[7053, 7051])).
% 13.62/13.81 tff(7055,plain,
% 13.62/13.81 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s51) | (~node3(c_bit2, s51, s52)) | m_counter_cell_v_value(c_bit2, s52))),
% 13.62/13.81 inference(quant_inst,[status(thm)],[])).
% 13.62/13.81 tff(7056,plain,
% 13.62/13.81 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s52) | node1(c_bit2, s51) | (~node3(c_bit2, s51, s52))),
% 13.62/13.81 inference(modus_ponens,[status(thm)],[7055, 7054])).
% 13.62/13.81 tff(7057,plain,
% 13.62/13.81 (m_counter_cell_v_value(c_bit2, s52) | node1(c_bit2, s51)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7056, 73, 7050])).
% 13.62/13.81 tff(7058,plain,
% 13.62/13.81 (m_counter_cell_v_value(c_bit2, s52)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7057, 7046])).
% 13.62/13.81 tff(7059,assumption,(~m_counter_cell_v_carry_in(c_bit2, s52)), introduced(assumption)).
% 13.62/13.81 tff(7060,plain,
% 13.62/13.81 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s52) | (~m_counter_cell_v_value(c_bit2, s52)) | (~node1(c_bit2, s52)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s52) | (~m_counter_cell_v_value(c_bit2, s52)) | (~node1(c_bit2, s52)))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7061,plain,
% 13.62/13.81 (((~node1(c_bit2, s52)) | m_counter_cell_v_carry_in(c_bit2, s52) | (~m_counter_cell_v_value(c_bit2, s52))) <=> (m_counter_cell_v_carry_in(c_bit2, s52) | (~m_counter_cell_v_value(c_bit2, s52)) | (~node1(c_bit2, s52)))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7062,plain,
% 13.62/13.81 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s52)) | m_counter_cell_v_carry_in(c_bit2, s52) | (~m_counter_cell_v_value(c_bit2, s52)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s52) | (~m_counter_cell_v_value(c_bit2, s52)) | (~node1(c_bit2, s52))))),
% 13.62/13.81 inference(monotonicity,[status(thm)],[7061])).
% 13.62/13.81 tff(7063,plain,
% 13.62/13.81 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s52)) | m_counter_cell_v_carry_in(c_bit2, s52) | (~m_counter_cell_v_value(c_bit2, s52)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s52) | (~m_counter_cell_v_value(c_bit2, s52)) | (~node1(c_bit2, s52)))),
% 13.62/13.81 inference(transitivity,[status(thm)],[7062, 7060])).
% 13.62/13.81 tff(7064,plain,
% 13.62/13.81 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s52)) | m_counter_cell_v_carry_in(c_bit2, s52) | (~m_counter_cell_v_value(c_bit2, s52)))),
% 13.62/13.81 inference(quant_inst,[status(thm)],[])).
% 13.62/13.81 tff(7065,plain,
% 13.62/13.81 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s52) | (~m_counter_cell_v_value(c_bit2, s52)) | (~node1(c_bit2, s52))),
% 13.62/13.81 inference(modus_ponens,[status(thm)],[7064, 7063])).
% 13.62/13.81 tff(7066,plain,
% 13.62/13.81 ((~m_counter_cell_v_value(c_bit2, s52)) | (~node1(c_bit2, s52))),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7065, 1569, 7059])).
% 13.62/13.81 tff(7067,plain,
% 13.62/13.81 (~node1(c_bit2, s52)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7066, 7058])).
% 13.62/13.81 tff(7068,plain,
% 13.62/13.81 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s52, s53)) | node3(c_bit2, s52, s53))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s52, s53)) | node3(c_bit2, s52, s53))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7069,plain,
% 13.62/13.81 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s52, s53)) | node3(c_bit2, s52, s53))),
% 13.62/13.81 inference(quant_inst,[status(thm)],[])).
% 13.62/13.81 tff(7070,plain,
% 13.62/13.81 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s52, s53)) | node3(c_bit2, s52, s53)),
% 13.62/13.81 inference(modus_ponens,[status(thm)],[7069, 7068])).
% 13.62/13.81 tff(7071,plain,
% 13.62/13.81 (node3(c_bit2, s52, s53)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7070, 59, 3383])).
% 13.62/13.81 tff(7072,plain,
% 13.62/13.81 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s53) | node1(c_bit2, s52) | (~node3(c_bit2, s52, s53)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s53) | node1(c_bit2, s52) | (~node3(c_bit2, s52, s53)))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7073,plain,
% 13.62/13.81 ((node1(c_bit2, s52) | (~node3(c_bit2, s52, s53)) | m_counter_cell_v_value(c_bit2, s53)) <=> (m_counter_cell_v_value(c_bit2, s53) | node1(c_bit2, s52) | (~node3(c_bit2, s52, s53)))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7074,plain,
% 13.62/13.81 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s52) | (~node3(c_bit2, s52, s53)) | m_counter_cell_v_value(c_bit2, s53))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s53) | node1(c_bit2, s52) | (~node3(c_bit2, s52, s53))))),
% 13.62/13.81 inference(monotonicity,[status(thm)],[7073])).
% 13.62/13.81 tff(7075,plain,
% 13.62/13.81 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s52) | (~node3(c_bit2, s52, s53)) | m_counter_cell_v_value(c_bit2, s53))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s53) | node1(c_bit2, s52) | (~node3(c_bit2, s52, s53)))),
% 13.62/13.81 inference(transitivity,[status(thm)],[7074, 7072])).
% 13.62/13.81 tff(7076,plain,
% 13.62/13.81 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s52) | (~node3(c_bit2, s52, s53)) | m_counter_cell_v_value(c_bit2, s53))),
% 13.62/13.81 inference(quant_inst,[status(thm)],[])).
% 13.62/13.81 tff(7077,plain,
% 13.62/13.81 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s53) | node1(c_bit2, s52) | (~node3(c_bit2, s52, s53))),
% 13.62/13.81 inference(modus_ponens,[status(thm)],[7076, 7075])).
% 13.62/13.81 tff(7078,plain,
% 13.62/13.81 (m_counter_cell_v_value(c_bit2, s53) | node1(c_bit2, s52)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7077, 73, 7071])).
% 13.62/13.81 tff(7079,plain,
% 13.62/13.81 (m_counter_cell_v_value(c_bit2, s53)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7078, 7067])).
% 13.62/13.81 tff(7080,plain,
% 13.62/13.81 (always5(s52)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[3953, 7031])).
% 13.62/13.81 tff(7081,plain,
% 13.62/13.81 (always5(s53)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[3945, 7080])).
% 13.62/13.81 tff(7082,plain,
% 13.62/13.81 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s53)) | (~m_counter_cell_v_carry_out(c_bit2, s53)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s53)) | (~m_counter_cell_v_carry_out(c_bit2, s53)))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7083,plain,
% 13.62/13.81 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s53)) | (~m_counter_cell_v_carry_out(c_bit2, s53)))),
% 13.62/13.81 inference(quant_inst,[status(thm)],[])).
% 13.62/13.81 tff(7084,plain,
% 13.62/13.81 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s53)) | (~m_counter_cell_v_carry_out(c_bit2, s53))),
% 13.62/13.81 inference(modus_ponens,[status(thm)],[7083, 7082])).
% 13.62/13.81 tff(7085,plain,
% 13.62/13.81 (~m_counter_cell_v_carry_out(c_bit2, s53)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7084, 6925, 7081])).
% 13.62/13.81 tff(7086,plain,
% 13.62/13.81 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s53)) | (~m_counter_cell_v_value(c_bit2, s53)) | m_counter_cell_v_carry_out(c_bit2, s53))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s53)) | (~m_counter_cell_v_value(c_bit2, s53)) | m_counter_cell_v_carry_out(c_bit2, s53))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7087,plain,
% 13.62/13.81 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s53)) | (~m_counter_cell_v_value(c_bit2, s53)) | m_counter_cell_v_carry_out(c_bit2, s53))),
% 13.62/13.81 inference(quant_inst,[status(thm)],[])).
% 13.62/13.81 tff(7088,plain,
% 13.62/13.81 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s53)) | (~m_counter_cell_v_value(c_bit2, s53)) | m_counter_cell_v_carry_out(c_bit2, s53)),
% 13.62/13.81 inference(modus_ponens,[status(thm)],[7087, 7086])).
% 13.62/13.81 tff(7089,plain,
% 13.62/13.81 ((~m_counter_cell_v_carry_in(c_bit2, s53)) | (~m_counter_cell_v_value(c_bit2, s53))),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7088, 1390, 7085])).
% 13.62/13.81 tff(7090,plain,
% 13.62/13.81 (~m_counter_cell_v_carry_in(c_bit2, s53)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7089, 7079])).
% 13.62/13.81 tff(7091,assumption,(node1(c_bit2, s55)), introduced(assumption)).
% 13.62/13.81 tff(7092,plain,
% 13.62/13.81 (always5(s54)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[3937, 7081])).
% 13.62/13.81 tff(7093,plain,
% 13.62/13.81 (always5(s55)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[3929, 7092])).
% 13.62/13.81 tff(7094,plain,
% 13.62/13.81 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s55)) | (~m_counter_cell_v_carry_out(c_bit2, s55)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s55)) | (~m_counter_cell_v_carry_out(c_bit2, s55)))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7095,plain,
% 13.62/13.81 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s55)) | (~m_counter_cell_v_carry_out(c_bit2, s55)))),
% 13.62/13.81 inference(quant_inst,[status(thm)],[])).
% 13.62/13.81 tff(7096,plain,
% 13.62/13.81 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s55)) | (~m_counter_cell_v_carry_out(c_bit2, s55))),
% 13.62/13.81 inference(modus_ponens,[status(thm)],[7095, 7094])).
% 13.62/13.81 tff(7097,plain,
% 13.62/13.81 (~m_counter_cell_v_carry_out(c_bit2, s55)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7096, 6925, 7093])).
% 13.62/13.81 tff(7098,assumption,(m_counter_cell_v_carry_in(c_bit2, s55)), introduced(assumption)).
% 13.62/13.81 tff(7099,assumption,(~m_counter_cell_v_carry_out(c_bit2, s55)), introduced(assumption)).
% 13.62/13.81 tff(7100,plain,
% 13.62/13.81 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s55)) | (~m_counter_cell_v_value(c_bit2, s55)) | m_counter_cell_v_carry_out(c_bit2, s55))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s55)) | (~m_counter_cell_v_value(c_bit2, s55)) | m_counter_cell_v_carry_out(c_bit2, s55))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7101,plain,
% 13.62/13.81 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s55)) | (~m_counter_cell_v_value(c_bit2, s55)) | m_counter_cell_v_carry_out(c_bit2, s55))),
% 13.62/13.81 inference(quant_inst,[status(thm)],[])).
% 13.62/13.81 tff(7102,plain,
% 13.62/13.81 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s55)) | (~m_counter_cell_v_value(c_bit2, s55)) | m_counter_cell_v_carry_out(c_bit2, s55)),
% 13.62/13.81 inference(modus_ponens,[status(thm)],[7101, 7100])).
% 13.62/13.81 tff(7103,plain,
% 13.62/13.81 ((~m_counter_cell_v_carry_in(c_bit2, s55)) | (~m_counter_cell_v_value(c_bit2, s55))),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7102, 1390, 7099])).
% 13.62/13.81 tff(7104,plain,
% 13.62/13.81 (~m_counter_cell_v_value(c_bit2, s55)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7103, 7098])).
% 13.62/13.81 tff(7105,plain,
% 13.62/13.81 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s55)) | m_counter_cell_v_value(c_bit2, s55) | (~node1(c_bit2, s55)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s55)) | m_counter_cell_v_value(c_bit2, s55) | (~node1(c_bit2, s55)))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7106,plain,
% 13.62/13.81 (((~node1(c_bit2, s55)) | (~m_counter_cell_v_carry_in(c_bit2, s55)) | m_counter_cell_v_value(c_bit2, s55)) <=> ((~m_counter_cell_v_carry_in(c_bit2, s55)) | m_counter_cell_v_value(c_bit2, s55) | (~node1(c_bit2, s55)))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7107,plain,
% 13.62/13.81 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s55)) | (~m_counter_cell_v_carry_in(c_bit2, s55)) | m_counter_cell_v_value(c_bit2, s55))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s55)) | m_counter_cell_v_value(c_bit2, s55) | (~node1(c_bit2, s55))))),
% 13.62/13.81 inference(monotonicity,[status(thm)],[7106])).
% 13.62/13.81 tff(7108,plain,
% 13.62/13.81 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s55)) | (~m_counter_cell_v_carry_in(c_bit2, s55)) | m_counter_cell_v_value(c_bit2, s55))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s55)) | m_counter_cell_v_value(c_bit2, s55) | (~node1(c_bit2, s55)))),
% 13.62/13.81 inference(transitivity,[status(thm)],[7107, 7105])).
% 13.62/13.81 tff(7109,plain,
% 13.62/13.81 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s55)) | (~m_counter_cell_v_carry_in(c_bit2, s55)) | m_counter_cell_v_value(c_bit2, s55))),
% 13.62/13.81 inference(quant_inst,[status(thm)],[])).
% 13.62/13.81 tff(7110,plain,
% 13.62/13.81 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s55)) | m_counter_cell_v_value(c_bit2, s55) | (~node1(c_bit2, s55))),
% 13.62/13.81 inference(modus_ponens,[status(thm)],[7109, 7108])).
% 13.62/13.81 tff(7111,plain,
% 13.62/13.81 ((~m_counter_cell_v_carry_in(c_bit2, s55)) | m_counter_cell_v_value(c_bit2, s55)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7110, 30, 7091])).
% 13.62/13.81 tff(7112,plain,
% 13.62/13.81 ($false),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7111, 7104, 7098])).
% 13.62/13.81 tff(7113,plain,((~m_counter_cell_v_carry_in(c_bit2, s55)) | (~node1(c_bit2, s55)) | m_counter_cell_v_carry_out(c_bit2, s55)), inference(lemma,lemma(discharge,[]))).
% 13.62/13.81 tff(7114,plain,
% 13.62/13.81 (~m_counter_cell_v_carry_in(c_bit2, s55)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7113, 7097, 7091])).
% 13.62/13.81 tff(7115,plain,
% 13.62/13.81 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s55) | (~m_counter_cell_v_value(c_bit2, s55)) | (~node1(c_bit2, s55)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s55) | (~m_counter_cell_v_value(c_bit2, s55)) | (~node1(c_bit2, s55)))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7116,plain,
% 13.62/13.81 (((~node1(c_bit2, s55)) | m_counter_cell_v_carry_in(c_bit2, s55) | (~m_counter_cell_v_value(c_bit2, s55))) <=> (m_counter_cell_v_carry_in(c_bit2, s55) | (~m_counter_cell_v_value(c_bit2, s55)) | (~node1(c_bit2, s55)))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7117,plain,
% 13.62/13.81 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s55)) | m_counter_cell_v_carry_in(c_bit2, s55) | (~m_counter_cell_v_value(c_bit2, s55)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s55) | (~m_counter_cell_v_value(c_bit2, s55)) | (~node1(c_bit2, s55))))),
% 13.62/13.81 inference(monotonicity,[status(thm)],[7116])).
% 13.62/13.81 tff(7118,plain,
% 13.62/13.81 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s55)) | m_counter_cell_v_carry_in(c_bit2, s55) | (~m_counter_cell_v_value(c_bit2, s55)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s55) | (~m_counter_cell_v_value(c_bit2, s55)) | (~node1(c_bit2, s55)))),
% 13.62/13.81 inference(transitivity,[status(thm)],[7117, 7115])).
% 13.62/13.81 tff(7119,plain,
% 13.62/13.81 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s55)) | m_counter_cell_v_carry_in(c_bit2, s55) | (~m_counter_cell_v_value(c_bit2, s55)))),
% 13.62/13.81 inference(quant_inst,[status(thm)],[])).
% 13.62/13.81 tff(7120,plain,
% 13.62/13.81 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s55) | (~m_counter_cell_v_value(c_bit2, s55)) | (~node1(c_bit2, s55))),
% 13.62/13.81 inference(modus_ponens,[status(thm)],[7119, 7118])).
% 13.62/13.81 tff(7121,plain,
% 13.62/13.81 (m_counter_cell_v_carry_in(c_bit2, s55) | (~m_counter_cell_v_value(c_bit2, s55))),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7120, 1569, 7091])).
% 13.62/13.81 tff(7122,plain,
% 13.62/13.81 (~m_counter_cell_v_value(c_bit2, s55)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7121, 7114])).
% 13.62/13.81 tff(7123,plain,
% 13.62/13.81 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s54, s55)) | node3(c_bit2, s54, s55))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s54, s55)) | node3(c_bit2, s54, s55))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7124,plain,
% 13.62/13.81 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s54, s55)) | node3(c_bit2, s54, s55))),
% 13.62/13.81 inference(quant_inst,[status(thm)],[])).
% 13.62/13.81 tff(7125,plain,
% 13.62/13.81 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s54, s55)) | node3(c_bit2, s54, s55)),
% 13.62/13.81 inference(modus_ponens,[status(thm)],[7124, 7123])).
% 13.62/13.81 tff(7126,plain,
% 13.62/13.81 (node3(c_bit2, s54, s55)),
% 13.62/13.81 inference(unit_resolution,[status(thm)],[7125, 59, 3512])).
% 13.62/13.81 tff(7127,plain,
% 13.62/13.81 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s55) | node1(c_bit2, s54) | (~node3(c_bit2, s54, s55)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s55) | node1(c_bit2, s54) | (~node3(c_bit2, s54, s55)))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.81 tff(7128,plain,
% 13.62/13.81 ((node1(c_bit2, s54) | (~node3(c_bit2, s54, s55)) | m_counter_cell_v_value(c_bit2, s55)) <=> (m_counter_cell_v_value(c_bit2, s55) | node1(c_bit2, s54) | (~node3(c_bit2, s54, s55)))),
% 13.62/13.81 inference(rewrite,[status(thm)],[])).
% 13.62/13.82 tff(7129,plain,
% 13.62/13.82 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s54) | (~node3(c_bit2, s54, s55)) | m_counter_cell_v_value(c_bit2, s55))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s55) | node1(c_bit2, s54) | (~node3(c_bit2, s54, s55))))),
% 13.62/13.82 inference(monotonicity,[status(thm)],[7128])).
% 13.62/13.82 tff(7130,plain,
% 13.62/13.82 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s54) | (~node3(c_bit2, s54, s55)) | m_counter_cell_v_value(c_bit2, s55))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s55) | node1(c_bit2, s54) | (~node3(c_bit2, s54, s55)))),
% 13.62/13.82 inference(transitivity,[status(thm)],[7129, 7127])).
% 13.62/13.82 tff(7131,plain,
% 13.62/13.82 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s54) | (~node3(c_bit2, s54, s55)) | m_counter_cell_v_value(c_bit2, s55))),
% 13.62/13.82 inference(quant_inst,[status(thm)],[])).
% 13.62/13.82 tff(7132,plain,
% 13.62/13.82 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s55) | node1(c_bit2, s54) | (~node3(c_bit2, s54, s55))),
% 13.62/13.82 inference(modus_ponens,[status(thm)],[7131, 7130])).
% 13.62/13.82 tff(7133,plain,
% 13.62/13.82 (m_counter_cell_v_value(c_bit2, s55) | node1(c_bit2, s54)),
% 13.62/13.82 inference(unit_resolution,[status(thm)],[7132, 73, 7126])).
% 13.62/13.82 tff(7134,plain,
% 13.62/13.82 (node1(c_bit2, s54)),
% 13.62/13.82 inference(unit_resolution,[status(thm)],[7133, 7122])).
% 13.62/13.82 tff(7135,plain,
% 13.62/13.82 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s54) | (~node4(c_bit1, s54)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s54) | (~node4(c_bit1, s54)))),
% 13.62/13.82 inference(rewrite,[status(thm)],[])).
% 13.62/13.82 tff(7136,plain,
% 13.62/13.82 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s54) | (~node4(c_bit1, s54)))),
% 13.62/13.82 inference(quant_inst,[status(thm)],[])).
% 13.62/13.82 tff(7137,plain,
% 13.62/13.82 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s54) | (~node4(c_bit1, s54))),
% 13.62/13.82 inference(modus_ponens,[status(thm)],[7136, 7135])).
% 13.62/13.82 tff(7138,plain,
% 13.62/13.82 (~node4(c_bit1, s54)),
% 13.62/13.82 inference(unit_resolution,[status(thm)],[7137, 2941, 3497])).
% 13.62/13.82 tff(7139,plain,
% 13.62/13.82 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s54)) | node4(c_bit1, s54))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s54)) | node4(c_bit1, s54))),
% 13.62/13.82 inference(rewrite,[status(thm)],[])).
% 13.62/13.82 tff(7140,plain,
% 13.62/13.82 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s54)) | node4(c_bit1, s54))),
% 13.62/13.82 inference(quant_inst,[status(thm)],[])).
% 13.62/13.82 tff(7141,plain,
% 13.62/13.82 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s54)) | node4(c_bit1, s54)),
% 13.62/13.82 inference(modus_ponens,[status(thm)],[7140, 7139])).
% 13.62/13.82 tff(7142,plain,
% 13.62/13.82 (~m_counter_cell_v_carry_out(c_bit1, s54)),
% 13.62/13.82 inference(unit_resolution,[status(thm)],[7141, 1359, 7138])).
% 13.62/13.82 tff(7143,plain,
% 13.62/13.82 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s54)) | m_counter_cell_v_carry_out(c_bit1, s54))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s54)) | m_counter_cell_v_carry_out(c_bit1, s54))),
% 13.62/13.82 inference(rewrite,[status(thm)],[])).
% 13.62/13.82 tff(7144,plain,
% 13.62/13.82 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s54)) | m_counter_cell_v_carry_out(c_bit1, s54))),
% 13.62/13.82 inference(quant_inst,[status(thm)],[])).
% 13.62/13.82 tff(7145,plain,
% 13.62/13.82 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s54)) | m_counter_cell_v_carry_out(c_bit1, s54)),
% 13.62/13.82 inference(modus_ponens,[status(thm)],[7144, 7143])).
% 13.62/13.82 tff(7146,plain,
% 13.62/13.82 (~m_counter_cell_v_carry_in(c_bit2, s54)),
% 13.62/13.82 inference(unit_resolution,[status(thm)],[7145, 3675, 7142])).
% 13.62/13.82 tff(7147,plain,
% 13.62/13.82 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s54) | (~m_counter_cell_v_value(c_bit2, s54)) | (~node1(c_bit2, s54)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s54) | (~m_counter_cell_v_value(c_bit2, s54)) | (~node1(c_bit2, s54)))),
% 13.62/13.82 inference(rewrite,[status(thm)],[])).
% 13.62/13.82 tff(7148,plain,
% 13.62/13.82 (((~node1(c_bit2, s54)) | m_counter_cell_v_carry_in(c_bit2, s54) | (~m_counter_cell_v_value(c_bit2, s54))) <=> (m_counter_cell_v_carry_in(c_bit2, s54) | (~m_counter_cell_v_value(c_bit2, s54)) | (~node1(c_bit2, s54)))),
% 13.62/13.82 inference(rewrite,[status(thm)],[])).
% 13.62/13.82 tff(7149,plain,
% 13.62/13.82 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s54)) | m_counter_cell_v_carry_in(c_bit2, s54) | (~m_counter_cell_v_value(c_bit2, s54)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s54) | (~m_counter_cell_v_value(c_bit2, s54)) | (~node1(c_bit2, s54))))),
% 13.62/13.82 inference(monotonicity,[status(thm)],[7148])).
% 13.62/13.82 tff(7150,plain,
% 13.62/13.82 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s54)) | m_counter_cell_v_carry_in(c_bit2, s54) | (~m_counter_cell_v_value(c_bit2, s54)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s54) | (~m_counter_cell_v_value(c_bit2, s54)) | (~node1(c_bit2, s54)))),
% 13.62/13.82 inference(transitivity,[status(thm)],[7149, 7147])).
% 13.62/13.82 tff(7151,plain,
% 13.62/13.82 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s54)) | m_counter_cell_v_carry_in(c_bit2, s54) | (~m_counter_cell_v_value(c_bit2, s54)))),
% 13.62/13.82 inference(quant_inst,[status(thm)],[])).
% 13.62/13.82 tff(7152,plain,
% 13.62/13.82 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s54) | (~m_counter_cell_v_value(c_bit2, s54)) | (~node1(c_bit2, s54))),
% 13.62/13.82 inference(modus_ponens,[status(thm)],[7151, 7150])).
% 13.62/13.82 tff(7153,plain,
% 13.62/13.82 ((~m_counter_cell_v_value(c_bit2, s54)) | (~node1(c_bit2, s54))),
% 13.62/13.82 inference(unit_resolution,[status(thm)],[7152, 1569, 7146])).
% 13.62/13.82 tff(7154,plain,
% 13.62/13.82 (~m_counter_cell_v_value(c_bit2, s54)),
% 13.62/13.82 inference(unit_resolution,[status(thm)],[7153, 7134])).
% 13.62/13.82 tff(7155,plain,
% 13.62/13.82 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s53, s54)) | node3(c_bit2, s53, s54))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s53, s54)) | node3(c_bit2, s53, s54))),
% 13.62/13.82 inference(rewrite,[status(thm)],[])).
% 13.62/13.82 tff(7156,plain,
% 13.62/13.82 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s53, s54)) | node3(c_bit2, s53, s54))),
% 13.62/13.82 inference(quant_inst,[status(thm)],[])).
% 13.62/13.82 tff(7157,plain,
% 13.62/13.82 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s53, s54)) | node3(c_bit2, s53, s54)),
% 13.62/13.82 inference(modus_ponens,[status(thm)],[7156, 7155])).
% 13.62/13.82 tff(7158,plain,
% 13.62/13.82 (node3(c_bit2, s53, s54)),
% 13.62/13.82 inference(unit_resolution,[status(thm)],[7157, 59, 3450])).
% 13.62/13.82 tff(7159,plain,
% 13.62/13.82 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s54) | node1(c_bit2, s53) | (~node3(c_bit2, s53, s54)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s54) | node1(c_bit2, s53) | (~node3(c_bit2, s53, s54)))),
% 13.67/13.82 inference(rewrite,[status(thm)],[])).
% 13.67/13.82 tff(7160,plain,
% 13.67/13.82 ((node1(c_bit2, s53) | (~node3(c_bit2, s53, s54)) | m_counter_cell_v_value(c_bit2, s54)) <=> (m_counter_cell_v_value(c_bit2, s54) | node1(c_bit2, s53) | (~node3(c_bit2, s53, s54)))),
% 13.67/13.82 inference(rewrite,[status(thm)],[])).
% 13.67/13.82 tff(7161,plain,
% 13.67/13.82 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s53) | (~node3(c_bit2, s53, s54)) | m_counter_cell_v_value(c_bit2, s54))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s54) | node1(c_bit2, s53) | (~node3(c_bit2, s53, s54))))),
% 13.67/13.82 inference(monotonicity,[status(thm)],[7160])).
% 13.67/13.82 tff(7162,plain,
% 13.67/13.82 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s53) | (~node3(c_bit2, s53, s54)) | m_counter_cell_v_value(c_bit2, s54))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s54) | node1(c_bit2, s53) | (~node3(c_bit2, s53, s54)))),
% 13.67/13.82 inference(transitivity,[status(thm)],[7161, 7159])).
% 13.67/13.82 tff(7163,plain,
% 13.67/13.82 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s53) | (~node3(c_bit2, s53, s54)) | m_counter_cell_v_value(c_bit2, s54))),
% 13.67/13.82 inference(quant_inst,[status(thm)],[])).
% 13.67/13.82 tff(7164,plain,
% 13.67/13.82 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s54) | node1(c_bit2, s53) | (~node3(c_bit2, s53, s54))),
% 13.67/13.82 inference(modus_ponens,[status(thm)],[7163, 7162])).
% 13.67/13.82 tff(7165,plain,
% 13.67/13.82 (m_counter_cell_v_value(c_bit2, s54) | node1(c_bit2, s53)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7164, 73, 7158])).
% 13.67/13.82 tff(7166,plain,
% 13.67/13.82 (node1(c_bit2, s53)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7165, 7154])).
% 13.67/13.82 tff(7167,plain,
% 13.67/13.82 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s53) | (~m_counter_cell_v_value(c_bit2, s53)) | (~node1(c_bit2, s53)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s53) | (~m_counter_cell_v_value(c_bit2, s53)) | (~node1(c_bit2, s53)))),
% 13.67/13.82 inference(rewrite,[status(thm)],[])).
% 13.67/13.82 tff(7168,plain,
% 13.67/13.82 (((~node1(c_bit2, s53)) | m_counter_cell_v_carry_in(c_bit2, s53) | (~m_counter_cell_v_value(c_bit2, s53))) <=> (m_counter_cell_v_carry_in(c_bit2, s53) | (~m_counter_cell_v_value(c_bit2, s53)) | (~node1(c_bit2, s53)))),
% 13.67/13.82 inference(rewrite,[status(thm)],[])).
% 13.67/13.82 tff(7169,plain,
% 13.67/13.82 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s53)) | m_counter_cell_v_carry_in(c_bit2, s53) | (~m_counter_cell_v_value(c_bit2, s53)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s53) | (~m_counter_cell_v_value(c_bit2, s53)) | (~node1(c_bit2, s53))))),
% 13.67/13.82 inference(monotonicity,[status(thm)],[7168])).
% 13.67/13.82 tff(7170,plain,
% 13.67/13.82 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s53)) | m_counter_cell_v_carry_in(c_bit2, s53) | (~m_counter_cell_v_value(c_bit2, s53)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s53) | (~m_counter_cell_v_value(c_bit2, s53)) | (~node1(c_bit2, s53)))),
% 13.67/13.82 inference(transitivity,[status(thm)],[7169, 7167])).
% 13.67/13.82 tff(7171,plain,
% 13.67/13.82 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s53)) | m_counter_cell_v_carry_in(c_bit2, s53) | (~m_counter_cell_v_value(c_bit2, s53)))),
% 13.67/13.82 inference(quant_inst,[status(thm)],[])).
% 13.67/13.82 tff(7172,plain,
% 13.67/13.82 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s53) | (~m_counter_cell_v_value(c_bit2, s53)) | (~node1(c_bit2, s53))),
% 13.67/13.82 inference(modus_ponens,[status(thm)],[7171, 7170])).
% 13.67/13.82 tff(7173,plain,
% 13.67/13.82 (m_counter_cell_v_carry_in(c_bit2, s53) | (~m_counter_cell_v_value(c_bit2, s53))),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7172, 1569, 7166])).
% 13.67/13.82 tff(7174,plain,
% 13.67/13.82 ($false),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7173, 7090, 7079])).
% 13.67/13.82 tff(7175,plain,((~always5(s51)) | m_counter_cell_v_carry_in(c_bit2, s52) | (~m_counter_cell_v_carry_in(c_bit2, s51)) | (~node1(c_bit2, s55))), inference(lemma,lemma(discharge,[]))).
% 13.67/13.82 tff(7176,plain,
% 13.67/13.82 (~always5(s51)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7175, 7029, 7017, 3311])).
% 13.67/13.82 tff(7177,plain,
% 13.67/13.82 (~always5(s50)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[3961, 7176])).
% 13.67/13.82 tff(7178,assumption,(~always5(s50)), introduced(assumption)).
% 13.67/13.82 tff(7179,plain,
% 13.67/13.82 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s50) | (~trans(s59, s50)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s50) | (~trans(s59, s50)))),
% 13.67/13.82 inference(rewrite,[status(thm)],[])).
% 13.67/13.82 tff(7180,plain,
% 13.67/13.82 (((~always5(s59)) | (~trans(s59, s50)) | always5(s50)) <=> ((~always5(s59)) | always5(s50) | (~trans(s59, s50)))),
% 13.67/13.82 inference(rewrite,[status(thm)],[])).
% 13.67/13.82 tff(7181,plain,
% 13.67/13.82 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s50)) | always5(s50))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s50) | (~trans(s59, s50))))),
% 13.67/13.82 inference(monotonicity,[status(thm)],[7180])).
% 13.67/13.82 tff(7182,plain,
% 13.67/13.82 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s50)) | always5(s50))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s50) | (~trans(s59, s50)))),
% 13.67/13.82 inference(transitivity,[status(thm)],[7181, 7179])).
% 13.67/13.82 tff(7183,plain,
% 13.67/13.82 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s50)) | always5(s50))),
% 13.67/13.82 inference(quant_inst,[status(thm)],[])).
% 13.67/13.82 tff(7184,plain,
% 13.67/13.82 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s50) | (~trans(s59, s50))),
% 13.67/13.82 inference(modus_ponens,[status(thm)],[7183, 7182])).
% 13.67/13.82 tff(7185,plain,
% 13.67/13.82 ($false),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7184, 6239, 3890, 6915, 7178])).
% 13.67/13.82 tff(7186,plain,((~trans(s59, s50)) | always5(s50)), inference(lemma,lemma(discharge,[]))).
% 13.67/13.82 tff(7187,plain,
% 13.67/13.82 (~trans(s59, s50)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7186, 7177])).
% 13.67/13.82 tff(7188,assumption,(~m_counter_cell_v_carry_out(c_bit1, s55)), introduced(assumption)).
% 13.67/13.82 tff(7189,plain,
% 13.67/13.82 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s55)) | (~m_counter_cell_v_value(c_bit1, s55)) | m_counter_cell_v_carry_out(c_bit1, s55))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s55)) | (~m_counter_cell_v_value(c_bit1, s55)) | m_counter_cell_v_carry_out(c_bit1, s55))),
% 13.67/13.82 inference(rewrite,[status(thm)],[])).
% 13.67/13.82 tff(7190,plain,
% 13.67/13.82 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s55)) | (~m_counter_cell_v_value(c_bit1, s55)) | m_counter_cell_v_carry_out(c_bit1, s55))),
% 13.67/13.82 inference(quant_inst,[status(thm)],[])).
% 13.67/13.82 tff(7191,plain,
% 13.67/13.82 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s55)) | (~m_counter_cell_v_value(c_bit1, s55)) | m_counter_cell_v_carry_out(c_bit1, s55)),
% 13.67/13.82 inference(modus_ponens,[status(thm)],[7190, 7189])).
% 13.67/13.82 tff(7192,plain,
% 13.67/13.82 ($false),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7191, 1390, 3562, 3525, 7188])).
% 13.67/13.82 tff(7193,plain,(m_counter_cell_v_carry_out(c_bit1, s55) | (~m_counter_cell_v_value(c_bit1, s55))), inference(lemma,lemma(discharge,[]))).
% 13.67/13.82 tff(7194,plain,
% 13.67/13.82 (m_counter_cell_v_carry_out(c_bit1, s55)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7193, 3525])).
% 13.67/13.82 tff(7195,assumption,(m_counter_cell_v_carry_out(c_bit1, s55)), introduced(assumption)).
% 13.67/13.82 tff(7196,assumption,(~m_counter_cell_v_carry_in(c_bit2, s55)), introduced(assumption)).
% 13.67/13.82 tff(7197,plain,
% 13.67/13.82 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s55)) | m_counter_cell_v_carry_in(c_bit2, s55))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s55)) | m_counter_cell_v_carry_in(c_bit2, s55))),
% 13.67/13.82 inference(rewrite,[status(thm)],[])).
% 13.67/13.82 tff(7198,plain,
% 13.67/13.82 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s55)) | m_counter_cell_v_carry_in(c_bit2, s55))),
% 13.67/13.82 inference(quant_inst,[status(thm)],[])).
% 13.67/13.82 tff(7199,plain,
% 13.67/13.82 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s55)) | m_counter_cell_v_carry_in(c_bit2, s55)),
% 13.67/13.82 inference(modus_ponens,[status(thm)],[7198, 7197])).
% 13.67/13.82 tff(7200,plain,
% 13.67/13.82 ($false),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7199, 3305, 7196, 7195])).
% 13.67/13.82 tff(7201,plain,(m_counter_cell_v_carry_in(c_bit2, s55) | (~m_counter_cell_v_carry_out(c_bit1, s55))), inference(lemma,lemma(discharge,[]))).
% 13.67/13.82 tff(7202,plain,
% 13.67/13.82 (m_counter_cell_v_carry_in(c_bit2, s55)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7201, 7194])).
% 13.67/13.82 tff(7203,plain,
% 13.67/13.82 (~node1(c_bit2, s55)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7113, 7202, 7099])).
% 13.67/13.82 tff(7204,plain,
% 13.67/13.82 (~node2(c_bit1, s55)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[3568, 3525])).
% 13.67/13.82 tff(7205,plain,
% 13.67/13.82 (~m_counter_cell_v_value(c_bit1, s56)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[3587, 7204])).
% 13.67/13.82 tff(7206,plain,
% 13.67/13.82 (~m_counter_cell_v_value(c_bit2, s56)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7004, 7205])).
% 13.67/13.82 tff(7207,plain,
% 13.67/13.82 ($false),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7016, 7206, 7203])).
% 13.67/13.82 tff(7208,plain,((~m_counter_cell_v_value(c_bit1, s55)) | m_counter_cell_v_carry_out(c_bit2, s55)), inference(lemma,lemma(discharge,[]))).
% 13.67/13.82 tff(7209,plain,
% 13.67/13.82 (m_counter_cell_v_carry_out(c_bit2, s55)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7208, 3524])).
% 13.67/13.82 tff(7210,plain,
% 13.67/13.82 (~always5(s55)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7096, 6925, 7209])).
% 13.67/13.82 tff(7211,plain,
% 13.67/13.82 (~always5(s54)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[3929, 7210])).
% 13.67/13.82 tff(7212,assumption,(~always5(s54)), introduced(assumption)).
% 13.67/13.82 tff(7213,plain,
% 13.67/13.82 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s54) | (~trans(s59, s54)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s54) | (~trans(s59, s54)))),
% 13.67/13.82 inference(rewrite,[status(thm)],[])).
% 13.67/13.82 tff(7214,plain,
% 13.67/13.82 (((~always5(s59)) | (~trans(s59, s54)) | always5(s54)) <=> ((~always5(s59)) | always5(s54) | (~trans(s59, s54)))),
% 13.67/13.82 inference(rewrite,[status(thm)],[])).
% 13.67/13.82 tff(7215,plain,
% 13.67/13.82 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s54)) | always5(s54))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s54) | (~trans(s59, s54))))),
% 13.67/13.82 inference(monotonicity,[status(thm)],[7214])).
% 13.67/13.82 tff(7216,plain,
% 13.67/13.82 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s54)) | always5(s54))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s54) | (~trans(s59, s54)))),
% 13.67/13.82 inference(transitivity,[status(thm)],[7215, 7213])).
% 13.67/13.82 tff(7217,plain,
% 13.67/13.82 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s54)) | always5(s54))),
% 13.67/13.82 inference(quant_inst,[status(thm)],[])).
% 13.67/13.82 tff(7218,plain,
% 13.67/13.82 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s54) | (~trans(s59, s54))),
% 13.67/13.82 inference(modus_ponens,[status(thm)],[7217, 7216])).
% 13.67/13.82 tff(7219,plain,
% 13.67/13.82 ($false),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7218, 6404, 3890, 6915, 7212])).
% 13.67/13.82 tff(7220,plain,((~trans(s59, s54)) | always5(s54)), inference(lemma,lemma(discharge,[]))).
% 13.67/13.82 tff(7221,plain,
% 13.67/13.82 (~trans(s59, s54)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7220, 7211])).
% 13.67/13.82 tff(7222,assumption,(~always5(s55)), introduced(assumption)).
% 13.67/13.82 tff(7223,plain,
% 13.67/13.82 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s55) | (~trans(s59, s55)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s55) | (~trans(s59, s55)))),
% 13.67/13.82 inference(rewrite,[status(thm)],[])).
% 13.67/13.82 tff(7224,plain,
% 13.67/13.82 (((~always5(s59)) | (~trans(s59, s55)) | always5(s55)) <=> ((~always5(s59)) | always5(s55) | (~trans(s59, s55)))),
% 13.67/13.82 inference(rewrite,[status(thm)],[])).
% 13.67/13.82 tff(7225,plain,
% 13.67/13.82 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s55)) | always5(s55))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s55) | (~trans(s59, s55))))),
% 13.67/13.82 inference(monotonicity,[status(thm)],[7224])).
% 13.67/13.82 tff(7226,plain,
% 13.67/13.82 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s55)) | always5(s55))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s55) | (~trans(s59, s55)))),
% 13.67/13.82 inference(transitivity,[status(thm)],[7225, 7223])).
% 13.67/13.82 tff(7227,plain,
% 13.67/13.82 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s55)) | always5(s55))),
% 13.67/13.82 inference(quant_inst,[status(thm)],[])).
% 13.67/13.82 tff(7228,plain,
% 13.67/13.82 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s55) | (~trans(s59, s55))),
% 13.67/13.82 inference(modus_ponens,[status(thm)],[7227, 7226])).
% 13.67/13.82 tff(7229,plain,
% 13.67/13.82 ($false),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7228, 5791, 3890, 6915, 7222])).
% 13.67/13.82 tff(7230,plain,((~trans(s59, s55)) | always5(s55)), inference(lemma,lemma(discharge,[]))).
% 13.67/13.82 tff(7231,plain,
% 13.67/13.82 (~trans(s59, s55)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7230, 7210])).
% 13.67/13.82 tff(7232,plain,
% 13.67/13.82 (~always5(s53)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[3937, 7211])).
% 13.67/13.82 tff(7233,plain,
% 13.67/13.82 (~always5(s52)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[3945, 7232])).
% 13.67/13.82 tff(7234,assumption,(~always5(s52)), introduced(assumption)).
% 13.67/13.82 tff(7235,plain,
% 13.67/13.82 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s52) | (~trans(s59, s52)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s52) | (~trans(s59, s52)))),
% 13.67/13.82 inference(rewrite,[status(thm)],[])).
% 13.67/13.82 tff(7236,plain,
% 13.67/13.82 (((~always5(s59)) | (~trans(s59, s52)) | always5(s52)) <=> ((~always5(s59)) | always5(s52) | (~trans(s59, s52)))),
% 13.67/13.82 inference(rewrite,[status(thm)],[])).
% 13.67/13.82 tff(7237,plain,
% 13.67/13.82 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s52)) | always5(s52))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s52) | (~trans(s59, s52))))),
% 13.67/13.82 inference(monotonicity,[status(thm)],[7236])).
% 13.67/13.82 tff(7238,plain,
% 13.67/13.82 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s52)) | always5(s52))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s52) | (~trans(s59, s52)))),
% 13.67/13.82 inference(transitivity,[status(thm)],[7237, 7235])).
% 13.67/13.82 tff(7239,plain,
% 13.67/13.82 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s52)) | always5(s52))),
% 13.67/13.82 inference(quant_inst,[status(thm)],[])).
% 13.67/13.82 tff(7240,plain,
% 13.67/13.82 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s52) | (~trans(s59, s52))),
% 13.67/13.82 inference(modus_ponens,[status(thm)],[7239, 7238])).
% 13.67/13.82 tff(7241,plain,
% 13.67/13.82 ($false),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7240, 6294, 3890, 6915, 7234])).
% 13.67/13.82 tff(7242,plain,((~trans(s59, s52)) | always5(s52)), inference(lemma,lemma(discharge,[]))).
% 13.67/13.82 tff(7243,plain,
% 13.67/13.82 (~trans(s59, s52)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7242, 7233])).
% 13.67/13.82 tff(7244,assumption,(node3(c_bit1, s59, s58)), introduced(assumption)).
% 13.67/13.82 tff(7245,assumption,(~m_counter_cell_v_value(c_bit1, s59)), introduced(assumption)).
% 13.67/13.82 tff(7246,plain,
% 13.67/13.82 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s59)) | m_counter_cell_v_value(c_bit1, s59) | (~node1(c_bit1, s59)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s59)) | m_counter_cell_v_value(c_bit1, s59) | (~node1(c_bit1, s59)))),
% 13.67/13.82 inference(rewrite,[status(thm)],[])).
% 13.67/13.82 tff(7247,plain,
% 13.67/13.82 (((~node1(c_bit1, s59)) | (~m_counter_cell_v_carry_in(c_bit1, s59)) | m_counter_cell_v_value(c_bit1, s59)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s59)) | m_counter_cell_v_value(c_bit1, s59) | (~node1(c_bit1, s59)))),
% 13.67/13.82 inference(rewrite,[status(thm)],[])).
% 13.67/13.82 tff(7248,plain,
% 13.67/13.82 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s59)) | (~m_counter_cell_v_carry_in(c_bit1, s59)) | m_counter_cell_v_value(c_bit1, s59))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s59)) | m_counter_cell_v_value(c_bit1, s59) | (~node1(c_bit1, s59))))),
% 13.67/13.82 inference(monotonicity,[status(thm)],[7247])).
% 13.67/13.82 tff(7249,plain,
% 13.67/13.82 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s59)) | (~m_counter_cell_v_carry_in(c_bit1, s59)) | m_counter_cell_v_value(c_bit1, s59))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s59)) | m_counter_cell_v_value(c_bit1, s59) | (~node1(c_bit1, s59)))),
% 13.67/13.82 inference(transitivity,[status(thm)],[7248, 7246])).
% 13.67/13.82 tff(7250,plain,
% 13.67/13.82 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s59)) | (~m_counter_cell_v_carry_in(c_bit1, s59)) | m_counter_cell_v_value(c_bit1, s59))),
% 13.67/13.82 inference(quant_inst,[status(thm)],[])).
% 13.67/13.82 tff(7251,plain,
% 13.67/13.82 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s59)) | m_counter_cell_v_value(c_bit1, s59) | (~node1(c_bit1, s59))),
% 13.67/13.82 inference(modus_ponens,[status(thm)],[7250, 7249])).
% 13.67/13.82 tff(7252,plain,
% 13.67/13.82 (m_counter_cell_v_value(c_bit1, s59) | (~node1(c_bit1, s59))),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7251, 30, 3866])).
% 13.67/13.82 tff(7253,plain,
% 13.67/13.82 (~node1(c_bit1, s59)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7252, 7245])).
% 13.67/13.82 tff(7254,plain,
% 13.67/13.82 (node1(c_bit1, s58)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[3828, 7245])).
% 13.67/13.82 tff(7255,plain,
% 13.67/13.82 (~m_counter_cell_v_value(c_bit1, s58)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[3809, 7254])).
% 13.67/13.82 tff(7256,plain,
% 13.67/13.82 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s59) | (~node3(c_bit1, s59, s58)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s59) | (~node3(c_bit1, s59, s58)))),
% 13.67/13.82 inference(rewrite,[status(thm)],[])).
% 13.67/13.82 tff(7257,plain,
% 13.67/13.82 ((node1(c_bit1, s59) | (~node3(c_bit1, s59, s58)) | m_counter_cell_v_value(c_bit1, s58)) <=> (m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s59) | (~node3(c_bit1, s59, s58)))),
% 13.67/13.82 inference(rewrite,[status(thm)],[])).
% 13.67/13.82 tff(7258,plain,
% 13.67/13.82 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s59) | (~node3(c_bit1, s59, s58)) | m_counter_cell_v_value(c_bit1, s58))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s59) | (~node3(c_bit1, s59, s58))))),
% 13.67/13.82 inference(monotonicity,[status(thm)],[7257])).
% 13.67/13.82 tff(7259,plain,
% 13.67/13.82 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s59) | (~node3(c_bit1, s59, s58)) | m_counter_cell_v_value(c_bit1, s58))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s59) | (~node3(c_bit1, s59, s58)))),
% 13.67/13.82 inference(transitivity,[status(thm)],[7258, 7256])).
% 13.67/13.82 tff(7260,plain,
% 13.67/13.82 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s59) | (~node3(c_bit1, s59, s58)) | m_counter_cell_v_value(c_bit1, s58))),
% 13.67/13.82 inference(quant_inst,[status(thm)],[])).
% 13.67/13.82 tff(7261,plain,
% 13.67/13.82 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s59) | (~node3(c_bit1, s59, s58))),
% 13.67/13.82 inference(modus_ponens,[status(thm)],[7260, 7259])).
% 13.67/13.82 tff(7262,plain,
% 13.67/13.82 (m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s59)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7261, 73, 7244])).
% 13.67/13.82 tff(7263,plain,
% 13.67/13.82 ($false),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7262, 7255, 7253])).
% 13.67/13.82 tff(7264,plain,(m_counter_cell_v_value(c_bit1, s59) | (~node3(c_bit1, s59, s58))), inference(lemma,lemma(discharge,[]))).
% 13.67/13.82 tff(7265,plain,
% 13.67/13.82 (m_counter_cell_v_value(c_bit1, s59)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7264, 7244])).
% 13.67/13.82 tff(7266,plain,
% 13.67/13.82 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s59)) | (~m_counter_cell_v_value(c_bit1, s59)) | (~node2(c_bit1, s59)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s59)) | (~m_counter_cell_v_value(c_bit1, s59)) | (~node2(c_bit1, s59)))),
% 13.67/13.82 inference(rewrite,[status(thm)],[])).
% 13.67/13.82 tff(7267,plain,
% 13.67/13.82 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s59)) | (~m_counter_cell_v_value(c_bit1, s59)) | (~node2(c_bit1, s59)))),
% 13.67/13.82 inference(quant_inst,[status(thm)],[])).
% 13.67/13.82 tff(7268,plain,
% 13.67/13.82 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s59)) | (~m_counter_cell_v_value(c_bit1, s59)) | (~node2(c_bit1, s59))),
% 13.67/13.82 inference(modus_ponens,[status(thm)],[7267, 7266])).
% 13.67/13.82 tff(7269,plain,
% 13.67/13.82 ((~m_counter_cell_v_value(c_bit1, s59)) | (~node2(c_bit1, s59))),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7268, 93, 3866])).
% 13.67/13.82 tff(7270,plain,
% 13.67/13.82 (~node2(c_bit1, s59)),
% 13.67/13.82 inference(unit_resolution,[status(thm)],[7269, 7265])).
% 13.67/13.82 tff(7271,plain,
% 13.67/13.82 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s59)) | node2(c_bit1, s58) | (~node3(c_bit1, s58, s59)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s59)) | node2(c_bit1, s58) | (~node3(c_bit1, s58, s59)))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7272,plain,
% 13.67/13.83 ((node2(c_bit1, s58) | (~node3(c_bit1, s58, s59)) | (~m_counter_cell_v_value(c_bit1, s59))) <=> ((~m_counter_cell_v_value(c_bit1, s59)) | node2(c_bit1, s58) | (~node3(c_bit1, s58, s59)))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7273,plain,
% 13.67/13.83 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s58) | (~node3(c_bit1, s58, s59)) | (~m_counter_cell_v_value(c_bit1, s59)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s59)) | node2(c_bit1, s58) | (~node3(c_bit1, s58, s59))))),
% 13.67/13.83 inference(monotonicity,[status(thm)],[7272])).
% 13.67/13.83 tff(7274,plain,
% 13.67/13.83 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s58) | (~node3(c_bit1, s58, s59)) | (~m_counter_cell_v_value(c_bit1, s59)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s59)) | node2(c_bit1, s58) | (~node3(c_bit1, s58, s59)))),
% 13.67/13.83 inference(transitivity,[status(thm)],[7273, 7271])).
% 13.67/13.83 tff(7275,plain,
% 13.67/13.83 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s58) | (~node3(c_bit1, s58, s59)) | (~m_counter_cell_v_value(c_bit1, s59)))),
% 13.67/13.83 inference(quant_inst,[status(thm)],[])).
% 13.67/13.83 tff(7276,plain,
% 13.67/13.83 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s59)) | node2(c_bit1, s58) | (~node3(c_bit1, s58, s59))),
% 13.67/13.83 inference(modus_ponens,[status(thm)],[7275, 7274])).
% 13.67/13.83 tff(7277,plain,
% 13.67/13.83 ((~m_counter_cell_v_value(c_bit1, s59)) | node2(c_bit1, s58)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7276, 121, 3821])).
% 13.67/13.83 tff(7278,plain,
% 13.67/13.83 (node2(c_bit1, s58)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7277, 7265])).
% 13.67/13.83 tff(7279,assumption,(~m_counter_cell_v_value(c_bit1, s58)), introduced(assumption)).
% 13.67/13.83 tff(7280,assumption,(node2(c_bit1, s58)), introduced(assumption)).
% 13.67/13.83 tff(7281,plain,
% 13.67/13.83 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s58) | m_counter_cell_v_value(c_bit1, s58) | (~node2(c_bit1, s58)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s58) | m_counter_cell_v_value(c_bit1, s58) | (~node2(c_bit1, s58)))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7282,plain,
% 13.67/13.83 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s58) | m_counter_cell_v_value(c_bit1, s58) | (~node2(c_bit1, s58)))),
% 13.67/13.83 inference(quant_inst,[status(thm)],[])).
% 13.67/13.83 tff(7283,plain,
% 13.67/13.83 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s58) | m_counter_cell_v_value(c_bit1, s58) | (~node2(c_bit1, s58))),
% 13.67/13.83 inference(modus_ponens,[status(thm)],[7282, 7281])).
% 13.67/13.83 tff(7284,plain,
% 13.67/13.83 ($false),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7283, 1498, 7280, 7279, 3781])).
% 13.67/13.83 tff(7285,plain,(m_counter_cell_v_value(c_bit1, s58) | (~node2(c_bit1, s58))), inference(lemma,lemma(discharge,[]))).
% 13.67/13.83 tff(7286,plain,
% 13.67/13.83 (m_counter_cell_v_value(c_bit1, s58)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7285, 7278])).
% 13.67/13.83 tff(7287,plain,
% 13.67/13.83 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s58)) | node2(c_bit1, s59) | (~node3(c_bit1, s59, s58)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s58)) | node2(c_bit1, s59) | (~node3(c_bit1, s59, s58)))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7288,plain,
% 13.67/13.83 ((node2(c_bit1, s59) | (~node3(c_bit1, s59, s58)) | (~m_counter_cell_v_value(c_bit1, s58))) <=> ((~m_counter_cell_v_value(c_bit1, s58)) | node2(c_bit1, s59) | (~node3(c_bit1, s59, s58)))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7289,plain,
% 13.67/13.83 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s59) | (~node3(c_bit1, s59, s58)) | (~m_counter_cell_v_value(c_bit1, s58)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s58)) | node2(c_bit1, s59) | (~node3(c_bit1, s59, s58))))),
% 13.67/13.83 inference(monotonicity,[status(thm)],[7288])).
% 13.67/13.83 tff(7290,plain,
% 13.67/13.83 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s59) | (~node3(c_bit1, s59, s58)) | (~m_counter_cell_v_value(c_bit1, s58)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s58)) | node2(c_bit1, s59) | (~node3(c_bit1, s59, s58)))),
% 13.67/13.83 inference(transitivity,[status(thm)],[7289, 7287])).
% 13.67/13.83 tff(7291,plain,
% 13.67/13.83 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s59) | (~node3(c_bit1, s59, s58)) | (~m_counter_cell_v_value(c_bit1, s58)))),
% 13.67/13.83 inference(quant_inst,[status(thm)],[])).
% 13.67/13.83 tff(7292,plain,
% 13.67/13.83 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s58)) | node2(c_bit1, s59) | (~node3(c_bit1, s59, s58))),
% 13.67/13.83 inference(modus_ponens,[status(thm)],[7291, 7290])).
% 13.67/13.83 tff(7293,plain,
% 13.67/13.83 ((~m_counter_cell_v_value(c_bit1, s58)) | node2(c_bit1, s59)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7292, 121, 7244])).
% 13.67/13.83 tff(7294,plain,
% 13.67/13.83 ($false),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7293, 7286, 7270])).
% 13.67/13.83 tff(7295,plain,(~node3(c_bit1, s59, s58)), inference(lemma,lemma(discharge,[]))).
% 13.67/13.83 tff(7296,plain,
% 13.67/13.83 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s58)) | node3(c_bit1, s59, s58))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s58)) | node3(c_bit1, s59, s58))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7297,plain,
% 13.67/13.83 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s58)) | node3(c_bit1, s59, s58))),
% 13.67/13.83 inference(quant_inst,[status(thm)],[])).
% 13.67/13.83 tff(7298,plain,
% 13.67/13.83 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s58)) | node3(c_bit1, s59, s58)),
% 13.67/13.83 inference(modus_ponens,[status(thm)],[7297, 7296])).
% 13.67/13.83 tff(7299,plain,
% 13.67/13.83 ((~trans(s59, s58)) | node3(c_bit1, s59, s58)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7298, 59])).
% 13.67/13.83 tff(7300,plain,
% 13.67/13.83 (~trans(s59, s58)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7299, 7295])).
% 13.67/13.83 tff(7301,assumption,(always5(s49)), introduced(assumption)).
% 13.67/13.83 tff(7302,plain,
% 13.67/13.83 (always5(s50)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[3969, 7301])).
% 13.67/13.83 tff(7303,plain,
% 13.67/13.83 (always5(s51)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[3961, 7302])).
% 13.67/13.83 tff(7304,plain,
% 13.67/13.83 (always5(s52)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[3953, 7303])).
% 13.67/13.83 tff(7305,plain,
% 13.67/13.83 (always5(s53)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[3945, 7304])).
% 13.67/13.83 tff(7306,plain,
% 13.67/13.83 (always5(s54)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[3937, 7305])).
% 13.67/13.83 tff(7307,plain,
% 13.67/13.83 (always5(s55)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[3929, 7306])).
% 13.67/13.83 tff(7308,plain,
% 13.67/13.83 (~m_counter_cell_v_carry_out(c_bit2, s55)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7096, 6925, 7307])).
% 13.67/13.83 tff(7309,plain,
% 13.67/13.83 (~m_counter_cell_v_value(c_bit1, s55)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7208, 7308])).
% 13.67/13.83 tff(7310,plain,
% 13.67/13.83 (node1(c_bit1, s54)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[3523, 7309])).
% 13.67/13.83 tff(7311,plain,
% 13.67/13.83 (~m_counter_cell_v_value(c_bit1, s54)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[3504, 7310])).
% 13.67/13.83 tff(7312,plain,
% 13.67/13.83 (node1(c_bit1, s53)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[3461, 7311])).
% 13.67/13.83 tff(7313,plain,
% 13.67/13.83 (m_counter_cell_v_value(c_bit1, s53)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[3442, 7312])).
% 13.67/13.83 tff(7314,plain,
% 13.67/13.83 (node2(c_bit1, s52)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[3394, 7313])).
% 13.67/13.83 tff(7315,plain,
% 13.67/13.83 (m_counter_cell_v_value(c_bit1, s52)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[3375, 7314])).
% 13.67/13.83 tff(7316,plain,
% 13.67/13.83 (node2(c_bit1, s51)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[3336, 7315])).
% 13.67/13.83 tff(7317,plain,
% 13.67/13.83 (~m_counter_cell_v_value(c_bit1, s51)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[3317, 7316])).
% 13.67/13.83 tff(7318,plain,
% 13.67/13.83 (node1(c_bit1, s50)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[3243, 7317])).
% 13.67/13.83 tff(7319,plain,
% 13.67/13.83 (m_counter_cell_v_value(c_bit1, s49)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[3224, 7318])).
% 13.67/13.83 tff(7320,plain,
% 13.67/13.83 (m_counter_cell_v_carry_out(c_bit0, s49)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[3173, 3133])).
% 13.67/13.83 tff(7321,plain,
% 13.67/13.83 (m_counter_cell_v_carry_in(c_bit1, s49)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[3177, 1405, 7320])).
% 13.67/13.83 tff(7322,assumption,(~m_counter_cell_v_carry_out(c_bit1, s49)), introduced(assumption)).
% 13.67/13.83 tff(7323,assumption,(m_counter_cell_v_value(c_bit1, s49)), introduced(assumption)).
% 13.67/13.83 tff(7324,plain,
% 13.67/13.83 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s49)) | (~m_counter_cell_v_value(c_bit1, s49)) | m_counter_cell_v_carry_out(c_bit1, s49))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s49)) | (~m_counter_cell_v_value(c_bit1, s49)) | m_counter_cell_v_carry_out(c_bit1, s49))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7325,plain,
% 13.67/13.83 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s49)) | (~m_counter_cell_v_value(c_bit1, s49)) | m_counter_cell_v_carry_out(c_bit1, s49))),
% 13.67/13.83 inference(quant_inst,[status(thm)],[])).
% 13.67/13.83 tff(7326,plain,
% 13.67/13.83 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s49)) | (~m_counter_cell_v_value(c_bit1, s49)) | m_counter_cell_v_carry_out(c_bit1, s49)),
% 13.67/13.83 inference(modus_ponens,[status(thm)],[7325, 7324])).
% 13.67/13.83 tff(7327,plain,
% 13.67/13.83 ($false),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7326, 1390, 7323, 3179, 7322])).
% 13.67/13.83 tff(7328,plain,(m_counter_cell_v_carry_out(c_bit1, s49) | (~m_counter_cell_v_value(c_bit1, s49)) | (~m_counter_cell_v_carry_in(c_bit1, s49))), inference(lemma,lemma(discharge,[]))).
% 13.67/13.83 tff(7329,plain,
% 13.67/13.83 (m_counter_cell_v_carry_out(c_bit1, s49) | (~m_counter_cell_v_value(c_bit1, s49))),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7328, 7321])).
% 13.67/13.83 tff(7330,plain,
% 13.67/13.83 (m_counter_cell_v_carry_out(c_bit1, s49)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7329, 7319])).
% 13.67/13.83 tff(7331,assumption,(~m_counter_cell_v_carry_in(c_bit2, s49)), introduced(assumption)).
% 13.67/13.83 tff(7332,assumption,(m_counter_cell_v_carry_out(c_bit1, s49)), introduced(assumption)).
% 13.67/13.83 tff(7333,plain,
% 13.67/13.83 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s49)) | m_counter_cell_v_carry_in(c_bit2, s49))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s49)) | m_counter_cell_v_carry_in(c_bit2, s49))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7334,plain,
% 13.67/13.83 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s49)) | m_counter_cell_v_carry_in(c_bit2, s49))),
% 13.67/13.83 inference(quant_inst,[status(thm)],[])).
% 13.67/13.83 tff(7335,plain,
% 13.67/13.83 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s49)) | m_counter_cell_v_carry_in(c_bit2, s49)),
% 13.67/13.83 inference(modus_ponens,[status(thm)],[7334, 7333])).
% 13.67/13.83 tff(7336,plain,
% 13.67/13.83 ($false),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7335, 3305, 7332, 7331])).
% 13.67/13.83 tff(7337,plain,(m_counter_cell_v_carry_in(c_bit2, s49) | (~m_counter_cell_v_carry_out(c_bit1, s49))), inference(lemma,lemma(discharge,[]))).
% 13.67/13.83 tff(7338,plain,
% 13.67/13.83 (m_counter_cell_v_carry_in(c_bit2, s49)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7337, 7330])).
% 13.67/13.83 tff(7339,plain,
% 13.67/13.83 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s49)) | (~m_counter_cell_v_carry_out(c_bit2, s49)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s49)) | (~m_counter_cell_v_carry_out(c_bit2, s49)))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7340,plain,
% 13.67/13.83 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s49)) | (~m_counter_cell_v_carry_out(c_bit2, s49)))),
% 13.67/13.83 inference(quant_inst,[status(thm)],[])).
% 13.67/13.83 tff(7341,plain,
% 13.67/13.83 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s49)) | (~m_counter_cell_v_carry_out(c_bit2, s49))),
% 13.67/13.83 inference(modus_ponens,[status(thm)],[7340, 7339])).
% 13.67/13.83 tff(7342,plain,
% 13.67/13.83 (~m_counter_cell_v_carry_out(c_bit2, s49)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7341, 6925, 7301])).
% 13.67/13.83 tff(7343,plain,
% 13.67/13.83 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s49)) | (~m_counter_cell_v_value(c_bit2, s49)) | m_counter_cell_v_carry_out(c_bit2, s49))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s49)) | (~m_counter_cell_v_value(c_bit2, s49)) | m_counter_cell_v_carry_out(c_bit2, s49))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7344,plain,
% 13.67/13.83 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s49)) | (~m_counter_cell_v_value(c_bit2, s49)) | m_counter_cell_v_carry_out(c_bit2, s49))),
% 13.67/13.83 inference(quant_inst,[status(thm)],[])).
% 13.67/13.83 tff(7345,plain,
% 13.67/13.83 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s49)) | (~m_counter_cell_v_value(c_bit2, s49)) | m_counter_cell_v_carry_out(c_bit2, s49)),
% 13.67/13.83 inference(modus_ponens,[status(thm)],[7344, 7343])).
% 13.67/13.83 tff(7346,plain,
% 13.67/13.83 ((~m_counter_cell_v_carry_in(c_bit2, s49)) | (~m_counter_cell_v_value(c_bit2, s49))),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7345, 1390, 7342])).
% 13.67/13.83 tff(7347,plain,
% 13.67/13.83 (~m_counter_cell_v_value(c_bit2, s49)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7346, 7338])).
% 13.67/13.83 tff(7348,plain,
% 13.67/13.83 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s49)) | m_counter_cell_v_value(c_bit2, s49) | (~node1(c_bit2, s49)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s49)) | m_counter_cell_v_value(c_bit2, s49) | (~node1(c_bit2, s49)))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7349,plain,
% 13.67/13.83 (((~node1(c_bit2, s49)) | (~m_counter_cell_v_carry_in(c_bit2, s49)) | m_counter_cell_v_value(c_bit2, s49)) <=> ((~m_counter_cell_v_carry_in(c_bit2, s49)) | m_counter_cell_v_value(c_bit2, s49) | (~node1(c_bit2, s49)))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7350,plain,
% 13.67/13.83 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s49)) | (~m_counter_cell_v_carry_in(c_bit2, s49)) | m_counter_cell_v_value(c_bit2, s49))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s49)) | m_counter_cell_v_value(c_bit2, s49) | (~node1(c_bit2, s49))))),
% 13.67/13.83 inference(monotonicity,[status(thm)],[7349])).
% 13.67/13.83 tff(7351,plain,
% 13.67/13.83 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s49)) | (~m_counter_cell_v_carry_in(c_bit2, s49)) | m_counter_cell_v_value(c_bit2, s49))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s49)) | m_counter_cell_v_value(c_bit2, s49) | (~node1(c_bit2, s49)))),
% 13.67/13.83 inference(transitivity,[status(thm)],[7350, 7348])).
% 13.67/13.83 tff(7352,plain,
% 13.67/13.83 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s49)) | (~m_counter_cell_v_carry_in(c_bit2, s49)) | m_counter_cell_v_value(c_bit2, s49))),
% 13.67/13.83 inference(quant_inst,[status(thm)],[])).
% 13.67/13.83 tff(7353,plain,
% 13.67/13.83 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s49)) | m_counter_cell_v_value(c_bit2, s49) | (~node1(c_bit2, s49))),
% 13.67/13.83 inference(modus_ponens,[status(thm)],[7352, 7351])).
% 13.67/13.83 tff(7354,plain,
% 13.67/13.83 (~node1(c_bit2, s49)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7353, 30, 7338, 7347])).
% 13.67/13.83 tff(7355,plain,
% 13.67/13.83 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s49, s50)) | node3(c_bit2, s49, s50))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s49, s50)) | node3(c_bit2, s49, s50))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7356,plain,
% 13.67/13.83 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s49, s50)) | node3(c_bit2, s49, s50))),
% 13.67/13.83 inference(quant_inst,[status(thm)],[])).
% 13.67/13.83 tff(7357,plain,
% 13.67/13.83 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s49, s50)) | node3(c_bit2, s49, s50)),
% 13.67/13.83 inference(modus_ponens,[status(thm)],[7356, 7355])).
% 13.67/13.83 tff(7358,plain,
% 13.67/13.83 (node3(c_bit2, s49, s50)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7357, 59, 3151])).
% 13.67/13.83 tff(7359,plain,
% 13.67/13.83 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s50) | node1(c_bit2, s49) | (~node3(c_bit2, s49, s50)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s50) | node1(c_bit2, s49) | (~node3(c_bit2, s49, s50)))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7360,plain,
% 13.67/13.83 ((node1(c_bit2, s49) | (~node3(c_bit2, s49, s50)) | m_counter_cell_v_value(c_bit2, s50)) <=> (m_counter_cell_v_value(c_bit2, s50) | node1(c_bit2, s49) | (~node3(c_bit2, s49, s50)))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7361,plain,
% 13.67/13.83 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s49) | (~node3(c_bit2, s49, s50)) | m_counter_cell_v_value(c_bit2, s50))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s50) | node1(c_bit2, s49) | (~node3(c_bit2, s49, s50))))),
% 13.67/13.83 inference(monotonicity,[status(thm)],[7360])).
% 13.67/13.83 tff(7362,plain,
% 13.67/13.83 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s49) | (~node3(c_bit2, s49, s50)) | m_counter_cell_v_value(c_bit2, s50))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s50) | node1(c_bit2, s49) | (~node3(c_bit2, s49, s50)))),
% 13.67/13.83 inference(transitivity,[status(thm)],[7361, 7359])).
% 13.67/13.83 tff(7363,plain,
% 13.67/13.83 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s49) | (~node3(c_bit2, s49, s50)) | m_counter_cell_v_value(c_bit2, s50))),
% 13.67/13.83 inference(quant_inst,[status(thm)],[])).
% 13.67/13.83 tff(7364,plain,
% 13.67/13.83 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s50) | node1(c_bit2, s49) | (~node3(c_bit2, s49, s50))),
% 13.67/13.83 inference(modus_ponens,[status(thm)],[7363, 7362])).
% 13.67/13.83 tff(7365,plain,
% 13.67/13.83 (m_counter_cell_v_value(c_bit2, s50) | node1(c_bit2, s49)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7364, 73, 7358])).
% 13.67/13.83 tff(7366,plain,
% 13.67/13.83 (m_counter_cell_v_value(c_bit2, s50)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7365, 7354])).
% 13.67/13.83 tff(7367,plain,
% 13.67/13.83 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s50)) | (~m_counter_cell_v_carry_out(c_bit2, s50)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s50)) | (~m_counter_cell_v_carry_out(c_bit2, s50)))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7368,plain,
% 13.67/13.83 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s50)) | (~m_counter_cell_v_carry_out(c_bit2, s50)))),
% 13.67/13.83 inference(quant_inst,[status(thm)],[])).
% 13.67/13.83 tff(7369,plain,
% 13.67/13.83 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s50)) | (~m_counter_cell_v_carry_out(c_bit2, s50))),
% 13.67/13.83 inference(modus_ponens,[status(thm)],[7368, 7367])).
% 13.67/13.83 tff(7370,plain,
% 13.67/13.83 (~m_counter_cell_v_carry_out(c_bit2, s50)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7369, 6925, 7302])).
% 13.67/13.83 tff(7371,plain,
% 13.67/13.83 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s50)) | (~m_counter_cell_v_value(c_bit2, s50)) | m_counter_cell_v_carry_out(c_bit2, s50))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s50)) | (~m_counter_cell_v_value(c_bit2, s50)) | m_counter_cell_v_carry_out(c_bit2, s50))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7372,plain,
% 13.67/13.83 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s50)) | (~m_counter_cell_v_value(c_bit2, s50)) | m_counter_cell_v_carry_out(c_bit2, s50))),
% 13.67/13.83 inference(quant_inst,[status(thm)],[])).
% 13.67/13.83 tff(7373,plain,
% 13.67/13.83 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s50)) | (~m_counter_cell_v_value(c_bit2, s50)) | m_counter_cell_v_carry_out(c_bit2, s50)),
% 13.67/13.83 inference(modus_ponens,[status(thm)],[7372, 7371])).
% 13.67/13.83 tff(7374,plain,
% 13.67/13.83 ((~m_counter_cell_v_carry_in(c_bit2, s50)) | (~m_counter_cell_v_value(c_bit2, s50))),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7373, 1390, 7370])).
% 13.67/13.83 tff(7375,plain,
% 13.67/13.83 (~m_counter_cell_v_carry_in(c_bit2, s50)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7374, 7366])).
% 13.67/13.83 tff(7376,plain,
% 13.67/13.83 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s50) | (~m_counter_cell_v_value(c_bit2, s50)) | (~node1(c_bit2, s50)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s50) | (~m_counter_cell_v_value(c_bit2, s50)) | (~node1(c_bit2, s50)))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7377,plain,
% 13.67/13.83 (((~node1(c_bit2, s50)) | m_counter_cell_v_carry_in(c_bit2, s50) | (~m_counter_cell_v_value(c_bit2, s50))) <=> (m_counter_cell_v_carry_in(c_bit2, s50) | (~m_counter_cell_v_value(c_bit2, s50)) | (~node1(c_bit2, s50)))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7378,plain,
% 13.67/13.83 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s50)) | m_counter_cell_v_carry_in(c_bit2, s50) | (~m_counter_cell_v_value(c_bit2, s50)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s50) | (~m_counter_cell_v_value(c_bit2, s50)) | (~node1(c_bit2, s50))))),
% 13.67/13.83 inference(monotonicity,[status(thm)],[7377])).
% 13.67/13.83 tff(7379,plain,
% 13.67/13.83 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s50)) | m_counter_cell_v_carry_in(c_bit2, s50) | (~m_counter_cell_v_value(c_bit2, s50)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s50) | (~m_counter_cell_v_value(c_bit2, s50)) | (~node1(c_bit2, s50)))),
% 13.67/13.83 inference(transitivity,[status(thm)],[7378, 7376])).
% 13.67/13.83 tff(7380,plain,
% 13.67/13.83 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s50)) | m_counter_cell_v_carry_in(c_bit2, s50) | (~m_counter_cell_v_value(c_bit2, s50)))),
% 13.67/13.83 inference(quant_inst,[status(thm)],[])).
% 13.67/13.83 tff(7381,plain,
% 13.67/13.83 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s50) | (~m_counter_cell_v_value(c_bit2, s50)) | (~node1(c_bit2, s50))),
% 13.67/13.83 inference(modus_ponens,[status(thm)],[7380, 7379])).
% 13.67/13.83 tff(7382,plain,
% 13.67/13.83 (~node1(c_bit2, s50)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7381, 1569, 7366, 7375])).
% 13.67/13.83 tff(7383,plain,
% 13.67/13.83 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s50, s51)) | node3(c_bit2, s50, s51))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s50, s51)) | node3(c_bit2, s50, s51))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7384,plain,
% 13.67/13.83 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s50, s51)) | node3(c_bit2, s50, s51))),
% 13.67/13.83 inference(quant_inst,[status(thm)],[])).
% 13.67/13.83 tff(7385,plain,
% 13.67/13.83 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s50, s51)) | node3(c_bit2, s50, s51)),
% 13.67/13.83 inference(modus_ponens,[status(thm)],[7384, 7383])).
% 13.67/13.83 tff(7386,plain,
% 13.67/13.83 (node3(c_bit2, s50, s51)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7385, 59, 3232])).
% 13.67/13.83 tff(7387,plain,
% 13.67/13.83 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s51) | node1(c_bit2, s50) | (~node3(c_bit2, s50, s51)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s51) | node1(c_bit2, s50) | (~node3(c_bit2, s50, s51)))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7388,plain,
% 13.67/13.83 ((node1(c_bit2, s50) | (~node3(c_bit2, s50, s51)) | m_counter_cell_v_value(c_bit2, s51)) <=> (m_counter_cell_v_value(c_bit2, s51) | node1(c_bit2, s50) | (~node3(c_bit2, s50, s51)))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7389,plain,
% 13.67/13.83 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s50) | (~node3(c_bit2, s50, s51)) | m_counter_cell_v_value(c_bit2, s51))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s51) | node1(c_bit2, s50) | (~node3(c_bit2, s50, s51))))),
% 13.67/13.83 inference(monotonicity,[status(thm)],[7388])).
% 13.67/13.83 tff(7390,plain,
% 13.67/13.83 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s50) | (~node3(c_bit2, s50, s51)) | m_counter_cell_v_value(c_bit2, s51))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s51) | node1(c_bit2, s50) | (~node3(c_bit2, s50, s51)))),
% 13.67/13.83 inference(transitivity,[status(thm)],[7389, 7387])).
% 13.67/13.83 tff(7391,plain,
% 13.67/13.83 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s50) | (~node3(c_bit2, s50, s51)) | m_counter_cell_v_value(c_bit2, s51))),
% 13.67/13.83 inference(quant_inst,[status(thm)],[])).
% 13.67/13.83 tff(7392,plain,
% 13.67/13.83 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s51) | node1(c_bit2, s50) | (~node3(c_bit2, s50, s51))),
% 13.67/13.83 inference(modus_ponens,[status(thm)],[7391, 7390])).
% 13.67/13.83 tff(7393,plain,
% 13.67/13.83 (m_counter_cell_v_value(c_bit2, s51) | node1(c_bit2, s50)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7392, 73, 7386])).
% 13.67/13.83 tff(7394,plain,
% 13.67/13.83 (m_counter_cell_v_value(c_bit2, s51)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7393, 7382])).
% 13.67/13.83 tff(7395,plain,
% 13.67/13.83 (~m_counter_cell_v_carry_out(c_bit2, s51)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7034, 6925, 7303])).
% 13.67/13.83 tff(7396,plain,
% 13.67/13.83 ((~m_counter_cell_v_carry_in(c_bit2, s51)) | (~m_counter_cell_v_value(c_bit2, s51))),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7038, 1390, 7395])).
% 13.67/13.83 tff(7397,plain,
% 13.67/13.83 (~m_counter_cell_v_carry_in(c_bit2, s51)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7396, 7394])).
% 13.67/13.83 tff(7398,plain,
% 13.67/13.83 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s51) | (~m_counter_cell_v_value(c_bit2, s51)) | (~node1(c_bit2, s51)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s51) | (~m_counter_cell_v_value(c_bit2, s51)) | (~node1(c_bit2, s51)))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7399,plain,
% 13.67/13.83 (((~node1(c_bit2, s51)) | m_counter_cell_v_carry_in(c_bit2, s51) | (~m_counter_cell_v_value(c_bit2, s51))) <=> (m_counter_cell_v_carry_in(c_bit2, s51) | (~m_counter_cell_v_value(c_bit2, s51)) | (~node1(c_bit2, s51)))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7400,plain,
% 13.67/13.83 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s51)) | m_counter_cell_v_carry_in(c_bit2, s51) | (~m_counter_cell_v_value(c_bit2, s51)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s51) | (~m_counter_cell_v_value(c_bit2, s51)) | (~node1(c_bit2, s51))))),
% 13.67/13.83 inference(monotonicity,[status(thm)],[7399])).
% 13.67/13.83 tff(7401,plain,
% 13.67/13.83 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s51)) | m_counter_cell_v_carry_in(c_bit2, s51) | (~m_counter_cell_v_value(c_bit2, s51)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s51) | (~m_counter_cell_v_value(c_bit2, s51)) | (~node1(c_bit2, s51)))),
% 13.67/13.83 inference(transitivity,[status(thm)],[7400, 7398])).
% 13.67/13.83 tff(7402,plain,
% 13.67/13.83 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s51)) | m_counter_cell_v_carry_in(c_bit2, s51) | (~m_counter_cell_v_value(c_bit2, s51)))),
% 13.67/13.83 inference(quant_inst,[status(thm)],[])).
% 13.67/13.83 tff(7403,plain,
% 13.67/13.83 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s51) | (~m_counter_cell_v_value(c_bit2, s51)) | (~node1(c_bit2, s51))),
% 13.67/13.83 inference(modus_ponens,[status(thm)],[7402, 7401])).
% 13.67/13.83 tff(7404,plain,
% 13.67/13.83 (~node1(c_bit2, s51)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7403, 1569, 7394, 7397])).
% 13.67/13.83 tff(7405,plain,
% 13.67/13.83 (m_counter_cell_v_value(c_bit2, s52)),
% 13.67/13.83 inference(unit_resolution,[status(thm)],[7057, 7404])).
% 13.67/13.83 tff(7406,plain,
% 13.67/13.83 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s52)) | (~m_counter_cell_v_carry_out(c_bit2, s52)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s52)) | (~m_counter_cell_v_carry_out(c_bit2, s52)))),
% 13.67/13.83 inference(rewrite,[status(thm)],[])).
% 13.67/13.83 tff(7407,plain,
% 13.67/13.83 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s52)) | (~m_counter_cell_v_carry_out(c_bit2, s52)))),
% 13.67/13.84 inference(quant_inst,[status(thm)],[])).
% 13.67/13.84 tff(7408,plain,
% 13.67/13.84 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s52)) | (~m_counter_cell_v_carry_out(c_bit2, s52))),
% 13.67/13.84 inference(modus_ponens,[status(thm)],[7407, 7406])).
% 13.67/13.84 tff(7409,plain,
% 13.67/13.84 (~m_counter_cell_v_carry_out(c_bit2, s52)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7408, 6925, 7304])).
% 13.67/13.84 tff(7410,plain,
% 13.67/13.84 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s52)) | (~m_counter_cell_v_value(c_bit2, s52)) | m_counter_cell_v_carry_out(c_bit2, s52))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s52)) | (~m_counter_cell_v_value(c_bit2, s52)) | m_counter_cell_v_carry_out(c_bit2, s52))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7411,plain,
% 13.67/13.84 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s52)) | (~m_counter_cell_v_value(c_bit2, s52)) | m_counter_cell_v_carry_out(c_bit2, s52))),
% 13.67/13.84 inference(quant_inst,[status(thm)],[])).
% 13.67/13.84 tff(7412,plain,
% 13.67/13.84 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s52)) | (~m_counter_cell_v_value(c_bit2, s52)) | m_counter_cell_v_carry_out(c_bit2, s52)),
% 13.67/13.84 inference(modus_ponens,[status(thm)],[7411, 7410])).
% 13.67/13.84 tff(7413,plain,
% 13.67/13.84 ((~m_counter_cell_v_carry_in(c_bit2, s52)) | (~m_counter_cell_v_value(c_bit2, s52))),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7412, 1390, 7409])).
% 13.67/13.84 tff(7414,plain,
% 13.67/13.84 (~m_counter_cell_v_carry_in(c_bit2, s52)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7413, 7405])).
% 13.67/13.84 tff(7415,assumption,(~m_counter_cell_v_carry_out(c_bit1, s53)), introduced(assumption)).
% 13.67/13.84 tff(7416,assumption,(m_counter_cell_v_value(c_bit1, s53)), introduced(assumption)).
% 13.67/13.84 tff(7417,plain,
% 13.67/13.84 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s53)) | (~m_counter_cell_v_value(c_bit1, s53)) | m_counter_cell_v_carry_out(c_bit1, s53))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s53)) | (~m_counter_cell_v_value(c_bit1, s53)) | m_counter_cell_v_carry_out(c_bit1, s53))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7418,plain,
% 13.67/13.84 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s53)) | (~m_counter_cell_v_value(c_bit1, s53)) | m_counter_cell_v_carry_out(c_bit1, s53))),
% 13.67/13.84 inference(quant_inst,[status(thm)],[])).
% 13.67/13.84 tff(7419,plain,
% 13.67/13.84 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s53)) | (~m_counter_cell_v_value(c_bit1, s53)) | m_counter_cell_v_carry_out(c_bit1, s53)),
% 13.67/13.84 inference(modus_ponens,[status(thm)],[7418, 7417])).
% 13.67/13.84 tff(7420,plain,
% 13.67/13.84 ($false),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7419, 1390, 7416, 3433, 7415])).
% 13.67/13.84 tff(7421,plain,(m_counter_cell_v_carry_out(c_bit1, s53) | (~m_counter_cell_v_value(c_bit1, s53))), inference(lemma,lemma(discharge,[]))).
% 13.67/13.84 tff(7422,plain,
% 13.67/13.84 (m_counter_cell_v_carry_out(c_bit1, s53)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7421, 7313])).
% 13.67/13.84 tff(7423,assumption,(~m_counter_cell_v_carry_in(c_bit2, s53)), introduced(assumption)).
% 13.67/13.84 tff(7424,assumption,(m_counter_cell_v_carry_out(c_bit1, s53)), introduced(assumption)).
% 13.67/13.84 tff(7425,plain,
% 13.67/13.84 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s53)) | m_counter_cell_v_carry_in(c_bit2, s53))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s53)) | m_counter_cell_v_carry_in(c_bit2, s53))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7426,plain,
% 13.67/13.84 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s53)) | m_counter_cell_v_carry_in(c_bit2, s53))),
% 13.67/13.84 inference(quant_inst,[status(thm)],[])).
% 13.67/13.84 tff(7427,plain,
% 13.67/13.84 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s53)) | m_counter_cell_v_carry_in(c_bit2, s53)),
% 13.67/13.84 inference(modus_ponens,[status(thm)],[7426, 7425])).
% 13.67/13.84 tff(7428,plain,
% 13.67/13.84 ($false),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7427, 3305, 7424, 7423])).
% 13.67/13.84 tff(7429,plain,(m_counter_cell_v_carry_in(c_bit2, s53) | (~m_counter_cell_v_carry_out(c_bit1, s53))), inference(lemma,lemma(discharge,[]))).
% 13.67/13.84 tff(7430,plain,
% 13.67/13.84 (m_counter_cell_v_carry_in(c_bit2, s53)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7429, 7422])).
% 13.67/13.84 tff(7431,plain,
% 13.67/13.84 (~m_counter_cell_v_carry_out(c_bit2, s53)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7084, 6925, 7305])).
% 13.67/13.84 tff(7432,plain,
% 13.67/13.84 ((~m_counter_cell_v_carry_in(c_bit2, s53)) | (~m_counter_cell_v_value(c_bit2, s53))),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7088, 1390, 7431])).
% 13.67/13.84 tff(7433,plain,
% 13.67/13.84 (~m_counter_cell_v_value(c_bit2, s53)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7432, 7430])).
% 13.67/13.84 tff(7434,plain,
% 13.67/13.84 (node1(c_bit2, s52)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7078, 7433])).
% 13.67/13.84 tff(7435,plain,
% 13.67/13.84 (m_counter_cell_v_carry_in(c_bit2, s52) | (~m_counter_cell_v_value(c_bit2, s52))),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7065, 1569, 7434])).
% 13.67/13.84 tff(7436,plain,
% 13.67/13.84 ($false),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7435, 7414, 7405])).
% 13.67/13.84 tff(7437,plain,(~always5(s49)), inference(lemma,lemma(discharge,[]))).
% 13.67/13.84 tff(7438,plain,
% 13.67/13.84 (~always5(s48)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[3977, 7437])).
% 13.67/13.84 tff(7439,plain,
% 13.67/13.84 (~always5(s47)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[3985, 7438])).
% 13.67/13.84 tff(7440,plain,
% 13.67/13.84 (~always5(s46)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[3993, 7439])).
% 13.67/13.84 tff(7441,plain,
% 13.67/13.84 (~always5(s45)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[4001, 7440])).
% 13.67/13.84 tff(7442,plain,
% 13.67/13.84 (~always5(s44)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[4009, 7441])).
% 13.67/13.84 tff(7443,plain,
% 13.67/13.84 (~always5(s43)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[4017, 7442])).
% 13.67/13.84 tff(7444,plain,
% 13.67/13.84 (~always5(s42)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[4025, 7443])).
% 13.67/13.84 tff(7445,plain,
% 13.67/13.84 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s42) | (~trans(s59, s42)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s42) | (~trans(s59, s42)))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7446,plain,
% 13.67/13.84 (((~always5(s59)) | (~trans(s59, s42)) | always5(s42)) <=> ((~always5(s59)) | always5(s42) | (~trans(s59, s42)))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7447,plain,
% 13.67/13.84 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s42)) | always5(s42))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s42) | (~trans(s59, s42))))),
% 13.67/13.84 inference(monotonicity,[status(thm)],[7446])).
% 13.67/13.84 tff(7448,plain,
% 13.67/13.84 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s42)) | always5(s42))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s42) | (~trans(s59, s42)))),
% 13.67/13.84 inference(transitivity,[status(thm)],[7447, 7445])).
% 13.67/13.84 tff(7449,plain,
% 13.67/13.84 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s42)) | always5(s42))),
% 13.67/13.84 inference(quant_inst,[status(thm)],[])).
% 13.67/13.84 tff(7450,plain,
% 13.67/13.84 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s42) | (~trans(s59, s42))),
% 13.67/13.84 inference(modus_ponens,[status(thm)],[7449, 7448])).
% 13.67/13.84 tff(7451,plain,
% 13.67/13.84 ($false),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7450, 6382, 3890, 6915, 7444])).
% 13.67/13.84 tff(7452,plain,(~trans(s59, s42)), inference(lemma,lemma(discharge,[]))).
% 13.67/13.84 tff(7453,plain,
% 13.67/13.84 (~always5(s41)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[4033, 7444])).
% 13.67/13.84 tff(7454,plain,
% 13.67/13.84 (~always5(s40)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[4041, 7453])).
% 13.67/13.84 tff(7455,plain,
% 13.67/13.84 (~always5(s39)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[4049, 7454])).
% 13.67/13.84 tff(7456,plain,
% 13.67/13.84 (~always5(s38)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[4057, 7455])).
% 13.67/13.84 tff(7457,plain,
% 13.67/13.84 (~always5(s37)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[4065, 7456])).
% 13.67/13.84 tff(7458,plain,
% 13.67/13.84 (~always5(s36)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[4073, 7457])).
% 13.67/13.84 tff(7459,plain,
% 13.67/13.84 (~always5(s35)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[4081, 7458])).
% 13.67/13.84 tff(7460,plain,
% 13.67/13.84 (~always5(s34)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[4089, 7459])).
% 13.67/13.84 tff(7461,plain,
% 13.67/13.84 (~always5(s33)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[4097, 7460])).
% 13.67/13.84 tff(7462,plain,
% 13.67/13.84 (~always5(s32)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[4105, 7461])).
% 13.67/13.84 tff(7463,plain,
% 13.67/13.84 (~always5(s31)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[4113, 7462])).
% 13.67/13.84 tff(7464,plain,
% 13.67/13.84 (~always5(s30)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[4121, 7463])).
% 13.67/13.84 tff(7465,plain,
% 13.67/13.84 (~always5(s29)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[4129, 7464])).
% 13.67/13.84 tff(7466,plain,
% 13.67/13.84 (~always5(s28)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[4137, 7465])).
% 13.67/13.84 tff(7467,plain,
% 13.67/13.84 (~always5(s27)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[4145, 7466])).
% 13.67/13.84 tff(7468,plain,
% 13.67/13.84 (~always5(s26)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[4153, 7467])).
% 13.67/13.84 tff(7469,plain,
% 13.67/13.84 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s26) | (~trans(s59, s26)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s26) | (~trans(s59, s26)))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7470,plain,
% 13.67/13.84 (((~always5(s59)) | (~trans(s59, s26)) | always5(s26)) <=> ((~always5(s59)) | always5(s26) | (~trans(s59, s26)))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7471,plain,
% 13.67/13.84 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s26)) | always5(s26))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s26) | (~trans(s59, s26))))),
% 13.67/13.84 inference(monotonicity,[status(thm)],[7470])).
% 13.67/13.84 tff(7472,plain,
% 13.67/13.84 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s26)) | always5(s26))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s26) | (~trans(s59, s26)))),
% 13.67/13.84 inference(transitivity,[status(thm)],[7471, 7469])).
% 13.67/13.84 tff(7473,plain,
% 13.67/13.84 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s26)) | always5(s26))),
% 13.67/13.84 inference(quant_inst,[status(thm)],[])).
% 13.67/13.84 tff(7474,plain,
% 13.67/13.84 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s26) | (~trans(s59, s26))),
% 13.67/13.84 inference(modus_ponens,[status(thm)],[7473, 7472])).
% 13.67/13.84 tff(7475,plain,
% 13.67/13.84 ($false),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7474, 5865, 3890, 6915, 7468])).
% 13.67/13.84 tff(7476,plain,(~trans(s59, s26)), inference(lemma,lemma(discharge,[]))).
% 13.67/13.84 tff(7477,plain,
% 13.67/13.84 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s38) | (~trans(s59, s38)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s38) | (~trans(s59, s38)))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7478,plain,
% 13.67/13.84 (((~always5(s59)) | (~trans(s59, s38)) | always5(s38)) <=> ((~always5(s59)) | always5(s38) | (~trans(s59, s38)))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7479,plain,
% 13.67/13.84 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s38)) | always5(s38))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s38) | (~trans(s59, s38))))),
% 13.67/13.84 inference(monotonicity,[status(thm)],[7478])).
% 13.67/13.84 tff(7480,plain,
% 13.67/13.84 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s38)) | always5(s38))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s38) | (~trans(s59, s38)))),
% 13.67/13.84 inference(transitivity,[status(thm)],[7479, 7477])).
% 13.67/13.84 tff(7481,plain,
% 13.67/13.84 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s38)) | always5(s38))),
% 13.67/13.84 inference(quant_inst,[status(thm)],[])).
% 13.67/13.84 tff(7482,plain,
% 13.67/13.84 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s38) | (~trans(s59, s38))),
% 13.67/13.84 inference(modus_ponens,[status(thm)],[7481, 7480])).
% 13.67/13.84 tff(7483,plain,
% 13.67/13.84 ($false),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7482, 5931, 3890, 6915, 7456])).
% 13.67/13.84 tff(7484,plain,(~trans(s59, s38)), inference(lemma,lemma(discharge,[]))).
% 13.67/13.84 tff(7485,plain,
% 13.67/13.84 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s34) | (~trans(s59, s34)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s34) | (~trans(s59, s34)))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7486,plain,
% 13.67/13.84 (((~always5(s59)) | (~trans(s59, s34)) | always5(s34)) <=> ((~always5(s59)) | always5(s34) | (~trans(s59, s34)))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7487,plain,
% 13.67/13.84 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s34)) | always5(s34))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s34) | (~trans(s59, s34))))),
% 13.67/13.84 inference(monotonicity,[status(thm)],[7486])).
% 13.67/13.84 tff(7488,plain,
% 13.67/13.84 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s34)) | always5(s34))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s34) | (~trans(s59, s34)))),
% 13.67/13.84 inference(transitivity,[status(thm)],[7487, 7485])).
% 13.67/13.84 tff(7489,plain,
% 13.67/13.84 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s34)) | always5(s34))),
% 13.67/13.84 inference(quant_inst,[status(thm)],[])).
% 13.67/13.84 tff(7490,plain,
% 13.67/13.84 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s34) | (~trans(s59, s34))),
% 13.67/13.84 inference(modus_ponens,[status(thm)],[7489, 7488])).
% 13.67/13.84 tff(7491,plain,
% 13.67/13.84 ($false),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7490, 5953, 3890, 6915, 7460])).
% 13.67/13.84 tff(7492,plain,(~trans(s59, s34)), inference(lemma,lemma(discharge,[]))).
% 13.67/13.84 tff(7493,assumption,(~always5(s39)), introduced(assumption)).
% 13.67/13.84 tff(7494,plain,
% 13.67/13.84 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s39) | (~trans(s59, s39)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s39) | (~trans(s59, s39)))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7495,plain,
% 13.67/13.84 (((~always5(s59)) | (~trans(s59, s39)) | always5(s39)) <=> ((~always5(s59)) | always5(s39) | (~trans(s59, s39)))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7496,plain,
% 13.67/13.84 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s39)) | always5(s39))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s39) | (~trans(s59, s39))))),
% 13.67/13.84 inference(monotonicity,[status(thm)],[7495])).
% 13.67/13.84 tff(7497,plain,
% 13.67/13.84 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s39)) | always5(s39))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s39) | (~trans(s59, s39)))),
% 13.67/13.84 inference(transitivity,[status(thm)],[7496, 7494])).
% 13.67/13.84 tff(7498,plain,
% 13.67/13.84 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s39)) | always5(s39))),
% 13.67/13.84 inference(quant_inst,[status(thm)],[])).
% 13.67/13.84 tff(7499,plain,
% 13.67/13.84 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s39) | (~trans(s59, s39))),
% 13.67/13.84 inference(modus_ponens,[status(thm)],[7498, 7497])).
% 13.67/13.84 tff(7500,plain,
% 13.67/13.84 ($false),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7499, 6283, 3890, 6915, 7493])).
% 13.67/13.84 tff(7501,plain,((~trans(s59, s39)) | always5(s39)), inference(lemma,lemma(discharge,[]))).
% 13.67/13.84 tff(7502,plain,
% 13.67/13.84 (~trans(s59, s39)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7501, 7455])).
% 13.67/13.84 tff(7503,plain,
% 13.67/13.84 (~always5(s25)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[4161, 7468])).
% 13.67/13.84 tff(7504,assumption,(~always5(s25)), introduced(assumption)).
% 13.67/13.84 tff(7505,plain,
% 13.67/13.84 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s25) | (~trans(s59, s25)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s25) | (~trans(s59, s25)))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7506,plain,
% 13.67/13.84 (((~always5(s59)) | (~trans(s59, s25)) | always5(s25)) <=> ((~always5(s59)) | always5(s25) | (~trans(s59, s25)))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7507,plain,
% 13.67/13.84 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s25)) | always5(s25))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s25) | (~trans(s59, s25))))),
% 13.67/13.84 inference(monotonicity,[status(thm)],[7506])).
% 13.67/13.84 tff(7508,plain,
% 13.67/13.84 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s25)) | always5(s25))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s25) | (~trans(s59, s25)))),
% 13.67/13.84 inference(transitivity,[status(thm)],[7507, 7505])).
% 13.67/13.84 tff(7509,plain,
% 13.67/13.84 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s25)) | always5(s25))),
% 13.67/13.84 inference(quant_inst,[status(thm)],[])).
% 13.67/13.84 tff(7510,plain,
% 13.67/13.84 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s25) | (~trans(s59, s25))),
% 13.67/13.84 inference(modus_ponens,[status(thm)],[7509, 7508])).
% 13.67/13.84 tff(7511,plain,
% 13.67/13.84 ($false),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7510, 5780, 3890, 6915, 7504])).
% 13.67/13.84 tff(7512,plain,((~trans(s59, s25)) | always5(s25)), inference(lemma,lemma(discharge,[]))).
% 13.67/13.84 tff(7513,plain,
% 13.67/13.84 (~trans(s59, s25)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7512, 7503])).
% 13.67/13.84 tff(7514,plain,
% 13.67/13.84 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s7)) | (~m_counter_cell_v_value(c_bit1, s7)) | m_counter_cell_v_carry_out(c_bit1, s7))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s7)) | (~m_counter_cell_v_value(c_bit1, s7)) | m_counter_cell_v_carry_out(c_bit1, s7))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7515,plain,
% 13.67/13.84 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s7)) | (~m_counter_cell_v_value(c_bit1, s7)) | m_counter_cell_v_carry_out(c_bit1, s7))),
% 13.67/13.84 inference(quant_inst,[status(thm)],[])).
% 13.67/13.84 tff(7516,plain,
% 13.67/13.84 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s7)) | (~m_counter_cell_v_value(c_bit1, s7)) | m_counter_cell_v_carry_out(c_bit1, s7)),
% 13.67/13.84 inference(modus_ponens,[status(thm)],[7515, 7514])).
% 13.67/13.84 tff(7517,plain,
% 13.67/13.84 ((~m_counter_cell_v_value(c_bit1, s7)) | m_counter_cell_v_carry_out(c_bit1, s7)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7516, 1390, 1714])).
% 13.67/13.84 tff(7518,plain,
% 13.67/13.84 (m_counter_cell_v_carry_out(c_bit1, s7)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7517, 1705])).
% 13.67/13.84 tff(7519,plain,
% 13.67/13.84 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s7)) | m_counter_cell_v_carry_in(c_bit2, s7))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s7)) | m_counter_cell_v_carry_in(c_bit2, s7))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7520,plain,
% 13.67/13.84 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s7)) | m_counter_cell_v_carry_in(c_bit2, s7))),
% 13.67/13.84 inference(quant_inst,[status(thm)],[])).
% 13.67/13.84 tff(7521,plain,
% 13.67/13.84 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s7)) | m_counter_cell_v_carry_in(c_bit2, s7)),
% 13.67/13.84 inference(modus_ponens,[status(thm)],[7520, 7519])).
% 13.67/13.84 tff(7522,plain,
% 13.67/13.84 (m_counter_cell_v_carry_in(c_bit2, s7)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7521, 3305, 7518])).
% 13.67/13.84 tff(7523,assumption,(~m_counter_cell_v_value(c_bit1, s4)), introduced(assumption)).
% 13.67/13.84 tff(7524,plain,
% 13.67/13.84 (~node2(c_bit1, s4)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[1631, 7523])).
% 13.67/13.84 tff(7525,plain,
% 13.67/13.84 (~m_counter_cell_v_value(c_bit1, s5)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[1643, 7524])).
% 13.67/13.84 tff(7526,plain,
% 13.67/13.84 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s5) | (~node4(c_bit1, s5)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s5) | (~node4(c_bit1, s5)))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7527,plain,
% 13.67/13.84 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s5) | (~node4(c_bit1, s5)))),
% 13.67/13.84 inference(quant_inst,[status(thm)],[])).
% 13.67/13.84 tff(7528,plain,
% 13.67/13.84 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s5) | (~node4(c_bit1, s5))),
% 13.67/13.84 inference(modus_ponens,[status(thm)],[7527, 7526])).
% 13.67/13.84 tff(7529,plain,
% 13.67/13.84 (~node4(c_bit1, s5)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7528, 1344, 7525])).
% 13.67/13.84 tff(7530,plain,
% 13.67/13.84 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s5)) | node4(c_bit1, s5))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s5)) | node4(c_bit1, s5))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7531,plain,
% 13.67/13.84 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s5)) | node4(c_bit1, s5))),
% 13.67/13.84 inference(quant_inst,[status(thm)],[])).
% 13.67/13.84 tff(7532,plain,
% 13.67/13.84 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s5)) | node4(c_bit1, s5)),
% 13.67/13.84 inference(modus_ponens,[status(thm)],[7531, 7530])).
% 13.67/13.84 tff(7533,plain,
% 13.67/13.84 (~m_counter_cell_v_carry_out(c_bit1, s5)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7532, 1359, 7529])).
% 13.67/13.84 tff(7534,plain,
% 13.67/13.84 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s5)) | m_counter_cell_v_carry_out(c_bit1, s5))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s5)) | m_counter_cell_v_carry_out(c_bit1, s5))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7535,plain,
% 13.67/13.84 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s5)) | m_counter_cell_v_carry_out(c_bit1, s5))),
% 13.67/13.84 inference(quant_inst,[status(thm)],[])).
% 13.67/13.84 tff(7536,plain,
% 13.67/13.84 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s5)) | m_counter_cell_v_carry_out(c_bit1, s5)),
% 13.67/13.84 inference(modus_ponens,[status(thm)],[7535, 7534])).
% 13.67/13.84 tff(7537,plain,
% 13.67/13.84 (~m_counter_cell_v_carry_in(c_bit2, s5)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7536, 3675, 7533])).
% 13.67/13.84 tff(7538,plain,
% 13.67/13.84 (~node1(c_bit1, s5)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[1660, 7525])).
% 13.67/13.84 tff(7539,plain,
% 13.67/13.84 (m_counter_cell_v_value(c_bit1, s6)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[1672, 7538])).
% 13.67/13.84 tff(7540,plain,
% 13.67/13.84 (~node1(c_bit1, s6)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[1692, 7539])).
% 13.67/13.84 tff(7541,plain,
% 13.67/13.84 (m_counter_cell_v_value(c_bit1, s7)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[1704, 7540])).
% 13.67/13.84 tff(7542,plain,
% 13.67/13.84 (m_counter_cell_v_carry_out(c_bit1, s7)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7517, 7541])).
% 13.67/13.84 tff(7543,plain,
% 13.67/13.84 (m_counter_cell_v_carry_in(c_bit2, s7)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7521, 3305, 7542])).
% 13.67/13.84 tff(7544,assumption,(node2(c_bit2, s7)), introduced(assumption)).
% 13.67/13.84 tff(7545,plain,
% 13.67/13.84 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit2, s7)) | (~m_counter_cell_v_value(c_bit2, s7)) | (~node2(c_bit2, s7)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit2, s7)) | (~m_counter_cell_v_value(c_bit2, s7)) | (~node2(c_bit2, s7)))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7546,plain,
% 13.67/13.84 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit2, s7)) | (~m_counter_cell_v_value(c_bit2, s7)) | (~node2(c_bit2, s7)))),
% 13.67/13.84 inference(quant_inst,[status(thm)],[])).
% 13.67/13.84 tff(7547,plain,
% 13.67/13.84 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit2, s7)) | (~m_counter_cell_v_value(c_bit2, s7)) | (~node2(c_bit2, s7))),
% 13.67/13.84 inference(modus_ponens,[status(thm)],[7546, 7545])).
% 13.67/13.84 tff(7548,plain,
% 13.67/13.84 ((~m_counter_cell_v_carry_in(c_bit2, s7)) | (~m_counter_cell_v_value(c_bit2, s7))),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7547, 93, 7544])).
% 13.67/13.84 tff(7549,plain,
% 13.67/13.84 (~m_counter_cell_v_value(c_bit2, s7)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7548, 7543])).
% 13.67/13.84 tff(7550,plain,
% 13.67/13.84 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s6, s7)) | node3(c_bit2, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s6, s7)) | node3(c_bit2, s6, s7))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7551,plain,
% 13.67/13.84 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s6, s7)) | node3(c_bit2, s6, s7))),
% 13.67/13.84 inference(quant_inst,[status(thm)],[])).
% 13.67/13.84 tff(7552,plain,
% 13.67/13.84 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s6, s7)) | node3(c_bit2, s6, s7)),
% 13.67/13.84 inference(modus_ponens,[status(thm)],[7551, 7550])).
% 13.67/13.84 tff(7553,plain,
% 13.67/13.84 (node3(c_bit2, s6, s7)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7552, 59, 253])).
% 13.67/13.84 tff(7554,plain,
% 13.67/13.84 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s6) | m_counter_cell_v_value(c_bit2, s7) | (~node3(c_bit2, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit2, s6) | m_counter_cell_v_value(c_bit2, s7) | (~node3(c_bit2, s6, s7)))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7555,plain,
% 13.67/13.84 ((node1(c_bit2, s6) | (~node3(c_bit2, s6, s7)) | m_counter_cell_v_value(c_bit2, s7)) <=> (node1(c_bit2, s6) | m_counter_cell_v_value(c_bit2, s7) | (~node3(c_bit2, s6, s7)))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7556,plain,
% 13.67/13.84 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s6) | (~node3(c_bit2, s6, s7)) | m_counter_cell_v_value(c_bit2, s7))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s6) | m_counter_cell_v_value(c_bit2, s7) | (~node3(c_bit2, s6, s7))))),
% 13.67/13.84 inference(monotonicity,[status(thm)],[7555])).
% 13.67/13.84 tff(7557,plain,
% 13.67/13.84 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s6) | (~node3(c_bit2, s6, s7)) | m_counter_cell_v_value(c_bit2, s7))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit2, s6) | m_counter_cell_v_value(c_bit2, s7) | (~node3(c_bit2, s6, s7)))),
% 13.67/13.84 inference(transitivity,[status(thm)],[7556, 7554])).
% 13.67/13.84 tff(7558,plain,
% 13.67/13.84 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s6) | (~node3(c_bit2, s6, s7)) | m_counter_cell_v_value(c_bit2, s7))),
% 13.67/13.84 inference(quant_inst,[status(thm)],[])).
% 13.67/13.84 tff(7559,plain,
% 13.67/13.84 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit2, s6) | m_counter_cell_v_value(c_bit2, s7) | (~node3(c_bit2, s6, s7))),
% 13.67/13.84 inference(modus_ponens,[status(thm)],[7558, 7557])).
% 13.67/13.84 tff(7560,plain,
% 13.67/13.84 (node1(c_bit2, s6) | m_counter_cell_v_value(c_bit2, s7)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7559, 73, 7553])).
% 13.67/13.84 tff(7561,plain,
% 13.67/13.84 (node1(c_bit2, s6)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7560, 7549])).
% 13.67/13.84 tff(7562,plain,
% 13.67/13.84 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | ((~node4(c_bit1, s6)) | m_counter_cell_v_carry_in(c_bit1, s6))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (~node4(c_bit1, s6)) | m_counter_cell_v_carry_in(c_bit1, s6))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7563,plain,
% 13.67/13.84 ((m_counter_cell_v_carry_in(c_bit1, s6) | (~node4(c_bit1, s6))) <=> ((~node4(c_bit1, s6)) | m_counter_cell_v_carry_in(c_bit1, s6))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7564,plain,
% 13.67/13.84 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s6) | (~node4(c_bit1, s6)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | ((~node4(c_bit1, s6)) | m_counter_cell_v_carry_in(c_bit1, s6)))),
% 13.67/13.84 inference(monotonicity,[status(thm)],[7563])).
% 13.67/13.84 tff(7565,plain,
% 13.67/13.84 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s6) | (~node4(c_bit1, s6)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (~node4(c_bit1, s6)) | m_counter_cell_v_carry_in(c_bit1, s6))),
% 13.67/13.84 inference(transitivity,[status(thm)],[7564, 7562])).
% 13.67/13.84 tff(7566,plain,
% 13.67/13.84 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s6) | (~node4(c_bit1, s6)))),
% 13.67/13.84 inference(quant_inst,[status(thm)],[])).
% 13.67/13.84 tff(7567,plain,
% 13.67/13.84 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (~node4(c_bit1, s6)) | m_counter_cell_v_carry_in(c_bit1, s6)),
% 13.67/13.84 inference(modus_ponens,[status(thm)],[7566, 7565])).
% 13.67/13.84 tff(7568,plain,
% 13.67/13.84 (~node4(c_bit1, s6)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7567, 2941, 1685])).
% 13.67/13.84 tff(7569,plain,
% 13.67/13.84 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s6)) | node4(c_bit1, s6))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s6)) | node4(c_bit1, s6))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7570,plain,
% 13.67/13.84 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s6)) | node4(c_bit1, s6))),
% 13.67/13.84 inference(quant_inst,[status(thm)],[])).
% 13.67/13.84 tff(7571,plain,
% 13.67/13.84 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s6)) | node4(c_bit1, s6)),
% 13.67/13.84 inference(modus_ponens,[status(thm)],[7570, 7569])).
% 13.67/13.84 tff(7572,plain,
% 13.67/13.84 (~m_counter_cell_v_carry_out(c_bit1, s6)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7571, 1359, 7568])).
% 13.67/13.84 tff(7573,plain,
% 13.67/13.84 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s6)) | m_counter_cell_v_carry_out(c_bit1, s6))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s6)) | m_counter_cell_v_carry_out(c_bit1, s6))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7574,plain,
% 13.67/13.84 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s6)) | m_counter_cell_v_carry_out(c_bit1, s6))),
% 13.67/13.84 inference(quant_inst,[status(thm)],[])).
% 13.67/13.84 tff(7575,plain,
% 13.67/13.84 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s6)) | m_counter_cell_v_carry_out(c_bit1, s6)),
% 13.67/13.84 inference(modus_ponens,[status(thm)],[7574, 7573])).
% 13.67/13.84 tff(7576,plain,
% 13.67/13.84 (~m_counter_cell_v_carry_in(c_bit2, s6)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7575, 3675, 7572])).
% 13.67/13.84 tff(7577,plain,
% 13.67/13.84 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s6) | (~m_counter_cell_v_value(c_bit2, s6)) | (~node1(c_bit2, s6)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s6) | (~m_counter_cell_v_value(c_bit2, s6)) | (~node1(c_bit2, s6)))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7578,plain,
% 13.67/13.84 (((~node1(c_bit2, s6)) | m_counter_cell_v_carry_in(c_bit2, s6) | (~m_counter_cell_v_value(c_bit2, s6))) <=> (m_counter_cell_v_carry_in(c_bit2, s6) | (~m_counter_cell_v_value(c_bit2, s6)) | (~node1(c_bit2, s6)))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.84 tff(7579,plain,
% 13.67/13.84 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s6)) | m_counter_cell_v_carry_in(c_bit2, s6) | (~m_counter_cell_v_value(c_bit2, s6)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s6) | (~m_counter_cell_v_value(c_bit2, s6)) | (~node1(c_bit2, s6))))),
% 13.67/13.84 inference(monotonicity,[status(thm)],[7578])).
% 13.67/13.84 tff(7580,plain,
% 13.67/13.84 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s6)) | m_counter_cell_v_carry_in(c_bit2, s6) | (~m_counter_cell_v_value(c_bit2, s6)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s6) | (~m_counter_cell_v_value(c_bit2, s6)) | (~node1(c_bit2, s6)))),
% 13.67/13.84 inference(transitivity,[status(thm)],[7579, 7577])).
% 13.67/13.84 tff(7581,plain,
% 13.67/13.84 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s6)) | m_counter_cell_v_carry_in(c_bit2, s6) | (~m_counter_cell_v_value(c_bit2, s6)))),
% 13.67/13.84 inference(quant_inst,[status(thm)],[])).
% 13.67/13.84 tff(7582,plain,
% 13.67/13.84 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s6) | (~m_counter_cell_v_value(c_bit2, s6)) | (~node1(c_bit2, s6))),
% 13.67/13.84 inference(modus_ponens,[status(thm)],[7581, 7580])).
% 13.67/13.84 tff(7583,plain,
% 13.67/13.84 ((~m_counter_cell_v_value(c_bit2, s6)) | (~node1(c_bit2, s6))),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7582, 1569, 7576])).
% 13.67/13.84 tff(7584,plain,
% 13.67/13.84 (~m_counter_cell_v_value(c_bit2, s6)),
% 13.67/13.84 inference(unit_resolution,[status(thm)],[7583, 7561])).
% 13.67/13.84 tff(7585,plain,
% 13.67/13.84 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s5, s6)) | node3(c_bit2, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s5, s6)) | node3(c_bit2, s5, s6))),
% 13.67/13.84 inference(rewrite,[status(thm)],[])).
% 13.67/13.85 tff(7586,plain,
% 13.67/13.85 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s5, s6)) | node3(c_bit2, s5, s6))),
% 13.67/13.85 inference(quant_inst,[status(thm)],[])).
% 13.67/13.85 tff(7587,plain,
% 13.67/13.85 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s5, s6)) | node3(c_bit2, s5, s6)),
% 13.67/13.85 inference(modus_ponens,[status(thm)],[7586, 7585])).
% 13.67/13.85 tff(7588,plain,
% 13.67/13.85 (node3(c_bit2, s5, s6)),
% 13.67/13.85 inference(unit_resolution,[status(thm)],[7587, 59, 224])).
% 13.67/13.85 tff(7589,plain,
% 13.67/13.85 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s5) | m_counter_cell_v_value(c_bit2, s6) | (~node3(c_bit2, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit2, s5) | m_counter_cell_v_value(c_bit2, s6) | (~node3(c_bit2, s5, s6)))),
% 13.67/13.85 inference(rewrite,[status(thm)],[])).
% 13.67/13.85 tff(7590,plain,
% 13.67/13.85 ((node1(c_bit2, s5) | (~node3(c_bit2, s5, s6)) | m_counter_cell_v_value(c_bit2, s6)) <=> (node1(c_bit2, s5) | m_counter_cell_v_value(c_bit2, s6) | (~node3(c_bit2, s5, s6)))),
% 13.67/13.85 inference(rewrite,[status(thm)],[])).
% 13.67/13.85 tff(7591,plain,
% 13.67/13.85 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s5) | (~node3(c_bit2, s5, s6)) | m_counter_cell_v_value(c_bit2, s6))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s5) | m_counter_cell_v_value(c_bit2, s6) | (~node3(c_bit2, s5, s6))))),
% 13.67/13.85 inference(monotonicity,[status(thm)],[7590])).
% 13.67/13.85 tff(7592,plain,
% 13.67/13.85 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s5) | (~node3(c_bit2, s5, s6)) | m_counter_cell_v_value(c_bit2, s6))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit2, s5) | m_counter_cell_v_value(c_bit2, s6) | (~node3(c_bit2, s5, s6)))),
% 13.67/13.85 inference(transitivity,[status(thm)],[7591, 7589])).
% 13.67/13.85 tff(7593,plain,
% 13.67/13.85 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s5) | (~node3(c_bit2, s5, s6)) | m_counter_cell_v_value(c_bit2, s6))),
% 13.67/13.85 inference(quant_inst,[status(thm)],[])).
% 13.67/13.85 tff(7594,plain,
% 13.67/13.85 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit2, s5) | m_counter_cell_v_value(c_bit2, s6) | (~node3(c_bit2, s5, s6))),
% 13.67/13.85 inference(modus_ponens,[status(thm)],[7593, 7592])).
% 13.67/13.85 tff(7595,plain,
% 13.67/13.85 (node1(c_bit2, s5) | m_counter_cell_v_value(c_bit2, s6)),
% 13.67/13.85 inference(unit_resolution,[status(thm)],[7594, 73, 7588])).
% 13.67/13.85 tff(7596,plain,
% 13.67/13.85 (node1(c_bit2, s5)),
% 13.67/13.85 inference(unit_resolution,[status(thm)],[7595, 7584])).
% 13.67/13.85 tff(7597,plain,
% 13.67/13.85 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s5) | (~m_counter_cell_v_value(c_bit2, s5)) | (~node1(c_bit2, s5)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s5) | (~m_counter_cell_v_value(c_bit2, s5)) | (~node1(c_bit2, s5)))),
% 13.67/13.85 inference(rewrite,[status(thm)],[])).
% 13.67/13.85 tff(7598,plain,
% 13.67/13.85 (((~node1(c_bit2, s5)) | m_counter_cell_v_carry_in(c_bit2, s5) | (~m_counter_cell_v_value(c_bit2, s5))) <=> (m_counter_cell_v_carry_in(c_bit2, s5) | (~m_counter_cell_v_value(c_bit2, s5)) | (~node1(c_bit2, s5)))),
% 13.67/13.85 inference(rewrite,[status(thm)],[])).
% 13.67/13.85 tff(7599,plain,
% 13.67/13.85 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s5)) | m_counter_cell_v_carry_in(c_bit2, s5) | (~m_counter_cell_v_value(c_bit2, s5)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s5) | (~m_counter_cell_v_value(c_bit2, s5)) | (~node1(c_bit2, s5))))),
% 13.67/13.85 inference(monotonicity,[status(thm)],[7598])).
% 13.70/13.85 tff(7600,plain,
% 13.70/13.85 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s5)) | m_counter_cell_v_carry_in(c_bit2, s5) | (~m_counter_cell_v_value(c_bit2, s5)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s5) | (~m_counter_cell_v_value(c_bit2, s5)) | (~node1(c_bit2, s5)))),
% 13.70/13.85 inference(transitivity,[status(thm)],[7599, 7597])).
% 13.70/13.85 tff(7601,plain,
% 13.70/13.85 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s5)) | m_counter_cell_v_carry_in(c_bit2, s5) | (~m_counter_cell_v_value(c_bit2, s5)))),
% 13.70/13.85 inference(quant_inst,[status(thm)],[])).
% 13.70/13.85 tff(7602,plain,
% 13.70/13.85 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s5) | (~m_counter_cell_v_value(c_bit2, s5)) | (~node1(c_bit2, s5))),
% 13.70/13.85 inference(modus_ponens,[status(thm)],[7601, 7600])).
% 13.70/13.85 tff(7603,plain,
% 13.70/13.85 (m_counter_cell_v_carry_in(c_bit2, s5) | (~m_counter_cell_v_value(c_bit2, s5))),
% 13.70/13.85 inference(unit_resolution,[status(thm)],[7602, 1569, 7596])).
% 13.70/13.85 tff(7604,plain,
% 13.70/13.85 (~m_counter_cell_v_value(c_bit2, s5)),
% 13.70/13.85 inference(unit_resolution,[status(thm)],[7603, 7537])).
% 13.70/13.85 tff(7605,plain,
% 13.70/13.85 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s4, s5)) | node3(c_bit2, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s4, s5)) | node3(c_bit2, s4, s5))),
% 13.70/13.85 inference(rewrite,[status(thm)],[])).
% 13.70/13.85 tff(7606,plain,
% 13.70/13.85 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s4, s5)) | node3(c_bit2, s4, s5))),
% 13.70/13.85 inference(quant_inst,[status(thm)],[])).
% 13.70/13.85 tff(7607,plain,
% 13.70/13.85 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s4, s5)) | node3(c_bit2, s4, s5)),
% 13.70/13.85 inference(modus_ponens,[status(thm)],[7606, 7605])).
% 13.70/13.85 tff(7608,plain,
% 13.70/13.85 (node3(c_bit2, s4, s5)),
% 13.70/13.85 inference(unit_resolution,[status(thm)],[7607, 59, 198])).
% 13.70/13.85 tff(7609,plain,
% 13.70/13.85 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s5) | node1(c_bit2, s4) | (~node3(c_bit2, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s5) | node1(c_bit2, s4) | (~node3(c_bit2, s4, s5)))),
% 13.70/13.85 inference(rewrite,[status(thm)],[])).
% 13.70/13.85 tff(7610,plain,
% 13.70/13.85 ((node1(c_bit2, s4) | (~node3(c_bit2, s4, s5)) | m_counter_cell_v_value(c_bit2, s5)) <=> (m_counter_cell_v_value(c_bit2, s5) | node1(c_bit2, s4) | (~node3(c_bit2, s4, s5)))),
% 13.70/13.85 inference(rewrite,[status(thm)],[])).
% 13.70/13.85 tff(7611,plain,
% 13.70/13.85 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s4) | (~node3(c_bit2, s4, s5)) | m_counter_cell_v_value(c_bit2, s5))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s5) | node1(c_bit2, s4) | (~node3(c_bit2, s4, s5))))),
% 13.70/13.85 inference(monotonicity,[status(thm)],[7610])).
% 13.70/13.85 tff(7612,plain,
% 13.70/13.85 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s4) | (~node3(c_bit2, s4, s5)) | m_counter_cell_v_value(c_bit2, s5))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s5) | node1(c_bit2, s4) | (~node3(c_bit2, s4, s5)))),
% 13.70/13.85 inference(transitivity,[status(thm)],[7611, 7609])).
% 13.70/13.85 tff(7613,plain,
% 13.70/13.85 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s4) | (~node3(c_bit2, s4, s5)) | m_counter_cell_v_value(c_bit2, s5))),
% 13.70/13.85 inference(quant_inst,[status(thm)],[])).
% 13.70/13.85 tff(7614,plain,
% 13.70/13.85 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s5) | node1(c_bit2, s4) | (~node3(c_bit2, s4, s5))),
% 13.70/13.85 inference(modus_ponens,[status(thm)],[7613, 7612])).
% 13.70/13.85 tff(7615,plain,
% 13.70/13.85 (m_counter_cell_v_value(c_bit2, s5) | node1(c_bit2, s4)),
% 13.70/13.85 inference(unit_resolution,[status(thm)],[7614, 73, 7608])).
% 13.70/13.85 tff(7616,plain,
% 13.70/13.85 (node1(c_bit2, s4)),
% 13.70/13.85 inference(unit_resolution,[status(thm)],[7615, 7604])).
% 13.70/13.85 tff(7617,plain,
% 13.70/13.85 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s4) | (~node4(c_bit1, s4)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s4) | (~node4(c_bit1, s4)))),
% 13.70/13.85 inference(rewrite,[status(thm)],[])).
% 13.70/13.85 tff(7618,plain,
% 13.70/13.85 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s4) | (~node4(c_bit1, s4)))),
% 13.70/13.85 inference(quant_inst,[status(thm)],[])).
% 13.70/13.85 tff(7619,plain,
% 13.70/13.85 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s4) | (~node4(c_bit1, s4))),
% 13.70/13.85 inference(modus_ponens,[status(thm)],[7618, 7617])).
% 13.70/13.85 tff(7620,plain,
% 13.70/13.85 (~node4(c_bit1, s4)),
% 13.70/13.85 inference(unit_resolution,[status(thm)],[7619, 2941, 1627])).
% 13.70/13.85 tff(7621,plain,
% 13.70/13.85 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s4)) | node4(c_bit1, s4))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s4)) | node4(c_bit1, s4))),
% 13.70/13.85 inference(rewrite,[status(thm)],[])).
% 13.70/13.85 tff(7622,plain,
% 13.70/13.85 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s4)) | node4(c_bit1, s4))),
% 13.70/13.85 inference(quant_inst,[status(thm)],[])).
% 13.70/13.85 tff(7623,plain,
% 13.70/13.85 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s4)) | node4(c_bit1, s4)),
% 13.70/13.85 inference(modus_ponens,[status(thm)],[7622, 7621])).
% 13.70/13.85 tff(7624,plain,
% 13.70/13.85 (~m_counter_cell_v_carry_out(c_bit1, s4)),
% 13.70/13.85 inference(unit_resolution,[status(thm)],[7623, 1359, 7620])).
% 13.70/13.85 tff(7625,plain,
% 13.70/13.85 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s4)) | m_counter_cell_v_carry_out(c_bit1, s4))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s4)) | m_counter_cell_v_carry_out(c_bit1, s4))),
% 13.70/13.85 inference(rewrite,[status(thm)],[])).
% 13.70/13.85 tff(7626,plain,
% 13.70/13.85 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s4)) | m_counter_cell_v_carry_out(c_bit1, s4))),
% 13.70/13.85 inference(quant_inst,[status(thm)],[])).
% 13.70/13.85 tff(7627,plain,
% 13.70/13.85 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s4)) | m_counter_cell_v_carry_out(c_bit1, s4)),
% 13.70/13.85 inference(modus_ponens,[status(thm)],[7626, 7625])).
% 13.70/13.85 tff(7628,plain,
% 13.70/13.85 (~m_counter_cell_v_carry_in(c_bit2, s4)),
% 13.70/13.85 inference(unit_resolution,[status(thm)],[7627, 3675, 7624])).
% 13.70/13.85 tff(7629,plain,
% 13.70/13.85 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s4)) | (~m_counter_cell_v_value(c_bit2, s4)) | m_counter_cell_v_carry_in(c_bit2, s4))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (~node1(c_bit2, s4)) | (~m_counter_cell_v_value(c_bit2, s4)) | m_counter_cell_v_carry_in(c_bit2, s4))),
% 13.70/13.85 inference(rewrite,[status(thm)],[])).
% 13.70/13.85 tff(7630,plain,
% 13.70/13.85 (((~node1(c_bit2, s4)) | m_counter_cell_v_carry_in(c_bit2, s4) | (~m_counter_cell_v_value(c_bit2, s4))) <=> ((~node1(c_bit2, s4)) | (~m_counter_cell_v_value(c_bit2, s4)) | m_counter_cell_v_carry_in(c_bit2, s4))),
% 13.70/13.85 inference(rewrite,[status(thm)],[])).
% 13.70/13.85 tff(7631,plain,
% 13.70/13.85 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s4)) | m_counter_cell_v_carry_in(c_bit2, s4) | (~m_counter_cell_v_value(c_bit2, s4)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s4)) | (~m_counter_cell_v_value(c_bit2, s4)) | m_counter_cell_v_carry_in(c_bit2, s4)))),
% 13.70/13.85 inference(monotonicity,[status(thm)],[7630])).
% 13.70/13.85 tff(7632,plain,
% 13.70/13.85 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s4)) | m_counter_cell_v_carry_in(c_bit2, s4) | (~m_counter_cell_v_value(c_bit2, s4)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (~node1(c_bit2, s4)) | (~m_counter_cell_v_value(c_bit2, s4)) | m_counter_cell_v_carry_in(c_bit2, s4))),
% 13.70/13.85 inference(transitivity,[status(thm)],[7631, 7629])).
% 13.70/13.85 tff(7633,plain,
% 13.70/13.85 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s4)) | m_counter_cell_v_carry_in(c_bit2, s4) | (~m_counter_cell_v_value(c_bit2, s4)))),
% 13.70/13.85 inference(quant_inst,[status(thm)],[])).
% 13.70/13.85 tff(7634,plain,
% 13.70/13.85 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (~node1(c_bit2, s4)) | (~m_counter_cell_v_value(c_bit2, s4)) | m_counter_cell_v_carry_in(c_bit2, s4)),
% 13.70/13.85 inference(modus_ponens,[status(thm)],[7633, 7632])).
% 13.70/13.85 tff(7635,plain,
% 13.70/13.85 ((~node1(c_bit2, s4)) | (~m_counter_cell_v_value(c_bit2, s4))),
% 13.70/13.85 inference(unit_resolution,[status(thm)],[7634, 1569, 7628])).
% 13.70/13.85 tff(7636,plain,
% 13.70/13.85 (~m_counter_cell_v_value(c_bit2, s4)),
% 13.70/13.85 inference(unit_resolution,[status(thm)],[7635, 7616])).
% 13.70/13.85 tff(7637,plain,
% 13.70/13.85 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s3, s4)) | node3(c_bit2, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s3, s4)) | node3(c_bit2, s3, s4))),
% 13.70/13.85 inference(rewrite,[status(thm)],[])).
% 13.70/13.85 tff(7638,plain,
% 13.70/13.85 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s3, s4)) | node3(c_bit2, s3, s4))),
% 13.70/13.85 inference(quant_inst,[status(thm)],[])).
% 13.70/13.85 tff(7639,plain,
% 13.70/13.85 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s3, s4)) | node3(c_bit2, s3, s4)),
% 13.70/13.85 inference(modus_ponens,[status(thm)],[7638, 7637])).
% 13.70/13.85 tff(7640,plain,
% 13.70/13.85 (node3(c_bit2, s3, s4)),
% 13.70/13.85 inference(unit_resolution,[status(thm)],[7639, 59, 169])).
% 13.70/13.85 tff(7641,plain,
% 13.70/13.85 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | ((~node3(c_bit2, s3, s4)) | m_counter_cell_v_value(c_bit2, s4) | node1(c_bit2, s3))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (~node3(c_bit2, s3, s4)) | m_counter_cell_v_value(c_bit2, s4) | node1(c_bit2, s3))),
% 13.70/13.85 inference(rewrite,[status(thm)],[])).
% 13.70/13.85 tff(7642,plain,
% 13.70/13.85 ((node1(c_bit2, s3) | (~node3(c_bit2, s3, s4)) | m_counter_cell_v_value(c_bit2, s4)) <=> ((~node3(c_bit2, s3, s4)) | m_counter_cell_v_value(c_bit2, s4) | node1(c_bit2, s3))),
% 13.70/13.85 inference(rewrite,[status(thm)],[])).
% 13.70/13.85 tff(7643,plain,
% 13.70/13.85 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s3) | (~node3(c_bit2, s3, s4)) | m_counter_cell_v_value(c_bit2, s4))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | ((~node3(c_bit2, s3, s4)) | m_counter_cell_v_value(c_bit2, s4) | node1(c_bit2, s3)))),
% 13.70/13.85 inference(monotonicity,[status(thm)],[7642])).
% 13.70/13.85 tff(7644,plain,
% 13.70/13.85 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s3) | (~node3(c_bit2, s3, s4)) | m_counter_cell_v_value(c_bit2, s4))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (~node3(c_bit2, s3, s4)) | m_counter_cell_v_value(c_bit2, s4) | node1(c_bit2, s3))),
% 13.70/13.85 inference(transitivity,[status(thm)],[7643, 7641])).
% 13.70/13.85 tff(7645,plain,
% 13.70/13.85 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s3) | (~node3(c_bit2, s3, s4)) | m_counter_cell_v_value(c_bit2, s4))),
% 13.70/13.85 inference(quant_inst,[status(thm)],[])).
% 13.70/13.85 tff(7646,plain,
% 13.70/13.85 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (~node3(c_bit2, s3, s4)) | m_counter_cell_v_value(c_bit2, s4) | node1(c_bit2, s3)),
% 13.70/13.85 inference(modus_ponens,[status(thm)],[7645, 7644])).
% 13.70/13.85 tff(7647,plain,
% 13.70/13.85 (m_counter_cell_v_value(c_bit2, s4) | node1(c_bit2, s3)),
% 13.70/13.85 inference(unit_resolution,[status(thm)],[7646, 73, 7640])).
% 13.70/13.85 tff(7648,plain,
% 13.70/13.85 (node1(c_bit2, s3)),
% 13.70/13.85 inference(unit_resolution,[status(thm)],[7647, 7636])).
% 13.70/13.85 tff(7649,plain,
% 13.70/13.85 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s4) | (~node3(c_bit1, s3, s4)) | node1(c_bit1, s3))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s4) | (~node3(c_bit1, s3, s4)) | node1(c_bit1, s3))),
% 13.70/13.85 inference(rewrite,[status(thm)],[])).
% 13.70/13.85 tff(7650,plain,
% 13.70/13.85 ((node1(c_bit1, s3) | (~node3(c_bit1, s3, s4)) | m_counter_cell_v_value(c_bit1, s4)) <=> (m_counter_cell_v_value(c_bit1, s4) | (~node3(c_bit1, s3, s4)) | node1(c_bit1, s3))),
% 13.70/13.85 inference(rewrite,[status(thm)],[])).
% 13.70/13.85 tff(7651,plain,
% 13.70/13.85 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s3) | (~node3(c_bit1, s3, s4)) | m_counter_cell_v_value(c_bit1, s4))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s4) | (~node3(c_bit1, s3, s4)) | node1(c_bit1, s3)))),
% 13.70/13.85 inference(monotonicity,[status(thm)],[7650])).
% 13.70/13.85 tff(7652,plain,
% 13.70/13.85 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s3) | (~node3(c_bit1, s3, s4)) | m_counter_cell_v_value(c_bit1, s4))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s4) | (~node3(c_bit1, s3, s4)) | node1(c_bit1, s3))),
% 13.70/13.85 inference(transitivity,[status(thm)],[7651, 7649])).
% 13.70/13.85 tff(7653,plain,
% 13.70/13.85 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s3) | (~node3(c_bit1, s3, s4)) | m_counter_cell_v_value(c_bit1, s4))),
% 13.70/13.85 inference(quant_inst,[status(thm)],[])).
% 13.70/13.85 tff(7654,plain,
% 13.70/13.85 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s4) | (~node3(c_bit1, s3, s4)) | node1(c_bit1, s3)),
% 13.70/13.85 inference(modus_ponens,[status(thm)],[7653, 7652])).
% 13.70/13.85 tff(7655,plain,
% 13.70/13.85 (m_counter_cell_v_value(c_bit1, s4) | node1(c_bit1, s3)),
% 13.70/13.85 inference(unit_resolution,[status(thm)],[7654, 73, 1607])).
% 13.70/13.85 tff(7656,plain,
% 13.70/13.85 (node1(c_bit1, s3)),
% 13.70/13.85 inference(unit_resolution,[status(thm)],[7655, 7523])).
% 13.70/13.85 tff(7657,plain,
% 13.70/13.85 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (m_counter_cell_v_value(c_bit1, s3) | (~m_counter_cell_v_carry_in(c_bit1, s3)) | (~node1(c_bit1, s3)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | m_counter_cell_v_value(c_bit1, s3) | (~m_counter_cell_v_carry_in(c_bit1, s3)) | (~node1(c_bit1, s3)))),
% 13.70/13.85 inference(rewrite,[status(thm)],[])).
% 13.70/13.85 tff(7658,plain,
% 13.70/13.85 (((~node1(c_bit1, s3)) | (~m_counter_cell_v_carry_in(c_bit1, s3)) | m_counter_cell_v_value(c_bit1, s3)) <=> (m_counter_cell_v_value(c_bit1, s3) | (~m_counter_cell_v_carry_in(c_bit1, s3)) | (~node1(c_bit1, s3)))),
% 13.70/13.85 inference(rewrite,[status(thm)],[])).
% 13.70/13.85 tff(7659,plain,
% 13.70/13.85 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s3)) | (~m_counter_cell_v_carry_in(c_bit1, s3)) | m_counter_cell_v_value(c_bit1, s3))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (m_counter_cell_v_value(c_bit1, s3) | (~m_counter_cell_v_carry_in(c_bit1, s3)) | (~node1(c_bit1, s3))))),
% 13.70/13.85 inference(monotonicity,[status(thm)],[7658])).
% 13.70/13.85 tff(7660,plain,
% 13.70/13.85 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s3)) | (~m_counter_cell_v_carry_in(c_bit1, s3)) | m_counter_cell_v_value(c_bit1, s3))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | m_counter_cell_v_value(c_bit1, s3) | (~m_counter_cell_v_carry_in(c_bit1, s3)) | (~node1(c_bit1, s3)))),
% 13.70/13.85 inference(transitivity,[status(thm)],[7659, 7657])).
% 13.70/13.85 tff(7661,plain,
% 13.70/13.85 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s3)) | (~m_counter_cell_v_carry_in(c_bit1, s3)) | m_counter_cell_v_value(c_bit1, s3))),
% 13.70/13.85 inference(quant_inst,[status(thm)],[])).
% 13.70/13.85 tff(7662,plain,
% 13.70/13.85 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | m_counter_cell_v_value(c_bit1, s3) | (~m_counter_cell_v_carry_in(c_bit1, s3)) | (~node1(c_bit1, s3))),
% 13.70/13.85 inference(modus_ponens,[status(thm)],[7661, 7660])).
% 13.70/13.85 tff(7663,plain,
% 13.70/13.85 (m_counter_cell_v_value(c_bit1, s3) | (~node1(c_bit1, s3))),
% 13.70/13.85 inference(unit_resolution,[status(thm)],[7662, 30, 1598])).
% 13.70/13.85 tff(7664,plain,
% 13.70/13.85 (m_counter_cell_v_value(c_bit1, s3)),
% 13.70/13.85 inference(unit_resolution,[status(thm)],[7663, 7656])).
% 13.70/13.85 tff(7665,plain,
% 13.70/13.85 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~node3(c_bit1, s2, s3)) | node2(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s3)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~node3(c_bit1, s2, s3)) | node2(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s3)))),
% 13.70/13.85 inference(rewrite,[status(thm)],[])).
% 13.70/13.85 tff(7666,plain,
% 13.70/13.85 ((node2(c_bit1, s2) | (~node3(c_bit1, s2, s3)) | (~m_counter_cell_v_value(c_bit1, s3))) <=> ((~node3(c_bit1, s2, s3)) | node2(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s3)))),
% 13.70/13.85 inference(rewrite,[status(thm)],[])).
% 13.70/13.85 tff(7667,plain,
% 13.70/13.85 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s2) | (~node3(c_bit1, s2, s3)) | (~m_counter_cell_v_value(c_bit1, s3)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~node3(c_bit1, s2, s3)) | node2(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s3))))),
% 13.70/13.85 inference(monotonicity,[status(thm)],[7666])).
% 13.70/13.85 tff(7668,plain,
% 13.70/13.85 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s2) | (~node3(c_bit1, s2, s3)) | (~m_counter_cell_v_value(c_bit1, s3)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~node3(c_bit1, s2, s3)) | node2(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s3)))),
% 13.70/13.85 inference(transitivity,[status(thm)],[7667, 7665])).
% 13.70/13.85 tff(7669,plain,
% 13.70/13.85 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s2) | (~node3(c_bit1, s2, s3)) | (~m_counter_cell_v_value(c_bit1, s3)))),
% 13.70/13.85 inference(quant_inst,[status(thm)],[])).
% 13.70/13.85 tff(7670,plain,
% 13.70/13.85 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~node3(c_bit1, s2, s3)) | node2(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s3))),
% 13.70/13.85 inference(modus_ponens,[status(thm)],[7669, 7668])).
% 13.70/13.85 tff(7671,plain,
% 13.70/13.85 (node2(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s3))),
% 13.70/13.85 inference(unit_resolution,[status(thm)],[7670, 121, 1581])).
% 13.70/13.85 tff(7672,plain,
% 13.70/13.85 (node2(c_bit1, s2)),
% 13.70/13.85 inference(unit_resolution,[status(thm)],[7671, 7664])).
% 13.70/13.85 tff(7673,plain,
% 13.70/13.85 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_value(c_bit1, s2) | (~node2(c_bit1, s2)) | m_counter_cell_v_carry_in(c_bit1, s2))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_value(c_bit1, s2) | (~node2(c_bit1, s2)) | m_counter_cell_v_carry_in(c_bit1, s2))),
% 13.70/13.85 inference(rewrite,[status(thm)],[])).
% 13.70/13.85 tff(7674,plain,
% 13.70/13.85 ((m_counter_cell_v_carry_in(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s2) | (~node2(c_bit1, s2))) <=> (m_counter_cell_v_value(c_bit1, s2) | (~node2(c_bit1, s2)) | m_counter_cell_v_carry_in(c_bit1, s2))),
% 13.70/13.85 inference(rewrite,[status(thm)],[])).
% 13.70/13.85 tff(7675,plain,
% 13.70/13.85 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s2) | (~node2(c_bit1, s2)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_value(c_bit1, s2) | (~node2(c_bit1, s2)) | m_counter_cell_v_carry_in(c_bit1, s2)))),
% 13.70/13.85 inference(monotonicity,[status(thm)],[7674])).
% 13.70/13.85 tff(7676,plain,
% 13.70/13.85 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s2) | (~node2(c_bit1, s2)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_value(c_bit1, s2) | (~node2(c_bit1, s2)) | m_counter_cell_v_carry_in(c_bit1, s2))),
% 13.70/13.85 inference(transitivity,[status(thm)],[7675, 7673])).
% 13.70/13.85 tff(7677,plain,
% 13.70/13.85 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s2) | (~node2(c_bit1, s2)))),
% 13.70/13.85 inference(quant_inst,[status(thm)],[])).
% 13.70/13.85 tff(7678,plain,
% 13.70/13.85 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_value(c_bit1, s2) | (~node2(c_bit1, s2)) | m_counter_cell_v_carry_in(c_bit1, s2)),
% 13.70/13.85 inference(modus_ponens,[status(thm)],[7677, 7676])).
% 13.70/13.85 tff(7679,plain,
% 13.70/13.85 (m_counter_cell_v_value(c_bit1, s2) | (~node2(c_bit1, s2))),
% 13.70/13.85 inference(unit_resolution,[status(thm)],[7678, 1498, 1559])).
% 13.70/13.85 tff(7680,plain,
% 13.70/13.85 (m_counter_cell_v_value(c_bit1, s2)),
% 13.70/13.85 inference(unit_resolution,[status(thm)],[7679, 7672])).
% 13.70/13.85 tff(7681,plain,
% 13.70/13.85 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s2)) | node2(c_bit1, s1) | (~node3(c_bit1, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s2)) | node2(c_bit1, s1) | (~node3(c_bit1, s1, s2)))),
% 13.70/13.85 inference(rewrite,[status(thm)],[])).
% 13.70/13.85 tff(7682,plain,
% 13.70/13.85 ((node2(c_bit1, s1) | (~node3(c_bit1, s1, s2)) | (~m_counter_cell_v_value(c_bit1, s2))) <=> ((~m_counter_cell_v_value(c_bit1, s2)) | node2(c_bit1, s1) | (~node3(c_bit1, s1, s2)))),
% 13.70/13.85 inference(rewrite,[status(thm)],[])).
% 13.70/13.85 tff(7683,plain,
% 13.70/13.85 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s1) | (~node3(c_bit1, s1, s2)) | (~m_counter_cell_v_value(c_bit1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s2)) | node2(c_bit1, s1) | (~node3(c_bit1, s1, s2))))),
% 13.70/13.85 inference(monotonicity,[status(thm)],[7682])).
% 13.70/13.85 tff(7684,plain,
% 13.70/13.85 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s1) | (~node3(c_bit1, s1, s2)) | (~m_counter_cell_v_value(c_bit1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s2)) | node2(c_bit1, s1) | (~node3(c_bit1, s1, s2)))),
% 13.70/13.86 inference(transitivity,[status(thm)],[7683, 7681])).
% 13.70/13.86 tff(7685,plain,
% 13.70/13.86 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s1) | (~node3(c_bit1, s1, s2)) | (~m_counter_cell_v_value(c_bit1, s2)))),
% 13.70/13.86 inference(quant_inst,[status(thm)],[])).
% 13.70/13.86 tff(7686,plain,
% 13.70/13.86 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s2)) | node2(c_bit1, s1) | (~node3(c_bit1, s1, s2))),
% 13.70/13.86 inference(modus_ponens,[status(thm)],[7685, 7684])).
% 13.70/13.86 tff(7687,plain,
% 13.70/13.86 ((~m_counter_cell_v_value(c_bit1, s2)) | node2(c_bit1, s1)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7686, 121, 1539])).
% 13.70/13.86 tff(7688,plain,
% 13.70/13.86 (node2(c_bit1, s1)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7687, 7680])).
% 13.70/13.86 tff(7689,plain,
% 13.70/13.86 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s1)) | (~m_counter_cell_v_value(c_bit1, s1)) | (~node2(c_bit1, s1)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s1)) | (~m_counter_cell_v_value(c_bit1, s1)) | (~node2(c_bit1, s1)))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7690,plain,
% 13.70/13.86 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s1)) | (~m_counter_cell_v_value(c_bit1, s1)) | (~node2(c_bit1, s1)))),
% 13.70/13.86 inference(quant_inst,[status(thm)],[])).
% 13.70/13.86 tff(7691,plain,
% 13.70/13.86 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s1)) | (~m_counter_cell_v_value(c_bit1, s1)) | (~node2(c_bit1, s1))),
% 13.70/13.86 inference(modus_ponens,[status(thm)],[7690, 7689])).
% 13.70/13.86 tff(7692,plain,
% 13.70/13.86 ((~m_counter_cell_v_value(c_bit1, s1)) | (~node2(c_bit1, s1))),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7691, 93, 1527])).
% 13.70/13.86 tff(7693,plain,
% 13.70/13.86 (~m_counter_cell_v_value(c_bit1, s1)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7692, 7688])).
% 13.70/13.86 tff(7694,plain,
% 13.70/13.86 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s1) | (~node4(c_bit1, s1)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s1) | (~node4(c_bit1, s1)))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7695,plain,
% 13.70/13.86 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s1) | (~node4(c_bit1, s1)))),
% 13.70/13.86 inference(quant_inst,[status(thm)],[])).
% 13.70/13.86 tff(7696,plain,
% 13.70/13.86 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s1) | (~node4(c_bit1, s1))),
% 13.70/13.86 inference(modus_ponens,[status(thm)],[7695, 7694])).
% 13.70/13.86 tff(7697,plain,
% 13.70/13.86 (~node4(c_bit1, s1)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7696, 1344, 7693])).
% 13.70/13.86 tff(7698,plain,
% 13.70/13.86 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s1)) | node4(c_bit1, s1))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s1)) | node4(c_bit1, s1))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7699,plain,
% 13.70/13.86 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s1)) | node4(c_bit1, s1))),
% 13.70/13.86 inference(quant_inst,[status(thm)],[])).
% 13.70/13.86 tff(7700,plain,
% 13.70/13.86 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s1)) | node4(c_bit1, s1)),
% 13.70/13.86 inference(modus_ponens,[status(thm)],[7699, 7698])).
% 13.70/13.86 tff(7701,plain,
% 13.70/13.86 (~m_counter_cell_v_carry_out(c_bit1, s1)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7700, 1359, 7697])).
% 13.70/13.86 tff(7702,plain,
% 13.70/13.86 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s1)) | m_counter_cell_v_carry_out(c_bit1, s1))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s1)) | m_counter_cell_v_carry_out(c_bit1, s1))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7703,plain,
% 13.70/13.86 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s1)) | m_counter_cell_v_carry_out(c_bit1, s1))),
% 13.70/13.86 inference(quant_inst,[status(thm)],[])).
% 13.70/13.86 tff(7704,plain,
% 13.70/13.86 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s1)) | m_counter_cell_v_carry_out(c_bit1, s1)),
% 13.70/13.86 inference(modus_ponens,[status(thm)],[7703, 7702])).
% 13.70/13.86 tff(7705,plain,
% 13.70/13.86 (~m_counter_cell_v_carry_in(c_bit2, s1)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7704, 3675, 7701])).
% 13.70/13.86 tff(7706,assumption,(m_counter_cell_v_value(c_bit2, s0)), introduced(assumption)).
% 13.70/13.86 tff(7707,plain,
% 13.70/13.86 ((~![I0: $i] : (~m_counter_cell_v_value(I0, s0))) | (~m_counter_cell_v_value(c_bit2, s0))),
% 13.70/13.86 inference(quant_inst,[status(thm)],[])).
% 13.70/13.86 tff(7708,plain,
% 13.70/13.86 ($false),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7707, 8, 7706])).
% 13.70/13.86 tff(7709,plain,(~m_counter_cell_v_value(c_bit2, s0)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.86 tff(7710,plain,
% 13.70/13.86 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | ((~node4(c_bit1, s0)) | m_counter_cell_v_carry_in(c_bit1, s0))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (~node4(c_bit1, s0)) | m_counter_cell_v_carry_in(c_bit1, s0))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7711,plain,
% 13.70/13.86 ((m_counter_cell_v_carry_in(c_bit1, s0) | (~node4(c_bit1, s0))) <=> ((~node4(c_bit1, s0)) | m_counter_cell_v_carry_in(c_bit1, s0))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7712,plain,
% 13.70/13.86 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s0) | (~node4(c_bit1, s0)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | ((~node4(c_bit1, s0)) | m_counter_cell_v_carry_in(c_bit1, s0)))),
% 13.70/13.86 inference(monotonicity,[status(thm)],[7711])).
% 13.70/13.86 tff(7713,plain,
% 13.70/13.86 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s0) | (~node4(c_bit1, s0)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (~node4(c_bit1, s0)) | m_counter_cell_v_carry_in(c_bit1, s0))),
% 13.70/13.86 inference(transitivity,[status(thm)],[7712, 7710])).
% 13.70/13.86 tff(7714,plain,
% 13.70/13.86 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s0) | (~node4(c_bit1, s0)))),
% 13.70/13.86 inference(quant_inst,[status(thm)],[])).
% 13.70/13.86 tff(7715,plain,
% 13.70/13.86 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (~node4(c_bit1, s0)) | m_counter_cell_v_carry_in(c_bit1, s0)),
% 13.70/13.86 inference(modus_ponens,[status(thm)],[7714, 7713])).
% 13.70/13.86 tff(7716,plain,
% 13.70/13.86 (~node4(c_bit1, s0)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7715, 2941, 1488])).
% 13.70/13.86 tff(7717,plain,
% 13.70/13.86 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s0)) | node4(c_bit1, s0))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s0)) | node4(c_bit1, s0))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7718,plain,
% 13.70/13.86 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s0)) | node4(c_bit1, s0))),
% 13.70/13.86 inference(quant_inst,[status(thm)],[])).
% 13.70/13.86 tff(7719,plain,
% 13.70/13.86 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s0)) | node4(c_bit1, s0)),
% 13.70/13.86 inference(modus_ponens,[status(thm)],[7718, 7717])).
% 13.70/13.86 tff(7720,plain,
% 13.70/13.86 (~m_counter_cell_v_carry_out(c_bit1, s0)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7719, 1359, 7716])).
% 13.70/13.86 tff(7721,plain,
% 13.70/13.86 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s0)) | m_counter_cell_v_carry_out(c_bit1, s0))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s0)) | m_counter_cell_v_carry_out(c_bit1, s0))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7722,plain,
% 13.70/13.86 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s0)) | m_counter_cell_v_carry_out(c_bit1, s0))),
% 13.70/13.86 inference(quant_inst,[status(thm)],[])).
% 13.70/13.86 tff(7723,plain,
% 13.70/13.86 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s0)) | m_counter_cell_v_carry_out(c_bit1, s0)),
% 13.70/13.86 inference(modus_ponens,[status(thm)],[7722, 7721])).
% 13.70/13.86 tff(7724,plain,
% 13.70/13.86 (~m_counter_cell_v_carry_in(c_bit2, s0)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7723, 3675, 7720])).
% 13.70/13.86 tff(7725,plain,
% 13.70/13.86 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | ((~node2(c_bit2, s0)) | m_counter_cell_v_value(c_bit2, s0) | m_counter_cell_v_carry_in(c_bit2, s0))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (~node2(c_bit2, s0)) | m_counter_cell_v_value(c_bit2, s0) | m_counter_cell_v_carry_in(c_bit2, s0))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7726,plain,
% 13.70/13.86 ((m_counter_cell_v_carry_in(c_bit2, s0) | m_counter_cell_v_value(c_bit2, s0) | (~node2(c_bit2, s0))) <=> ((~node2(c_bit2, s0)) | m_counter_cell_v_value(c_bit2, s0) | m_counter_cell_v_carry_in(c_bit2, s0))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7727,plain,
% 13.70/13.86 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s0) | m_counter_cell_v_value(c_bit2, s0) | (~node2(c_bit2, s0)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | ((~node2(c_bit2, s0)) | m_counter_cell_v_value(c_bit2, s0) | m_counter_cell_v_carry_in(c_bit2, s0)))),
% 13.70/13.86 inference(monotonicity,[status(thm)],[7726])).
% 13.70/13.86 tff(7728,plain,
% 13.70/13.86 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s0) | m_counter_cell_v_value(c_bit2, s0) | (~node2(c_bit2, s0)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (~node2(c_bit2, s0)) | m_counter_cell_v_value(c_bit2, s0) | m_counter_cell_v_carry_in(c_bit2, s0))),
% 13.70/13.86 inference(transitivity,[status(thm)],[7727, 7725])).
% 13.70/13.86 tff(7729,plain,
% 13.70/13.86 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s0) | m_counter_cell_v_value(c_bit2, s0) | (~node2(c_bit2, s0)))),
% 13.70/13.86 inference(quant_inst,[status(thm)],[])).
% 13.70/13.86 tff(7730,plain,
% 13.70/13.86 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (~node2(c_bit2, s0)) | m_counter_cell_v_value(c_bit2, s0) | m_counter_cell_v_carry_in(c_bit2, s0)),
% 13.70/13.86 inference(modus_ponens,[status(thm)],[7729, 7728])).
% 13.70/13.86 tff(7731,plain,
% 13.70/13.86 ((~node2(c_bit2, s0)) | m_counter_cell_v_value(c_bit2, s0)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7730, 1498, 7724])).
% 13.70/13.86 tff(7732,plain,
% 13.70/13.86 (~node2(c_bit2, s0)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7731, 7709])).
% 13.70/13.86 tff(7733,plain,
% 13.70/13.86 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s0, s1)) | node3(c_bit2, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s0, s1)) | node3(c_bit2, s0, s1))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7734,plain,
% 13.70/13.86 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s0, s1)) | node3(c_bit2, s0, s1))),
% 13.70/13.86 inference(quant_inst,[status(thm)],[])).
% 13.70/13.86 tff(7735,plain,
% 13.70/13.86 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s0, s1)) | node3(c_bit2, s0, s1)),
% 13.70/13.86 inference(modus_ponens,[status(thm)],[7734, 7733])).
% 13.70/13.86 tff(7736,plain,
% 13.70/13.86 (node3(c_bit2, s0, s1)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7735, 59, 52])).
% 13.70/13.86 tff(7737,plain,
% 13.70/13.86 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s0) | (~m_counter_cell_v_value(c_bit2, s1)) | (~node3(c_bit2, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit2, s0) | (~m_counter_cell_v_value(c_bit2, s1)) | (~node3(c_bit2, s0, s1)))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7738,plain,
% 13.70/13.86 ((node2(c_bit2, s0) | (~node3(c_bit2, s0, s1)) | (~m_counter_cell_v_value(c_bit2, s1))) <=> (node2(c_bit2, s0) | (~m_counter_cell_v_value(c_bit2, s1)) | (~node3(c_bit2, s0, s1)))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7739,plain,
% 13.70/13.86 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s0) | (~node3(c_bit2, s0, s1)) | (~m_counter_cell_v_value(c_bit2, s1)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s0) | (~m_counter_cell_v_value(c_bit2, s1)) | (~node3(c_bit2, s0, s1))))),
% 13.70/13.86 inference(monotonicity,[status(thm)],[7738])).
% 13.70/13.86 tff(7740,plain,
% 13.70/13.86 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s0) | (~node3(c_bit2, s0, s1)) | (~m_counter_cell_v_value(c_bit2, s1)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit2, s0) | (~m_counter_cell_v_value(c_bit2, s1)) | (~node3(c_bit2, s0, s1)))),
% 13.70/13.86 inference(transitivity,[status(thm)],[7739, 7737])).
% 13.70/13.86 tff(7741,plain,
% 13.70/13.86 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s0) | (~node3(c_bit2, s0, s1)) | (~m_counter_cell_v_value(c_bit2, s1)))),
% 13.70/13.86 inference(quant_inst,[status(thm)],[])).
% 13.70/13.86 tff(7742,plain,
% 13.70/13.86 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit2, s0) | (~m_counter_cell_v_value(c_bit2, s1)) | (~node3(c_bit2, s0, s1))),
% 13.70/13.86 inference(modus_ponens,[status(thm)],[7741, 7740])).
% 13.70/13.86 tff(7743,plain,
% 13.70/13.86 (node2(c_bit2, s0) | (~m_counter_cell_v_value(c_bit2, s1))),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7742, 121, 7736])).
% 13.70/13.86 tff(7744,plain,
% 13.70/13.86 (~m_counter_cell_v_value(c_bit2, s1)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7743, 7732])).
% 13.70/13.86 tff(7745,plain,
% 13.70/13.86 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | ((~node2(c_bit2, s1)) | m_counter_cell_v_value(c_bit2, s1) | m_counter_cell_v_carry_in(c_bit2, s1))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (~node2(c_bit2, s1)) | m_counter_cell_v_value(c_bit2, s1) | m_counter_cell_v_carry_in(c_bit2, s1))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7746,plain,
% 13.70/13.86 ((m_counter_cell_v_carry_in(c_bit2, s1) | m_counter_cell_v_value(c_bit2, s1) | (~node2(c_bit2, s1))) <=> ((~node2(c_bit2, s1)) | m_counter_cell_v_value(c_bit2, s1) | m_counter_cell_v_carry_in(c_bit2, s1))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7747,plain,
% 13.70/13.86 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s1) | m_counter_cell_v_value(c_bit2, s1) | (~node2(c_bit2, s1)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | ((~node2(c_bit2, s1)) | m_counter_cell_v_value(c_bit2, s1) | m_counter_cell_v_carry_in(c_bit2, s1)))),
% 13.70/13.86 inference(monotonicity,[status(thm)],[7746])).
% 13.70/13.86 tff(7748,plain,
% 13.70/13.86 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s1) | m_counter_cell_v_value(c_bit2, s1) | (~node2(c_bit2, s1)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (~node2(c_bit2, s1)) | m_counter_cell_v_value(c_bit2, s1) | m_counter_cell_v_carry_in(c_bit2, s1))),
% 13.70/13.86 inference(transitivity,[status(thm)],[7747, 7745])).
% 13.70/13.86 tff(7749,plain,
% 13.70/13.86 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s1) | m_counter_cell_v_value(c_bit2, s1) | (~node2(c_bit2, s1)))),
% 13.70/13.86 inference(quant_inst,[status(thm)],[])).
% 13.70/13.86 tff(7750,plain,
% 13.70/13.86 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (~node2(c_bit2, s1)) | m_counter_cell_v_value(c_bit2, s1) | m_counter_cell_v_carry_in(c_bit2, s1)),
% 13.70/13.86 inference(modus_ponens,[status(thm)],[7749, 7748])).
% 13.70/13.86 tff(7751,plain,
% 13.70/13.86 ((~node2(c_bit2, s1)) | m_counter_cell_v_carry_in(c_bit2, s1)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7750, 1498, 7744])).
% 13.70/13.86 tff(7752,plain,
% 13.70/13.86 (~node2(c_bit2, s1)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7751, 7705])).
% 13.70/13.86 tff(7753,plain,
% 13.70/13.86 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s1, s2)) | node3(c_bit2, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s1, s2)) | node3(c_bit2, s1, s2))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7754,plain,
% 13.70/13.86 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s1, s2)) | node3(c_bit2, s1, s2))),
% 13.70/13.86 inference(quant_inst,[status(thm)],[])).
% 13.70/13.86 tff(7755,plain,
% 13.70/13.86 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s1, s2)) | node3(c_bit2, s1, s2)),
% 13.70/13.86 inference(modus_ponens,[status(thm)],[7754, 7753])).
% 13.70/13.86 tff(7756,plain,
% 13.70/13.86 (node3(c_bit2, s1, s2)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7755, 59, 106])).
% 13.70/13.86 tff(7757,plain,
% 13.70/13.86 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s2)) | (~node3(c_bit2, s1, s2)) | node2(c_bit2, s1))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s2)) | (~node3(c_bit2, s1, s2)) | node2(c_bit2, s1))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7758,plain,
% 13.70/13.86 ((node2(c_bit2, s1) | (~node3(c_bit2, s1, s2)) | (~m_counter_cell_v_value(c_bit2, s2))) <=> ((~m_counter_cell_v_value(c_bit2, s2)) | (~node3(c_bit2, s1, s2)) | node2(c_bit2, s1))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7759,plain,
% 13.70/13.86 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s1) | (~node3(c_bit2, s1, s2)) | (~m_counter_cell_v_value(c_bit2, s2)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s2)) | (~node3(c_bit2, s1, s2)) | node2(c_bit2, s1)))),
% 13.70/13.86 inference(monotonicity,[status(thm)],[7758])).
% 13.70/13.86 tff(7760,plain,
% 13.70/13.86 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s1) | (~node3(c_bit2, s1, s2)) | (~m_counter_cell_v_value(c_bit2, s2)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s2)) | (~node3(c_bit2, s1, s2)) | node2(c_bit2, s1))),
% 13.70/13.86 inference(transitivity,[status(thm)],[7759, 7757])).
% 13.70/13.86 tff(7761,plain,
% 13.70/13.86 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s1) | (~node3(c_bit2, s1, s2)) | (~m_counter_cell_v_value(c_bit2, s2)))),
% 13.70/13.86 inference(quant_inst,[status(thm)],[])).
% 13.70/13.86 tff(7762,plain,
% 13.70/13.86 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s2)) | (~node3(c_bit2, s1, s2)) | node2(c_bit2, s1)),
% 13.70/13.86 inference(modus_ponens,[status(thm)],[7761, 7760])).
% 13.70/13.86 tff(7763,plain,
% 13.70/13.86 ((~m_counter_cell_v_value(c_bit2, s2)) | node2(c_bit2, s1)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7762, 121, 7756])).
% 13.70/13.86 tff(7764,plain,
% 13.70/13.86 (~m_counter_cell_v_value(c_bit2, s2)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7763, 7752])).
% 13.70/13.86 tff(7765,plain,
% 13.70/13.86 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s2) | (~node4(c_bit1, s2)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s2) | (~node4(c_bit1, s2)))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7766,plain,
% 13.70/13.86 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s2) | (~node4(c_bit1, s2)))),
% 13.70/13.86 inference(quant_inst,[status(thm)],[])).
% 13.70/13.86 tff(7767,plain,
% 13.70/13.86 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s2) | (~node4(c_bit1, s2))),
% 13.70/13.86 inference(modus_ponens,[status(thm)],[7766, 7765])).
% 13.70/13.86 tff(7768,plain,
% 13.70/13.86 (~node4(c_bit1, s2)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7767, 2941, 1559])).
% 13.70/13.86 tff(7769,plain,
% 13.70/13.86 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s2)) | node4(c_bit1, s2))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s2)) | node4(c_bit1, s2))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7770,plain,
% 13.70/13.86 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s2)) | node4(c_bit1, s2))),
% 13.70/13.86 inference(quant_inst,[status(thm)],[])).
% 13.70/13.86 tff(7771,plain,
% 13.70/13.86 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s2)) | node4(c_bit1, s2)),
% 13.70/13.86 inference(modus_ponens,[status(thm)],[7770, 7769])).
% 13.70/13.86 tff(7772,plain,
% 13.70/13.86 (~m_counter_cell_v_carry_out(c_bit1, s2)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7771, 1359, 7768])).
% 13.70/13.86 tff(7773,plain,
% 13.70/13.86 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s2)) | m_counter_cell_v_carry_out(c_bit1, s2))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s2)) | m_counter_cell_v_carry_out(c_bit1, s2))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7774,plain,
% 13.70/13.86 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s2)) | m_counter_cell_v_carry_out(c_bit1, s2))),
% 13.70/13.86 inference(quant_inst,[status(thm)],[])).
% 13.70/13.86 tff(7775,plain,
% 13.70/13.86 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s2)) | m_counter_cell_v_carry_out(c_bit1, s2)),
% 13.70/13.86 inference(modus_ponens,[status(thm)],[7774, 7773])).
% 13.70/13.86 tff(7776,plain,
% 13.70/13.86 (~m_counter_cell_v_carry_in(c_bit2, s2)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7775, 3675, 7772])).
% 13.70/13.86 tff(7777,plain,
% 13.70/13.86 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s2) | m_counter_cell_v_value(c_bit2, s2) | (~node2(c_bit2, s2)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s2) | m_counter_cell_v_value(c_bit2, s2) | (~node2(c_bit2, s2)))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7778,plain,
% 13.70/13.86 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s2) | m_counter_cell_v_value(c_bit2, s2) | (~node2(c_bit2, s2)))),
% 13.70/13.86 inference(quant_inst,[status(thm)],[])).
% 13.70/13.86 tff(7779,plain,
% 13.70/13.86 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s2) | m_counter_cell_v_value(c_bit2, s2) | (~node2(c_bit2, s2))),
% 13.70/13.86 inference(modus_ponens,[status(thm)],[7778, 7777])).
% 13.70/13.86 tff(7780,plain,
% 13.70/13.86 (m_counter_cell_v_value(c_bit2, s2) | (~node2(c_bit2, s2))),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7779, 1498, 7776])).
% 13.70/13.86 tff(7781,plain,
% 13.70/13.86 (~node2(c_bit2, s2)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7780, 7764])).
% 13.70/13.86 tff(7782,plain,
% 13.70/13.86 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s2, s3)) | node3(c_bit2, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s2, s3)) | node3(c_bit2, s2, s3))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7783,plain,
% 13.70/13.86 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s2, s3)) | node3(c_bit2, s2, s3))),
% 13.70/13.86 inference(quant_inst,[status(thm)],[])).
% 13.70/13.86 tff(7784,plain,
% 13.70/13.86 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s2, s3)) | node3(c_bit2, s2, s3)),
% 13.70/13.86 inference(modus_ponens,[status(thm)],[7783, 7782])).
% 13.70/13.86 tff(7785,plain,
% 13.70/13.86 (node3(c_bit2, s2, s3)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7784, 59, 143])).
% 13.70/13.86 tff(7786,plain,
% 13.70/13.86 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s2) | (~m_counter_cell_v_value(c_bit2, s3)) | (~node3(c_bit2, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit2, s2) | (~m_counter_cell_v_value(c_bit2, s3)) | (~node3(c_bit2, s2, s3)))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7787,plain,
% 13.70/13.86 ((node2(c_bit2, s2) | (~node3(c_bit2, s2, s3)) | (~m_counter_cell_v_value(c_bit2, s3))) <=> (node2(c_bit2, s2) | (~m_counter_cell_v_value(c_bit2, s3)) | (~node3(c_bit2, s2, s3)))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7788,plain,
% 13.70/13.86 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s2) | (~node3(c_bit2, s2, s3)) | (~m_counter_cell_v_value(c_bit2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s2) | (~m_counter_cell_v_value(c_bit2, s3)) | (~node3(c_bit2, s2, s3))))),
% 13.70/13.86 inference(monotonicity,[status(thm)],[7787])).
% 13.70/13.86 tff(7789,plain,
% 13.70/13.86 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s2) | (~node3(c_bit2, s2, s3)) | (~m_counter_cell_v_value(c_bit2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit2, s2) | (~m_counter_cell_v_value(c_bit2, s3)) | (~node3(c_bit2, s2, s3)))),
% 13.70/13.86 inference(transitivity,[status(thm)],[7788, 7786])).
% 13.70/13.86 tff(7790,plain,
% 13.70/13.86 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s2) | (~node3(c_bit2, s2, s3)) | (~m_counter_cell_v_value(c_bit2, s3)))),
% 13.70/13.86 inference(quant_inst,[status(thm)],[])).
% 13.70/13.86 tff(7791,plain,
% 13.70/13.86 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit2, s2) | (~m_counter_cell_v_value(c_bit2, s3)) | (~node3(c_bit2, s2, s3))),
% 13.70/13.86 inference(modus_ponens,[status(thm)],[7790, 7789])).
% 13.70/13.86 tff(7792,plain,
% 13.70/13.86 (node2(c_bit2, s2) | (~m_counter_cell_v_value(c_bit2, s3))),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7791, 121, 7785])).
% 13.70/13.86 tff(7793,plain,
% 13.70/13.86 (~m_counter_cell_v_value(c_bit2, s3)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7792, 7781])).
% 13.70/13.86 tff(7794,plain,
% 13.70/13.86 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s3)) | (~m_counter_cell_v_value(c_bit1, s3)) | m_counter_cell_v_carry_out(c_bit1, s3))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s3)) | (~m_counter_cell_v_value(c_bit1, s3)) | m_counter_cell_v_carry_out(c_bit1, s3))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7795,plain,
% 13.70/13.86 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s3)) | (~m_counter_cell_v_value(c_bit1, s3)) | m_counter_cell_v_carry_out(c_bit1, s3))),
% 13.70/13.86 inference(quant_inst,[status(thm)],[])).
% 13.70/13.86 tff(7796,plain,
% 13.70/13.86 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s3)) | (~m_counter_cell_v_value(c_bit1, s3)) | m_counter_cell_v_carry_out(c_bit1, s3)),
% 13.70/13.86 inference(modus_ponens,[status(thm)],[7795, 7794])).
% 13.70/13.86 tff(7797,plain,
% 13.70/13.86 ((~m_counter_cell_v_value(c_bit1, s3)) | m_counter_cell_v_carry_out(c_bit1, s3)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7796, 1390, 1598])).
% 13.70/13.86 tff(7798,plain,
% 13.70/13.86 (m_counter_cell_v_carry_out(c_bit1, s3)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7797, 7664])).
% 13.70/13.86 tff(7799,plain,
% 13.70/13.86 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s3)) | m_counter_cell_v_carry_in(c_bit2, s3))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s3)) | m_counter_cell_v_carry_in(c_bit2, s3))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7800,plain,
% 13.70/13.86 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s3)) | m_counter_cell_v_carry_in(c_bit2, s3))),
% 13.70/13.86 inference(quant_inst,[status(thm)],[])).
% 13.70/13.86 tff(7801,plain,
% 13.70/13.86 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s3)) | m_counter_cell_v_carry_in(c_bit2, s3)),
% 13.70/13.86 inference(modus_ponens,[status(thm)],[7800, 7799])).
% 13.70/13.86 tff(7802,plain,
% 13.70/13.86 (m_counter_cell_v_carry_in(c_bit2, s3)),
% 13.70/13.86 inference(unit_resolution,[status(thm)],[7801, 3305, 7798])).
% 13.70/13.86 tff(7803,plain,
% 13.70/13.86 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (m_counter_cell_v_value(c_bit2, s3) | (~node1(c_bit2, s3)) | (~m_counter_cell_v_carry_in(c_bit2, s3)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | m_counter_cell_v_value(c_bit2, s3) | (~node1(c_bit2, s3)) | (~m_counter_cell_v_carry_in(c_bit2, s3)))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7804,plain,
% 13.70/13.86 (((~node1(c_bit2, s3)) | (~m_counter_cell_v_carry_in(c_bit2, s3)) | m_counter_cell_v_value(c_bit2, s3)) <=> (m_counter_cell_v_value(c_bit2, s3) | (~node1(c_bit2, s3)) | (~m_counter_cell_v_carry_in(c_bit2, s3)))),
% 13.70/13.86 inference(rewrite,[status(thm)],[])).
% 13.70/13.86 tff(7805,plain,
% 13.70/13.86 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s3)) | (~m_counter_cell_v_carry_in(c_bit2, s3)) | m_counter_cell_v_value(c_bit2, s3))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (m_counter_cell_v_value(c_bit2, s3) | (~node1(c_bit2, s3)) | (~m_counter_cell_v_carry_in(c_bit2, s3))))),
% 13.70/13.86 inference(monotonicity,[status(thm)],[7804])).
% 13.70/13.86 tff(7806,plain,
% 13.70/13.86 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s3)) | (~m_counter_cell_v_carry_in(c_bit2, s3)) | m_counter_cell_v_value(c_bit2, s3))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | m_counter_cell_v_value(c_bit2, s3) | (~node1(c_bit2, s3)) | (~m_counter_cell_v_carry_in(c_bit2, s3)))),
% 13.70/13.86 inference(transitivity,[status(thm)],[7805, 7803])).
% 13.70/13.86 tff(7807,plain,
% 13.70/13.86 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s3)) | (~m_counter_cell_v_carry_in(c_bit2, s3)) | m_counter_cell_v_value(c_bit2, s3))),
% 13.70/13.86 inference(quant_inst,[status(thm)],[])).
% 13.70/13.87 tff(7808,plain,
% 13.70/13.87 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | m_counter_cell_v_value(c_bit2, s3) | (~node1(c_bit2, s3)) | (~m_counter_cell_v_carry_in(c_bit2, s3))),
% 13.70/13.87 inference(modus_ponens,[status(thm)],[7807, 7806])).
% 13.70/13.87 tff(7809,plain,
% 13.70/13.87 (m_counter_cell_v_value(c_bit2, s3) | (~node1(c_bit2, s3))),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7808, 30, 7802])).
% 13.70/13.87 tff(7810,plain,
% 13.70/13.87 ($false),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7809, 7793, 7648])).
% 13.70/13.87 tff(7811,plain,(m_counter_cell_v_value(c_bit1, s4) | (~node2(c_bit2, s7))), inference(lemma,lemma(discharge,[]))).
% 13.70/13.87 tff(7812,plain,
% 13.70/13.87 (~node2(c_bit2, s7)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7811, 1615])).
% 13.70/13.87 tff(7813,plain,
% 13.70/13.87 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s7, s8)) | node3(c_bit2, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s7, s8)) | node3(c_bit2, s7, s8))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7814,plain,
% 13.70/13.87 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s7, s8)) | node3(c_bit2, s7, s8))),
% 13.70/13.87 inference(quant_inst,[status(thm)],[])).
% 13.70/13.87 tff(7815,plain,
% 13.70/13.87 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s7, s8)) | node3(c_bit2, s7, s8)),
% 13.70/13.87 inference(modus_ponens,[status(thm)],[7814, 7813])).
% 13.70/13.87 tff(7816,plain,
% 13.70/13.87 (node3(c_bit2, s7, s8)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7815, 59, 279])).
% 13.70/13.87 tff(7817,plain,
% 13.70/13.87 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s8)) | (~node3(c_bit2, s7, s8)) | node2(c_bit2, s7))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s8)) | (~node3(c_bit2, s7, s8)) | node2(c_bit2, s7))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7818,plain,
% 13.70/13.87 ((node2(c_bit2, s7) | (~node3(c_bit2, s7, s8)) | (~m_counter_cell_v_value(c_bit2, s8))) <=> ((~m_counter_cell_v_value(c_bit2, s8)) | (~node3(c_bit2, s7, s8)) | node2(c_bit2, s7))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7819,plain,
% 13.70/13.87 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s7) | (~node3(c_bit2, s7, s8)) | (~m_counter_cell_v_value(c_bit2, s8)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s8)) | (~node3(c_bit2, s7, s8)) | node2(c_bit2, s7)))),
% 13.70/13.87 inference(monotonicity,[status(thm)],[7818])).
% 13.70/13.87 tff(7820,plain,
% 13.70/13.87 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s7) | (~node3(c_bit2, s7, s8)) | (~m_counter_cell_v_value(c_bit2, s8)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s8)) | (~node3(c_bit2, s7, s8)) | node2(c_bit2, s7))),
% 13.70/13.87 inference(transitivity,[status(thm)],[7819, 7817])).
% 13.70/13.87 tff(7821,plain,
% 13.70/13.87 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s7) | (~node3(c_bit2, s7, s8)) | (~m_counter_cell_v_value(c_bit2, s8)))),
% 13.70/13.87 inference(quant_inst,[status(thm)],[])).
% 13.70/13.87 tff(7822,plain,
% 13.70/13.87 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s8)) | (~node3(c_bit2, s7, s8)) | node2(c_bit2, s7)),
% 13.70/13.87 inference(modus_ponens,[status(thm)],[7821, 7820])).
% 13.70/13.87 tff(7823,plain,
% 13.70/13.87 ((~m_counter_cell_v_value(c_bit2, s8)) | node2(c_bit2, s7)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7822, 121, 7816])).
% 13.70/13.87 tff(7824,plain,
% 13.70/13.87 (~m_counter_cell_v_value(c_bit2, s8)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7823, 7812])).
% 13.70/13.87 tff(7825,plain,
% 13.70/13.87 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s8) | (~node3(c_bit2, s7, s8)) | node1(c_bit2, s7))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s8) | (~node3(c_bit2, s7, s8)) | node1(c_bit2, s7))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7826,plain,
% 13.70/13.87 ((node1(c_bit2, s7) | (~node3(c_bit2, s7, s8)) | m_counter_cell_v_value(c_bit2, s8)) <=> (m_counter_cell_v_value(c_bit2, s8) | (~node3(c_bit2, s7, s8)) | node1(c_bit2, s7))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7827,plain,
% 13.70/13.87 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s7) | (~node3(c_bit2, s7, s8)) | m_counter_cell_v_value(c_bit2, s8))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s8) | (~node3(c_bit2, s7, s8)) | node1(c_bit2, s7)))),
% 13.70/13.87 inference(monotonicity,[status(thm)],[7826])).
% 13.70/13.87 tff(7828,plain,
% 13.70/13.87 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s7) | (~node3(c_bit2, s7, s8)) | m_counter_cell_v_value(c_bit2, s8))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s8) | (~node3(c_bit2, s7, s8)) | node1(c_bit2, s7))),
% 13.70/13.87 inference(transitivity,[status(thm)],[7827, 7825])).
% 13.70/13.87 tff(7829,plain,
% 13.70/13.87 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s7) | (~node3(c_bit2, s7, s8)) | m_counter_cell_v_value(c_bit2, s8))),
% 13.70/13.87 inference(quant_inst,[status(thm)],[])).
% 13.70/13.87 tff(7830,plain,
% 13.70/13.87 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s8) | (~node3(c_bit2, s7, s8)) | node1(c_bit2, s7)),
% 13.70/13.87 inference(modus_ponens,[status(thm)],[7829, 7828])).
% 13.70/13.87 tff(7831,plain,
% 13.70/13.87 (m_counter_cell_v_value(c_bit2, s8) | node1(c_bit2, s7)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7830, 73, 7816])).
% 13.70/13.87 tff(7832,plain,
% 13.70/13.87 (node1(c_bit2, s7)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7831, 7824])).
% 13.70/13.87 tff(7833,plain,
% 13.70/13.87 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (m_counter_cell_v_value(c_bit2, s7) | (~node1(c_bit2, s7)) | (~m_counter_cell_v_carry_in(c_bit2, s7)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | m_counter_cell_v_value(c_bit2, s7) | (~node1(c_bit2, s7)) | (~m_counter_cell_v_carry_in(c_bit2, s7)))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7834,plain,
% 13.70/13.87 (((~node1(c_bit2, s7)) | (~m_counter_cell_v_carry_in(c_bit2, s7)) | m_counter_cell_v_value(c_bit2, s7)) <=> (m_counter_cell_v_value(c_bit2, s7) | (~node1(c_bit2, s7)) | (~m_counter_cell_v_carry_in(c_bit2, s7)))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7835,plain,
% 13.70/13.87 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s7)) | (~m_counter_cell_v_carry_in(c_bit2, s7)) | m_counter_cell_v_value(c_bit2, s7))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (m_counter_cell_v_value(c_bit2, s7) | (~node1(c_bit2, s7)) | (~m_counter_cell_v_carry_in(c_bit2, s7))))),
% 13.70/13.87 inference(monotonicity,[status(thm)],[7834])).
% 13.70/13.87 tff(7836,plain,
% 13.70/13.87 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s7)) | (~m_counter_cell_v_carry_in(c_bit2, s7)) | m_counter_cell_v_value(c_bit2, s7))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | m_counter_cell_v_value(c_bit2, s7) | (~node1(c_bit2, s7)) | (~m_counter_cell_v_carry_in(c_bit2, s7)))),
% 13.70/13.87 inference(transitivity,[status(thm)],[7835, 7833])).
% 13.70/13.87 tff(7837,plain,
% 13.70/13.87 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s7)) | (~m_counter_cell_v_carry_in(c_bit2, s7)) | m_counter_cell_v_value(c_bit2, s7))),
% 13.70/13.87 inference(quant_inst,[status(thm)],[])).
% 13.70/13.87 tff(7838,plain,
% 13.70/13.87 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | m_counter_cell_v_value(c_bit2, s7) | (~node1(c_bit2, s7)) | (~m_counter_cell_v_carry_in(c_bit2, s7))),
% 13.70/13.87 inference(modus_ponens,[status(thm)],[7837, 7836])).
% 13.70/13.87 tff(7839,plain,
% 13.70/13.87 (m_counter_cell_v_value(c_bit2, s7) | (~m_counter_cell_v_carry_in(c_bit2, s7))),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7838, 30, 7832])).
% 13.70/13.87 tff(7840,plain,
% 13.70/13.87 (m_counter_cell_v_value(c_bit2, s7)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7839, 7522])).
% 13.70/13.87 tff(7841,plain,
% 13.70/13.87 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s7)) | (~m_counter_cell_v_value(c_bit2, s7)) | m_counter_cell_v_carry_out(c_bit2, s7))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s7)) | (~m_counter_cell_v_value(c_bit2, s7)) | m_counter_cell_v_carry_out(c_bit2, s7))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7842,plain,
% 13.70/13.87 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s7)) | (~m_counter_cell_v_value(c_bit2, s7)) | m_counter_cell_v_carry_out(c_bit2, s7))),
% 13.70/13.87 inference(quant_inst,[status(thm)],[])).
% 13.70/13.87 tff(7843,plain,
% 13.70/13.87 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s7)) | (~m_counter_cell_v_value(c_bit2, s7)) | m_counter_cell_v_carry_out(c_bit2, s7)),
% 13.70/13.87 inference(modus_ponens,[status(thm)],[7842, 7841])).
% 13.70/13.87 tff(7844,plain,
% 13.70/13.87 (m_counter_cell_v_carry_out(c_bit2, s7)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7843, 1390, 7840, 7522])).
% 13.70/13.87 tff(7845,plain,
% 13.70/13.87 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s7)) | (~m_counter_cell_v_carry_out(c_bit2, s7)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s7)) | (~m_counter_cell_v_carry_out(c_bit2, s7)))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7846,plain,
% 13.70/13.87 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s7)) | (~m_counter_cell_v_carry_out(c_bit2, s7)))),
% 13.70/13.87 inference(quant_inst,[status(thm)],[])).
% 13.70/13.87 tff(7847,plain,
% 13.70/13.87 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s7)) | (~m_counter_cell_v_carry_out(c_bit2, s7))),
% 13.70/13.87 inference(modus_ponens,[status(thm)],[7846, 7845])).
% 13.70/13.87 tff(7848,plain,
% 13.70/13.87 (~always5(s7)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7847, 6925, 7844])).
% 13.70/13.87 tff(7849,plain,
% 13.70/13.87 (~always5(s6)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[4313, 7848])).
% 13.70/13.87 tff(7850,plain,
% 13.70/13.87 (~always5(s5)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[4321, 7849])).
% 13.70/13.87 tff(7851,plain,
% 13.70/13.87 (~always5(s4)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[4329, 7850])).
% 13.70/13.87 tff(7852,plain,
% 13.70/13.87 (~always5(s3)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[4337, 7851])).
% 13.70/13.87 tff(7853,plain,
% 13.70/13.87 (~always5(s2)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[4345, 7852])).
% 13.70/13.87 tff(7854,plain,
% 13.70/13.87 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s2) | (~trans(s59, s2)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s2) | (~trans(s59, s2)))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7855,plain,
% 13.70/13.87 (((~always5(s59)) | (~trans(s59, s2)) | always5(s2)) <=> ((~always5(s59)) | always5(s2) | (~trans(s59, s2)))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7856,plain,
% 13.70/13.87 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s2)) | always5(s2))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s2) | (~trans(s59, s2))))),
% 13.70/13.87 inference(monotonicity,[status(thm)],[7855])).
% 13.70/13.87 tff(7857,plain,
% 13.70/13.87 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s2)) | always5(s2))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s2) | (~trans(s59, s2)))),
% 13.70/13.87 inference(transitivity,[status(thm)],[7856, 7854])).
% 13.70/13.87 tff(7858,plain,
% 13.70/13.87 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s2)) | always5(s2))),
% 13.70/13.87 inference(quant_inst,[status(thm)],[])).
% 13.70/13.87 tff(7859,plain,
% 13.70/13.87 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s2) | (~trans(s59, s2))),
% 13.70/13.87 inference(modus_ponens,[status(thm)],[7858, 7857])).
% 13.70/13.87 tff(7860,plain,
% 13.70/13.87 ($false),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7859, 5986, 3890, 6915, 7853])).
% 13.70/13.87 tff(7861,plain,(~trans(s59, s2)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.87 tff(7862,assumption,(~always5(s48)), introduced(assumption)).
% 13.70/13.87 tff(7863,plain,
% 13.70/13.87 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s48) | (~trans(s59, s48)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s48) | (~trans(s59, s48)))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7864,plain,
% 13.70/13.87 (((~always5(s59)) | (~trans(s59, s48)) | always5(s48)) <=> ((~always5(s59)) | always5(s48) | (~trans(s59, s48)))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7865,plain,
% 13.70/13.87 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s48)) | always5(s48))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s48) | (~trans(s59, s48))))),
% 13.70/13.87 inference(monotonicity,[status(thm)],[7864])).
% 13.70/13.87 tff(7866,plain,
% 13.70/13.87 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s48)) | always5(s48))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s48) | (~trans(s59, s48)))),
% 13.70/13.87 inference(transitivity,[status(thm)],[7865, 7863])).
% 13.70/13.87 tff(7867,plain,
% 13.70/13.87 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s48)) | always5(s48))),
% 13.70/13.87 inference(quant_inst,[status(thm)],[])).
% 13.70/13.87 tff(7868,plain,
% 13.70/13.87 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s48) | (~trans(s59, s48))),
% 13.70/13.87 inference(modus_ponens,[status(thm)],[7867, 7866])).
% 13.70/13.87 tff(7869,plain,
% 13.70/13.87 ($false),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7868, 5887, 3890, 6915, 7862])).
% 13.70/13.87 tff(7870,plain,((~trans(s59, s48)) | always5(s48)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.87 tff(7871,plain,
% 13.70/13.87 (~trans(s59, s48)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7870, 7438])).
% 13.70/13.87 tff(7872,plain,
% 13.70/13.87 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s44) | (~trans(s59, s44)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s44) | (~trans(s59, s44)))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7873,plain,
% 13.70/13.87 (((~always5(s59)) | (~trans(s59, s44)) | always5(s44)) <=> ((~always5(s59)) | always5(s44) | (~trans(s59, s44)))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7874,plain,
% 13.70/13.87 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s44)) | always5(s44))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s44) | (~trans(s59, s44))))),
% 13.70/13.87 inference(monotonicity,[status(thm)],[7873])).
% 13.70/13.87 tff(7875,plain,
% 13.70/13.87 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s44)) | always5(s44))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s44) | (~trans(s59, s44)))),
% 13.70/13.87 inference(transitivity,[status(thm)],[7874, 7872])).
% 13.70/13.87 tff(7876,plain,
% 13.70/13.87 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s44)) | always5(s44))),
% 13.70/13.87 inference(quant_inst,[status(thm)],[])).
% 13.70/13.87 tff(7877,plain,
% 13.70/13.87 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s44) | (~trans(s59, s44))),
% 13.70/13.87 inference(modus_ponens,[status(thm)],[7876, 7875])).
% 13.70/13.87 tff(7878,plain,
% 13.70/13.87 ($false),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7877, 6008, 3890, 6915, 7442])).
% 13.70/13.87 tff(7879,plain,(~trans(s59, s44)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.87 tff(7880,assumption,(~always5(s47)), introduced(assumption)).
% 13.70/13.87 tff(7881,plain,
% 13.70/13.87 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s47) | (~trans(s59, s47)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s47) | (~trans(s59, s47)))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7882,plain,
% 13.70/13.87 (((~always5(s59)) | (~trans(s59, s47)) | always5(s47)) <=> ((~always5(s59)) | always5(s47) | (~trans(s59, s47)))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7883,plain,
% 13.70/13.87 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s47)) | always5(s47))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s47) | (~trans(s59, s47))))),
% 13.70/13.87 inference(monotonicity,[status(thm)],[7882])).
% 13.70/13.87 tff(7884,plain,
% 13.70/13.87 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s47)) | always5(s47))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s47) | (~trans(s59, s47)))),
% 13.70/13.87 inference(transitivity,[status(thm)],[7883, 7881])).
% 13.70/13.87 tff(7885,plain,
% 13.70/13.87 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s47)) | always5(s47))),
% 13.70/13.87 inference(quant_inst,[status(thm)],[])).
% 13.70/13.87 tff(7886,plain,
% 13.70/13.87 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s47) | (~trans(s59, s47))),
% 13.70/13.87 inference(modus_ponens,[status(thm)],[7885, 7884])).
% 13.70/13.87 tff(7887,plain,
% 13.70/13.87 ($false),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7886, 6151, 3890, 6915, 7880])).
% 13.70/13.87 tff(7888,plain,((~trans(s59, s47)) | always5(s47)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.87 tff(7889,plain,
% 13.70/13.87 (~trans(s59, s47)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7888, 7439])).
% 13.70/13.87 tff(7890,assumption,(~always5(s27)), introduced(assumption)).
% 13.70/13.87 tff(7891,plain,
% 13.70/13.87 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s27) | (~trans(s59, s27)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s27) | (~trans(s59, s27)))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7892,plain,
% 13.70/13.87 (((~always5(s59)) | (~trans(s59, s27)) | always5(s27)) <=> ((~always5(s59)) | always5(s27) | (~trans(s59, s27)))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7893,plain,
% 13.70/13.87 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s27)) | always5(s27))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s27) | (~trans(s59, s27))))),
% 13.70/13.87 inference(monotonicity,[status(thm)],[7892])).
% 13.70/13.87 tff(7894,plain,
% 13.70/13.87 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s27)) | always5(s27))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s27) | (~trans(s59, s27)))),
% 13.70/13.87 inference(transitivity,[status(thm)],[7893, 7891])).
% 13.70/13.87 tff(7895,plain,
% 13.70/13.87 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s27)) | always5(s27))),
% 13.70/13.87 inference(quant_inst,[status(thm)],[])).
% 13.70/13.87 tff(7896,plain,
% 13.70/13.87 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s27) | (~trans(s59, s27))),
% 13.70/13.87 inference(modus_ponens,[status(thm)],[7895, 7894])).
% 13.70/13.87 tff(7897,plain,
% 13.70/13.87 ($false),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7896, 6217, 3890, 6915, 7890])).
% 13.70/13.87 tff(7898,plain,((~trans(s59, s27)) | always5(s27)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.87 tff(7899,plain,
% 13.70/13.87 (~trans(s59, s27)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7898, 7467])).
% 13.70/13.87 tff(7900,assumption,(~always5(s43)), introduced(assumption)).
% 13.70/13.87 tff(7901,plain,
% 13.70/13.87 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s43) | (~trans(s59, s43)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s43) | (~trans(s59, s43)))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7902,plain,
% 13.70/13.87 (((~always5(s59)) | (~trans(s59, s43)) | always5(s43)) <=> ((~always5(s59)) | always5(s43) | (~trans(s59, s43)))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7903,plain,
% 13.70/13.87 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s43)) | always5(s43))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s43) | (~trans(s59, s43))))),
% 13.70/13.87 inference(monotonicity,[status(thm)],[7902])).
% 13.70/13.87 tff(7904,plain,
% 13.70/13.87 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s43)) | always5(s43))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s43) | (~trans(s59, s43)))),
% 13.70/13.87 inference(transitivity,[status(thm)],[7903, 7901])).
% 13.70/13.87 tff(7905,plain,
% 13.70/13.87 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s43)) | always5(s43))),
% 13.70/13.87 inference(quant_inst,[status(thm)],[])).
% 13.70/13.87 tff(7906,plain,
% 13.70/13.87 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s43) | (~trans(s59, s43))),
% 13.70/13.87 inference(modus_ponens,[status(thm)],[7905, 7904])).
% 13.70/13.87 tff(7907,plain,
% 13.70/13.87 ($false),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7906, 5964, 3890, 6915, 7900])).
% 13.70/13.87 tff(7908,plain,((~trans(s59, s43)) | always5(s43)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.87 tff(7909,plain,
% 13.70/13.87 (~trans(s59, s43)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7908, 7443])).
% 13.70/13.87 tff(7910,assumption,(~always5(s40)), introduced(assumption)).
% 13.70/13.87 tff(7911,plain,
% 13.70/13.87 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s40) | (~trans(s59, s40)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s40) | (~trans(s59, s40)))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7912,plain,
% 13.70/13.87 (((~always5(s59)) | (~trans(s59, s40)) | always5(s40)) <=> ((~always5(s59)) | always5(s40) | (~trans(s59, s40)))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7913,plain,
% 13.70/13.87 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s40)) | always5(s40))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s40) | (~trans(s59, s40))))),
% 13.70/13.87 inference(monotonicity,[status(thm)],[7912])).
% 13.70/13.87 tff(7914,plain,
% 13.70/13.87 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s40)) | always5(s40))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s40) | (~trans(s59, s40)))),
% 13.70/13.87 inference(transitivity,[status(thm)],[7913, 7911])).
% 13.70/13.87 tff(7915,plain,
% 13.70/13.87 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s40)) | always5(s40))),
% 13.70/13.87 inference(quant_inst,[status(thm)],[])).
% 13.70/13.87 tff(7916,plain,
% 13.70/13.87 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s40) | (~trans(s59, s40))),
% 13.70/13.87 inference(modus_ponens,[status(thm)],[7915, 7914])).
% 13.70/13.87 tff(7917,plain,
% 13.70/13.87 ($false),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7916, 6206, 3890, 6915, 7910])).
% 13.70/13.87 tff(7918,plain,((~trans(s59, s40)) | always5(s40)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.87 tff(7919,plain,
% 13.70/13.87 (~trans(s59, s40)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7918, 7454])).
% 13.70/13.87 tff(7920,assumption,(~always5(s36)), introduced(assumption)).
% 13.70/13.87 tff(7921,plain,
% 13.70/13.87 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s36) | (~trans(s59, s36)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s36) | (~trans(s59, s36)))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7922,plain,
% 13.70/13.87 (((~always5(s59)) | (~trans(s59, s36)) | always5(s36)) <=> ((~always5(s59)) | always5(s36) | (~trans(s59, s36)))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7923,plain,
% 13.70/13.87 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s36)) | always5(s36))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s36) | (~trans(s59, s36))))),
% 13.70/13.87 inference(monotonicity,[status(thm)],[7922])).
% 13.70/13.87 tff(7924,plain,
% 13.70/13.87 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s36)) | always5(s36))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s36) | (~trans(s59, s36)))),
% 13.70/13.87 inference(transitivity,[status(thm)],[7923, 7921])).
% 13.70/13.87 tff(7925,plain,
% 13.70/13.87 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s36)) | always5(s36))),
% 13.70/13.87 inference(quant_inst,[status(thm)],[])).
% 13.70/13.87 tff(7926,plain,
% 13.70/13.87 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s36) | (~trans(s59, s36))),
% 13.70/13.87 inference(modus_ponens,[status(thm)],[7925, 7924])).
% 13.70/13.87 tff(7927,plain,
% 13.70/13.87 ($false),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7926, 5997, 3890, 6915, 7920])).
% 13.70/13.87 tff(7928,plain,((~trans(s59, s36)) | always5(s36)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.87 tff(7929,plain,
% 13.70/13.87 (~trans(s59, s36)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7928, 7458])).
% 13.70/13.87 tff(7930,assumption,(always5(s21)), introduced(assumption)).
% 13.70/13.87 tff(7931,plain,
% 13.70/13.87 (always5(s22)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[4193, 7930])).
% 13.70/13.87 tff(7932,plain,
% 13.70/13.87 (always5(s23)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[4185, 7931])).
% 13.70/13.87 tff(7933,plain,
% 13.70/13.87 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s23)) | (~m_counter_cell_v_carry_out(c_bit2, s23)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s23)) | (~m_counter_cell_v_carry_out(c_bit2, s23)))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7934,plain,
% 13.70/13.87 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s23)) | (~m_counter_cell_v_carry_out(c_bit2, s23)))),
% 13.70/13.87 inference(quant_inst,[status(thm)],[])).
% 13.70/13.87 tff(7935,plain,
% 13.70/13.87 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s23)) | (~m_counter_cell_v_carry_out(c_bit2, s23))),
% 13.70/13.87 inference(modus_ponens,[status(thm)],[7934, 7933])).
% 13.70/13.87 tff(7936,plain,
% 13.70/13.87 (~m_counter_cell_v_carry_out(c_bit2, s23)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7935, 6925, 7932])).
% 13.70/13.87 tff(7937,assumption,(~m_counter_cell_v_carry_in(c_bit2, s23)), introduced(assumption)).
% 13.70/13.87 tff(7938,assumption,(~m_counter_cell_v_carry_out(c_bit1, s23)), introduced(assumption)).
% 13.70/13.87 tff(7939,assumption,(m_counter_cell_v_value(c_bit1, s23)), introduced(assumption)).
% 13.70/13.87 tff(7940,plain,
% 13.70/13.87 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s23)) | (~m_counter_cell_v_value(c_bit1, s23)) | m_counter_cell_v_carry_out(c_bit1, s23))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s23)) | (~m_counter_cell_v_value(c_bit1, s23)) | m_counter_cell_v_carry_out(c_bit1, s23))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7941,plain,
% 13.70/13.87 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s23)) | (~m_counter_cell_v_value(c_bit1, s23)) | m_counter_cell_v_carry_out(c_bit1, s23))),
% 13.70/13.87 inference(quant_inst,[status(thm)],[])).
% 13.70/13.87 tff(7942,plain,
% 13.70/13.87 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s23)) | (~m_counter_cell_v_value(c_bit1, s23)) | m_counter_cell_v_carry_out(c_bit1, s23)),
% 13.70/13.87 inference(modus_ponens,[status(thm)],[7941, 7940])).
% 13.70/13.87 tff(7943,plain,
% 13.70/13.87 ($false),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7942, 1390, 2180, 7939, 7938])).
% 13.70/13.87 tff(7944,plain,(m_counter_cell_v_carry_out(c_bit1, s23) | (~m_counter_cell_v_value(c_bit1, s23))), inference(lemma,lemma(discharge,[]))).
% 13.70/13.87 tff(7945,plain,
% 13.70/13.87 (m_counter_cell_v_carry_out(c_bit1, s23)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7944, 2171])).
% 13.70/13.87 tff(7946,plain,
% 13.70/13.87 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s23)) | m_counter_cell_v_carry_in(c_bit2, s23))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s23)) | m_counter_cell_v_carry_in(c_bit2, s23))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7947,plain,
% 13.70/13.87 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s23)) | m_counter_cell_v_carry_in(c_bit2, s23))),
% 13.70/13.87 inference(quant_inst,[status(thm)],[])).
% 13.70/13.87 tff(7948,plain,
% 13.70/13.87 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s23)) | m_counter_cell_v_carry_in(c_bit2, s23)),
% 13.70/13.87 inference(modus_ponens,[status(thm)],[7947, 7946])).
% 13.70/13.87 tff(7949,plain,
% 13.70/13.87 ($false),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7948, 3305, 7945, 7937])).
% 13.70/13.87 tff(7950,plain,(m_counter_cell_v_carry_in(c_bit2, s23)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.87 tff(7951,plain,
% 13.70/13.87 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s23)) | (~m_counter_cell_v_value(c_bit2, s23)) | m_counter_cell_v_carry_out(c_bit2, s23))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s23)) | (~m_counter_cell_v_value(c_bit2, s23)) | m_counter_cell_v_carry_out(c_bit2, s23))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7952,plain,
% 13.70/13.87 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s23)) | (~m_counter_cell_v_value(c_bit2, s23)) | m_counter_cell_v_carry_out(c_bit2, s23))),
% 13.70/13.87 inference(quant_inst,[status(thm)],[])).
% 13.70/13.87 tff(7953,plain,
% 13.70/13.87 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s23)) | (~m_counter_cell_v_value(c_bit2, s23)) | m_counter_cell_v_carry_out(c_bit2, s23)),
% 13.70/13.87 inference(modus_ponens,[status(thm)],[7952, 7951])).
% 13.70/13.87 tff(7954,plain,
% 13.70/13.87 ((~m_counter_cell_v_value(c_bit2, s23)) | m_counter_cell_v_carry_out(c_bit2, s23)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7953, 1390, 7950])).
% 13.70/13.87 tff(7955,plain,
% 13.70/13.87 (~m_counter_cell_v_value(c_bit2, s23)),
% 13.70/13.87 inference(unit_resolution,[status(thm)],[7954, 7936])).
% 13.70/13.87 tff(7956,plain,
% 13.70/13.87 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s22, s23)) | node3(c_bit2, s22, s23))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s22, s23)) | node3(c_bit2, s22, s23))),
% 13.70/13.87 inference(rewrite,[status(thm)],[])).
% 13.70/13.87 tff(7957,plain,
% 13.70/13.87 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s22, s23)) | node3(c_bit2, s22, s23))),
% 13.70/13.87 inference(quant_inst,[status(thm)],[])).
% 13.70/13.87 tff(7958,plain,
% 13.70/13.88 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s22, s23)) | node3(c_bit2, s22, s23)),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[7957, 7956])).
% 13.70/13.88 tff(7959,plain,
% 13.70/13.88 (node3(c_bit2, s22, s23)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[7958, 59, 705])).
% 13.70/13.88 tff(7960,plain,
% 13.70/13.88 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s23) | node1(c_bit2, s22) | (~node3(c_bit2, s22, s23)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s23) | node1(c_bit2, s22) | (~node3(c_bit2, s22, s23)))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(7961,plain,
% 13.70/13.88 ((node1(c_bit2, s22) | (~node3(c_bit2, s22, s23)) | m_counter_cell_v_value(c_bit2, s23)) <=> (m_counter_cell_v_value(c_bit2, s23) | node1(c_bit2, s22) | (~node3(c_bit2, s22, s23)))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(7962,plain,
% 13.70/13.88 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s22) | (~node3(c_bit2, s22, s23)) | m_counter_cell_v_value(c_bit2, s23))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s23) | node1(c_bit2, s22) | (~node3(c_bit2, s22, s23))))),
% 13.70/13.88 inference(monotonicity,[status(thm)],[7961])).
% 13.70/13.88 tff(7963,plain,
% 13.70/13.88 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s22) | (~node3(c_bit2, s22, s23)) | m_counter_cell_v_value(c_bit2, s23))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s23) | node1(c_bit2, s22) | (~node3(c_bit2, s22, s23)))),
% 13.70/13.88 inference(transitivity,[status(thm)],[7962, 7960])).
% 13.70/13.88 tff(7964,plain,
% 13.70/13.88 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s22) | (~node3(c_bit2, s22, s23)) | m_counter_cell_v_value(c_bit2, s23))),
% 13.70/13.88 inference(quant_inst,[status(thm)],[])).
% 13.70/13.88 tff(7965,plain,
% 13.70/13.88 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s23) | node1(c_bit2, s22) | (~node3(c_bit2, s22, s23))),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[7964, 7963])).
% 13.70/13.88 tff(7966,plain,
% 13.70/13.88 (m_counter_cell_v_value(c_bit2, s23) | node1(c_bit2, s22)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[7965, 73, 7959])).
% 13.70/13.88 tff(7967,plain,
% 13.70/13.88 (node1(c_bit2, s22)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[7966, 7955])).
% 13.70/13.88 tff(7968,plain,
% 13.70/13.88 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s21)) | (~m_counter_cell_v_carry_out(c_bit2, s21)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s21)) | (~m_counter_cell_v_carry_out(c_bit2, s21)))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(7969,plain,
% 13.70/13.88 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s21)) | (~m_counter_cell_v_carry_out(c_bit2, s21)))),
% 13.70/13.88 inference(quant_inst,[status(thm)],[])).
% 13.70/13.88 tff(7970,plain,
% 13.70/13.88 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s21)) | (~m_counter_cell_v_carry_out(c_bit2, s21))),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[7969, 7968])).
% 13.70/13.88 tff(7971,plain,
% 13.70/13.88 (~m_counter_cell_v_carry_out(c_bit2, s21)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[7970, 6925, 7930])).
% 13.70/13.88 tff(7972,assumption,(~m_counter_cell_v_carry_out(c_bit1, s19)), introduced(assumption)).
% 13.70/13.88 tff(7973,assumption,(m_counter_cell_v_carry_in(c_bit1, s19)), introduced(assumption)).
% 13.70/13.88 tff(7974,plain,
% 13.70/13.88 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s19)) | (~m_counter_cell_v_value(c_bit1, s19)) | m_counter_cell_v_carry_out(c_bit1, s19))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s19)) | (~m_counter_cell_v_value(c_bit1, s19)) | m_counter_cell_v_carry_out(c_bit1, s19))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(7975,plain,
% 13.70/13.88 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s19)) | (~m_counter_cell_v_value(c_bit1, s19)) | m_counter_cell_v_carry_out(c_bit1, s19))),
% 13.70/13.88 inference(quant_inst,[status(thm)],[])).
% 13.70/13.88 tff(7976,plain,
% 13.70/13.88 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s19)) | (~m_counter_cell_v_value(c_bit1, s19)) | m_counter_cell_v_carry_out(c_bit1, s19)),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[7975, 7974])).
% 13.70/13.88 tff(7977,plain,
% 13.70/13.88 ($false),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[7976, 1390, 7973, 2062, 7972])).
% 13.70/13.88 tff(7978,plain,(m_counter_cell_v_carry_out(c_bit1, s19) | (~m_counter_cell_v_carry_in(c_bit1, s19)) | (~m_counter_cell_v_value(c_bit1, s19))), inference(lemma,lemma(discharge,[]))).
% 13.70/13.88 tff(7979,plain,
% 13.70/13.88 (m_counter_cell_v_carry_out(c_bit1, s19) | (~m_counter_cell_v_value(c_bit1, s19))),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[7978, 2061])).
% 13.70/13.88 tff(7980,plain,
% 13.70/13.88 (m_counter_cell_v_carry_out(c_bit1, s19)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[7979, 2052])).
% 13.70/13.88 tff(7981,assumption,(~m_counter_cell_v_carry_in(c_bit2, s19)), introduced(assumption)).
% 13.70/13.88 tff(7982,assumption,(m_counter_cell_v_carry_out(c_bit1, s19)), introduced(assumption)).
% 13.70/13.88 tff(7983,plain,
% 13.70/13.88 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s19)) | m_counter_cell_v_carry_in(c_bit2, s19))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s19)) | m_counter_cell_v_carry_in(c_bit2, s19))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(7984,plain,
% 13.70/13.88 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s19)) | m_counter_cell_v_carry_in(c_bit2, s19))),
% 13.70/13.88 inference(quant_inst,[status(thm)],[])).
% 13.70/13.88 tff(7985,plain,
% 13.70/13.88 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s19)) | m_counter_cell_v_carry_in(c_bit2, s19)),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[7984, 7983])).
% 13.70/13.88 tff(7986,plain,
% 13.70/13.88 ($false),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[7985, 3305, 7982, 7981])).
% 13.70/13.88 tff(7987,plain,(m_counter_cell_v_carry_in(c_bit2, s19) | (~m_counter_cell_v_carry_out(c_bit1, s19))), inference(lemma,lemma(discharge,[]))).
% 13.70/13.88 tff(7988,plain,
% 13.70/13.88 (m_counter_cell_v_carry_in(c_bit2, s19)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[7987, 7980])).
% 13.70/13.88 tff(7989,assumption,(node4(c_bit1, s18)), introduced(assumption)).
% 13.70/13.88 tff(7990,plain,
% 13.70/13.88 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s18) | (~node4(c_bit1, s18)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s18) | (~node4(c_bit1, s18)))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(7991,plain,
% 13.70/13.88 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s18) | (~node4(c_bit1, s18)))),
% 13.70/13.88 inference(quant_inst,[status(thm)],[])).
% 13.70/13.88 tff(7992,plain,
% 13.70/13.88 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s18) | (~node4(c_bit1, s18))),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[7991, 7990])).
% 13.70/13.88 tff(7993,plain,
% 13.70/13.88 ($false),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[7992, 2941, 2029, 7989])).
% 13.70/13.88 tff(7994,plain,(~node4(c_bit1, s18)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.88 tff(7995,plain,
% 13.70/13.88 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s18)) | node4(c_bit1, s18))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s18)) | node4(c_bit1, s18))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(7996,plain,
% 13.70/13.88 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s18)) | node4(c_bit1, s18))),
% 13.70/13.88 inference(quant_inst,[status(thm)],[])).
% 13.70/13.88 tff(7997,plain,
% 13.70/13.88 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s18)) | node4(c_bit1, s18)),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[7996, 7995])).
% 13.70/13.88 tff(7998,plain,
% 13.70/13.88 (~m_counter_cell_v_carry_out(c_bit1, s18)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[7997, 1359, 7994])).
% 13.70/13.88 tff(7999,plain,
% 13.70/13.88 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s18)) | m_counter_cell_v_carry_out(c_bit1, s18))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s18)) | m_counter_cell_v_carry_out(c_bit1, s18))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(8000,plain,
% 13.70/13.88 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s18)) | m_counter_cell_v_carry_out(c_bit1, s18))),
% 13.70/13.88 inference(quant_inst,[status(thm)],[])).
% 13.70/13.88 tff(8001,plain,
% 13.70/13.88 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s18)) | m_counter_cell_v_carry_out(c_bit1, s18)),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[8000, 7999])).
% 13.70/13.88 tff(8002,plain,
% 13.70/13.88 (~m_counter_cell_v_carry_in(c_bit2, s18)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[8001, 3675, 7998])).
% 13.70/13.88 tff(8003,plain,
% 13.70/13.88 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s12, s13)) | node3(c_bit2, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s12, s13)) | node3(c_bit2, s12, s13))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(8004,plain,
% 13.70/13.88 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s12, s13)) | node3(c_bit2, s12, s13))),
% 13.70/13.88 inference(quant_inst,[status(thm)],[])).
% 13.70/13.88 tff(8005,plain,
% 13.70/13.88 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s12, s13)) | node3(c_bit2, s12, s13)),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[8004, 8003])).
% 13.70/13.88 tff(8006,plain,
% 13.70/13.88 (node3(c_bit2, s12, s13)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[8005, 59, 418])).
% 13.70/13.88 tff(8007,plain,
% 13.70/13.88 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s9) | (~node4(c_bit1, s9)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s9) | (~node4(c_bit1, s9)))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(8008,plain,
% 13.70/13.88 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s9) | (~node4(c_bit1, s9)))),
% 13.70/13.88 inference(quant_inst,[status(thm)],[])).
% 13.70/13.88 tff(8009,plain,
% 13.70/13.88 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s9) | (~node4(c_bit1, s9))),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[8008, 8007])).
% 13.70/13.88 tff(8010,plain,
% 13.70/13.88 (~node4(c_bit1, s9)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[8009, 1344, 1763])).
% 13.70/13.88 tff(8011,plain,
% 13.70/13.88 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s9)) | node4(c_bit1, s9))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s9)) | node4(c_bit1, s9))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(8012,plain,
% 13.70/13.88 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s9)) | node4(c_bit1, s9))),
% 13.70/13.88 inference(quant_inst,[status(thm)],[])).
% 13.70/13.88 tff(8013,plain,
% 13.70/13.88 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s9)) | node4(c_bit1, s9)),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[8012, 8011])).
% 13.70/13.88 tff(8014,plain,
% 13.70/13.88 (~m_counter_cell_v_carry_out(c_bit1, s9)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[8013, 1359, 8010])).
% 13.70/13.88 tff(8015,plain,
% 13.70/13.88 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s9)) | m_counter_cell_v_carry_out(c_bit1, s9))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s9)) | m_counter_cell_v_carry_out(c_bit1, s9))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(8016,plain,
% 13.70/13.88 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s9)) | m_counter_cell_v_carry_out(c_bit1, s9))),
% 13.70/13.88 inference(quant_inst,[status(thm)],[])).
% 13.70/13.88 tff(8017,plain,
% 13.70/13.88 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s9)) | m_counter_cell_v_carry_out(c_bit1, s9)),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[8016, 8015])).
% 13.70/13.88 tff(8018,plain,
% 13.70/13.88 (~m_counter_cell_v_carry_in(c_bit2, s9)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[8017, 3675, 8014])).
% 13.70/13.88 tff(8019,plain,
% 13.70/13.88 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | ((~node4(c_bit1, s8)) | m_counter_cell_v_carry_in(c_bit1, s8))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (~node4(c_bit1, s8)) | m_counter_cell_v_carry_in(c_bit1, s8))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(8020,plain,
% 13.70/13.88 ((m_counter_cell_v_carry_in(c_bit1, s8) | (~node4(c_bit1, s8))) <=> ((~node4(c_bit1, s8)) | m_counter_cell_v_carry_in(c_bit1, s8))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(8021,plain,
% 13.70/13.88 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s8) | (~node4(c_bit1, s8)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | ((~node4(c_bit1, s8)) | m_counter_cell_v_carry_in(c_bit1, s8)))),
% 13.70/13.88 inference(monotonicity,[status(thm)],[8020])).
% 13.70/13.88 tff(8022,plain,
% 13.70/13.88 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s8) | (~node4(c_bit1, s8)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (~node4(c_bit1, s8)) | m_counter_cell_v_carry_in(c_bit1, s8))),
% 13.70/13.88 inference(transitivity,[status(thm)],[8021, 8019])).
% 13.70/13.88 tff(8023,plain,
% 13.70/13.88 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s8) | (~node4(c_bit1, s8)))),
% 13.70/13.88 inference(quant_inst,[status(thm)],[])).
% 13.70/13.88 tff(8024,plain,
% 13.70/13.88 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (~node4(c_bit1, s8)) | m_counter_cell_v_carry_in(c_bit1, s8)),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[8023, 8022])).
% 13.70/13.88 tff(8025,plain,
% 13.70/13.88 (~node4(c_bit1, s8)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[8024, 2941, 1743])).
% 13.70/13.88 tff(8026,plain,
% 13.70/13.88 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s8)) | node4(c_bit1, s8))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s8)) | node4(c_bit1, s8))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(8027,plain,
% 13.70/13.88 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s8)) | node4(c_bit1, s8))),
% 13.70/13.88 inference(quant_inst,[status(thm)],[])).
% 13.70/13.88 tff(8028,plain,
% 13.70/13.88 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s8)) | node4(c_bit1, s8)),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[8027, 8026])).
% 13.70/13.88 tff(8029,plain,
% 13.70/13.88 (~m_counter_cell_v_carry_out(c_bit1, s8)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[8028, 1359, 8025])).
% 13.70/13.88 tff(8030,plain,
% 13.70/13.88 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s8)) | m_counter_cell_v_carry_out(c_bit1, s8))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s8)) | m_counter_cell_v_carry_out(c_bit1, s8))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(8031,plain,
% 13.70/13.88 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s8)) | m_counter_cell_v_carry_out(c_bit1, s8))),
% 13.70/13.88 inference(quant_inst,[status(thm)],[])).
% 13.70/13.88 tff(8032,plain,
% 13.70/13.88 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s8)) | m_counter_cell_v_carry_out(c_bit1, s8)),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[8031, 8030])).
% 13.70/13.88 tff(8033,plain,
% 13.70/13.88 (~m_counter_cell_v_carry_in(c_bit2, s8)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[8032, 3675, 8029])).
% 13.70/13.88 tff(8034,plain,
% 13.70/13.88 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s8) | m_counter_cell_v_value(c_bit2, s8) | (~node2(c_bit2, s8)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s8) | m_counter_cell_v_value(c_bit2, s8) | (~node2(c_bit2, s8)))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(8035,plain,
% 13.70/13.88 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s8) | m_counter_cell_v_value(c_bit2, s8) | (~node2(c_bit2, s8)))),
% 13.70/13.88 inference(quant_inst,[status(thm)],[])).
% 13.70/13.88 tff(8036,plain,
% 13.70/13.88 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s8) | m_counter_cell_v_value(c_bit2, s8) | (~node2(c_bit2, s8))),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[8035, 8034])).
% 13.70/13.88 tff(8037,plain,
% 13.70/13.88 (m_counter_cell_v_value(c_bit2, s8) | (~node2(c_bit2, s8))),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[8036, 1498, 8033])).
% 13.70/13.88 tff(8038,plain,
% 13.70/13.88 (~node2(c_bit2, s8)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[8037, 7824])).
% 13.70/13.88 tff(8039,plain,
% 13.70/13.88 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s8, s9)) | node3(c_bit2, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s8, s9)) | node3(c_bit2, s8, s9))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(8040,plain,
% 13.70/13.88 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s8, s9)) | node3(c_bit2, s8, s9))),
% 13.70/13.88 inference(quant_inst,[status(thm)],[])).
% 13.70/13.88 tff(8041,plain,
% 13.70/13.88 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s8, s9)) | node3(c_bit2, s8, s9)),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[8040, 8039])).
% 13.70/13.88 tff(8042,plain,
% 13.70/13.88 (node3(c_bit2, s8, s9)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[8041, 59, 308])).
% 13.70/13.88 tff(8043,plain,
% 13.70/13.88 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s9)) | node2(c_bit2, s8) | (~node3(c_bit2, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s9)) | node2(c_bit2, s8) | (~node3(c_bit2, s8, s9)))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(8044,plain,
% 13.70/13.88 ((node2(c_bit2, s8) | (~node3(c_bit2, s8, s9)) | (~m_counter_cell_v_value(c_bit2, s9))) <=> ((~m_counter_cell_v_value(c_bit2, s9)) | node2(c_bit2, s8) | (~node3(c_bit2, s8, s9)))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(8045,plain,
% 13.70/13.88 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s8) | (~node3(c_bit2, s8, s9)) | (~m_counter_cell_v_value(c_bit2, s9)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s9)) | node2(c_bit2, s8) | (~node3(c_bit2, s8, s9))))),
% 13.70/13.88 inference(monotonicity,[status(thm)],[8044])).
% 13.70/13.88 tff(8046,plain,
% 13.70/13.88 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s8) | (~node3(c_bit2, s8, s9)) | (~m_counter_cell_v_value(c_bit2, s9)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s9)) | node2(c_bit2, s8) | (~node3(c_bit2, s8, s9)))),
% 13.70/13.88 inference(transitivity,[status(thm)],[8045, 8043])).
% 13.70/13.88 tff(8047,plain,
% 13.70/13.88 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s8) | (~node3(c_bit2, s8, s9)) | (~m_counter_cell_v_value(c_bit2, s9)))),
% 13.70/13.88 inference(quant_inst,[status(thm)],[])).
% 13.70/13.88 tff(8048,plain,
% 13.70/13.88 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s9)) | node2(c_bit2, s8) | (~node3(c_bit2, s8, s9))),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[8047, 8046])).
% 13.70/13.88 tff(8049,plain,
% 13.70/13.88 ((~m_counter_cell_v_value(c_bit2, s9)) | node2(c_bit2, s8)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[8048, 121, 8042])).
% 13.70/13.88 tff(8050,plain,
% 13.70/13.88 (~m_counter_cell_v_value(c_bit2, s9)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[8049, 8038])).
% 13.70/13.88 tff(8051,plain,
% 13.70/13.88 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s9) | m_counter_cell_v_value(c_bit2, s9) | (~node2(c_bit2, s9)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s9) | m_counter_cell_v_value(c_bit2, s9) | (~node2(c_bit2, s9)))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(8052,plain,
% 13.70/13.88 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s9) | m_counter_cell_v_value(c_bit2, s9) | (~node2(c_bit2, s9)))),
% 13.70/13.88 inference(quant_inst,[status(thm)],[])).
% 13.70/13.88 tff(8053,plain,
% 13.70/13.88 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s9) | m_counter_cell_v_value(c_bit2, s9) | (~node2(c_bit2, s9))),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[8052, 8051])).
% 13.70/13.88 tff(8054,plain,
% 13.70/13.88 (m_counter_cell_v_carry_in(c_bit2, s9) | (~node2(c_bit2, s9))),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[8053, 1498, 8050])).
% 13.70/13.88 tff(8055,plain,
% 13.70/13.88 (~node2(c_bit2, s9)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[8054, 8018])).
% 13.70/13.88 tff(8056,plain,
% 13.70/13.88 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s9, s10)) | node3(c_bit2, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s9, s10)) | node3(c_bit2, s9, s10))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(8057,plain,
% 13.70/13.88 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s9, s10)) | node3(c_bit2, s9, s10))),
% 13.70/13.88 inference(quant_inst,[status(thm)],[])).
% 13.70/13.88 tff(8058,plain,
% 13.70/13.88 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s9, s10)) | node3(c_bit2, s9, s10)),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[8057, 8056])).
% 13.70/13.88 tff(8059,plain,
% 13.70/13.88 (node3(c_bit2, s9, s10)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[8058, 59, 334])).
% 13.70/13.88 tff(8060,plain,
% 13.70/13.88 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s10)) | node2(c_bit2, s9) | (~node3(c_bit2, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s10)) | node2(c_bit2, s9) | (~node3(c_bit2, s9, s10)))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(8061,plain,
% 13.70/13.88 ((node2(c_bit2, s9) | (~node3(c_bit2, s9, s10)) | (~m_counter_cell_v_value(c_bit2, s10))) <=> ((~m_counter_cell_v_value(c_bit2, s10)) | node2(c_bit2, s9) | (~node3(c_bit2, s9, s10)))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(8062,plain,
% 13.70/13.88 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s9) | (~node3(c_bit2, s9, s10)) | (~m_counter_cell_v_value(c_bit2, s10)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s10)) | node2(c_bit2, s9) | (~node3(c_bit2, s9, s10))))),
% 13.70/13.88 inference(monotonicity,[status(thm)],[8061])).
% 13.70/13.88 tff(8063,plain,
% 13.70/13.88 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s9) | (~node3(c_bit2, s9, s10)) | (~m_counter_cell_v_value(c_bit2, s10)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s10)) | node2(c_bit2, s9) | (~node3(c_bit2, s9, s10)))),
% 13.70/13.88 inference(transitivity,[status(thm)],[8062, 8060])).
% 13.70/13.88 tff(8064,plain,
% 13.70/13.88 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s9) | (~node3(c_bit2, s9, s10)) | (~m_counter_cell_v_value(c_bit2, s10)))),
% 13.70/13.88 inference(quant_inst,[status(thm)],[])).
% 13.70/13.88 tff(8065,plain,
% 13.70/13.88 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s10)) | node2(c_bit2, s9) | (~node3(c_bit2, s9, s10))),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[8064, 8063])).
% 13.70/13.88 tff(8066,plain,
% 13.70/13.88 ((~m_counter_cell_v_value(c_bit2, s10)) | node2(c_bit2, s9)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[8065, 121, 8059])).
% 13.70/13.88 tff(8067,plain,
% 13.70/13.88 (~m_counter_cell_v_value(c_bit2, s10)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[8066, 8055])).
% 13.70/13.88 tff(8068,plain,
% 13.70/13.88 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s10) | (~node4(c_bit1, s10)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s10) | (~node4(c_bit1, s10)))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(8069,plain,
% 13.70/13.88 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s10) | (~node4(c_bit1, s10)))),
% 13.70/13.88 inference(quant_inst,[status(thm)],[])).
% 13.70/13.88 tff(8070,plain,
% 13.70/13.88 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s10) | (~node4(c_bit1, s10))),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[8069, 8068])).
% 13.70/13.88 tff(8071,plain,
% 13.70/13.88 (~node4(c_bit1, s10)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[8070, 2941, 1804])).
% 13.70/13.88 tff(8072,plain,
% 13.70/13.88 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s10)) | node4(c_bit1, s10))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s10)) | node4(c_bit1, s10))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(8073,plain,
% 13.70/13.88 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s10)) | node4(c_bit1, s10))),
% 13.70/13.88 inference(quant_inst,[status(thm)],[])).
% 13.70/13.88 tff(8074,plain,
% 13.70/13.88 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s10)) | node4(c_bit1, s10)),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[8073, 8072])).
% 13.70/13.88 tff(8075,plain,
% 13.70/13.88 (~m_counter_cell_v_carry_out(c_bit1, s10)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[8074, 1359, 8071])).
% 13.70/13.88 tff(8076,plain,
% 13.70/13.88 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s10)) | m_counter_cell_v_carry_out(c_bit1, s10))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s10)) | m_counter_cell_v_carry_out(c_bit1, s10))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(8077,plain,
% 13.70/13.88 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s10)) | m_counter_cell_v_carry_out(c_bit1, s10))),
% 13.70/13.88 inference(quant_inst,[status(thm)],[])).
% 13.70/13.88 tff(8078,plain,
% 13.70/13.88 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s10)) | m_counter_cell_v_carry_out(c_bit1, s10)),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[8077, 8076])).
% 13.70/13.88 tff(8079,plain,
% 13.70/13.88 (~m_counter_cell_v_carry_in(c_bit2, s10)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[8078, 3675, 8075])).
% 13.70/13.88 tff(8080,plain,
% 13.70/13.88 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s10) | m_counter_cell_v_value(c_bit2, s10) | (~node2(c_bit2, s10)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s10) | m_counter_cell_v_value(c_bit2, s10) | (~node2(c_bit2, s10)))),
% 13.70/13.88 inference(rewrite,[status(thm)],[])).
% 13.70/13.88 tff(8081,plain,
% 13.70/13.88 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s10) | m_counter_cell_v_value(c_bit2, s10) | (~node2(c_bit2, s10)))),
% 13.70/13.88 inference(quant_inst,[status(thm)],[])).
% 13.70/13.88 tff(8082,plain,
% 13.70/13.88 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s10) | m_counter_cell_v_value(c_bit2, s10) | (~node2(c_bit2, s10))),
% 13.70/13.88 inference(modus_ponens,[status(thm)],[8081, 8080])).
% 13.70/13.88 tff(8083,plain,
% 13.70/13.88 (m_counter_cell_v_value(c_bit2, s10) | (~node2(c_bit2, s10))),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[8082, 1498, 8079])).
% 13.70/13.88 tff(8084,plain,
% 13.70/13.88 (~node2(c_bit2, s10)),
% 13.70/13.88 inference(unit_resolution,[status(thm)],[8083, 8067])).
% 13.70/13.88 tff(8085,plain,
% 13.70/13.89 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s10, s11)) | node3(c_bit2, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s10, s11)) | node3(c_bit2, s10, s11))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8086,plain,
% 13.70/13.89 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s10, s11)) | node3(c_bit2, s10, s11))),
% 13.70/13.89 inference(quant_inst,[status(thm)],[])).
% 13.70/13.89 tff(8087,plain,
% 13.70/13.89 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s10, s11)) | node3(c_bit2, s10, s11)),
% 13.70/13.89 inference(modus_ponens,[status(thm)],[8086, 8085])).
% 13.70/13.89 tff(8088,plain,
% 13.70/13.89 (node3(c_bit2, s10, s11)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8087, 59, 363])).
% 13.70/13.89 tff(8089,plain,
% 13.70/13.89 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s11)) | node2(c_bit2, s10) | (~node3(c_bit2, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s11)) | node2(c_bit2, s10) | (~node3(c_bit2, s10, s11)))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8090,plain,
% 13.70/13.89 ((node2(c_bit2, s10) | (~node3(c_bit2, s10, s11)) | (~m_counter_cell_v_value(c_bit2, s11))) <=> ((~m_counter_cell_v_value(c_bit2, s11)) | node2(c_bit2, s10) | (~node3(c_bit2, s10, s11)))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8091,plain,
% 13.70/13.89 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s10) | (~node3(c_bit2, s10, s11)) | (~m_counter_cell_v_value(c_bit2, s11)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s11)) | node2(c_bit2, s10) | (~node3(c_bit2, s10, s11))))),
% 13.70/13.89 inference(monotonicity,[status(thm)],[8090])).
% 13.70/13.89 tff(8092,plain,
% 13.70/13.89 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s10) | (~node3(c_bit2, s10, s11)) | (~m_counter_cell_v_value(c_bit2, s11)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s11)) | node2(c_bit2, s10) | (~node3(c_bit2, s10, s11)))),
% 13.70/13.89 inference(transitivity,[status(thm)],[8091, 8089])).
% 13.70/13.89 tff(8093,plain,
% 13.70/13.89 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s10) | (~node3(c_bit2, s10, s11)) | (~m_counter_cell_v_value(c_bit2, s11)))),
% 13.70/13.89 inference(quant_inst,[status(thm)],[])).
% 13.70/13.89 tff(8094,plain,
% 13.70/13.89 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s11)) | node2(c_bit2, s10) | (~node3(c_bit2, s10, s11))),
% 13.70/13.89 inference(modus_ponens,[status(thm)],[8093, 8092])).
% 13.70/13.89 tff(8095,plain,
% 13.70/13.89 ((~m_counter_cell_v_value(c_bit2, s11)) | node2(c_bit2, s10)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8094, 121, 8088])).
% 13.70/13.89 tff(8096,plain,
% 13.70/13.89 (~m_counter_cell_v_value(c_bit2, s11)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8095, 8084])).
% 13.70/13.89 tff(8097,plain,
% 13.70/13.89 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s11)) | (~m_counter_cell_v_value(c_bit1, s11)) | m_counter_cell_v_carry_out(c_bit1, s11))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s11)) | (~m_counter_cell_v_value(c_bit1, s11)) | m_counter_cell_v_carry_out(c_bit1, s11))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8098,plain,
% 13.70/13.89 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s11)) | (~m_counter_cell_v_value(c_bit1, s11)) | m_counter_cell_v_carry_out(c_bit1, s11))),
% 13.70/13.89 inference(quant_inst,[status(thm)],[])).
% 13.70/13.89 tff(8099,plain,
% 13.70/13.89 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s11)) | (~m_counter_cell_v_value(c_bit1, s11)) | m_counter_cell_v_carry_out(c_bit1, s11)),
% 13.70/13.89 inference(modus_ponens,[status(thm)],[8098, 8097])).
% 13.70/13.89 tff(8100,plain,
% 13.70/13.89 ((~m_counter_cell_v_value(c_bit1, s11)) | m_counter_cell_v_carry_out(c_bit1, s11)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8099, 1390, 1833])).
% 13.70/13.89 tff(8101,plain,
% 13.70/13.89 (m_counter_cell_v_carry_out(c_bit1, s11)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8100, 1824])).
% 13.70/13.89 tff(8102,plain,
% 13.70/13.89 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s11)) | m_counter_cell_v_carry_in(c_bit2, s11))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s11)) | m_counter_cell_v_carry_in(c_bit2, s11))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8103,plain,
% 13.70/13.89 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s11)) | m_counter_cell_v_carry_in(c_bit2, s11))),
% 13.70/13.89 inference(quant_inst,[status(thm)],[])).
% 13.70/13.89 tff(8104,plain,
% 13.70/13.89 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s11)) | m_counter_cell_v_carry_in(c_bit2, s11)),
% 13.70/13.89 inference(modus_ponens,[status(thm)],[8103, 8102])).
% 13.70/13.89 tff(8105,plain,
% 13.70/13.89 (m_counter_cell_v_carry_in(c_bit2, s11)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8104, 3305, 8101])).
% 13.70/13.89 tff(8106,plain,
% 13.70/13.89 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s11)) | m_counter_cell_v_value(c_bit2, s11) | (~node1(c_bit2, s11)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s11)) | m_counter_cell_v_value(c_bit2, s11) | (~node1(c_bit2, s11)))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8107,plain,
% 13.70/13.89 (((~node1(c_bit2, s11)) | (~m_counter_cell_v_carry_in(c_bit2, s11)) | m_counter_cell_v_value(c_bit2, s11)) <=> ((~m_counter_cell_v_carry_in(c_bit2, s11)) | m_counter_cell_v_value(c_bit2, s11) | (~node1(c_bit2, s11)))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8108,plain,
% 13.70/13.89 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s11)) | (~m_counter_cell_v_carry_in(c_bit2, s11)) | m_counter_cell_v_value(c_bit2, s11))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s11)) | m_counter_cell_v_value(c_bit2, s11) | (~node1(c_bit2, s11))))),
% 13.70/13.89 inference(monotonicity,[status(thm)],[8107])).
% 13.70/13.89 tff(8109,plain,
% 13.70/13.89 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s11)) | (~m_counter_cell_v_carry_in(c_bit2, s11)) | m_counter_cell_v_value(c_bit2, s11))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s11)) | m_counter_cell_v_value(c_bit2, s11) | (~node1(c_bit2, s11)))),
% 13.70/13.89 inference(transitivity,[status(thm)],[8108, 8106])).
% 13.70/13.89 tff(8110,plain,
% 13.70/13.89 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s11)) | (~m_counter_cell_v_carry_in(c_bit2, s11)) | m_counter_cell_v_value(c_bit2, s11))),
% 13.70/13.89 inference(quant_inst,[status(thm)],[])).
% 13.70/13.89 tff(8111,plain,
% 13.70/13.89 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s11)) | m_counter_cell_v_value(c_bit2, s11) | (~node1(c_bit2, s11))),
% 13.70/13.89 inference(modus_ponens,[status(thm)],[8110, 8109])).
% 13.70/13.89 tff(8112,plain,
% 13.70/13.89 (m_counter_cell_v_value(c_bit2, s11) | (~node1(c_bit2, s11))),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8111, 30, 8105])).
% 13.70/13.89 tff(8113,plain,
% 13.70/13.89 (~node1(c_bit2, s11)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8112, 8096])).
% 13.70/13.89 tff(8114,plain,
% 13.70/13.89 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s11, s12)) | node3(c_bit2, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s11, s12)) | node3(c_bit2, s11, s12))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8115,plain,
% 13.70/13.89 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s11, s12)) | node3(c_bit2, s11, s12))),
% 13.70/13.89 inference(quant_inst,[status(thm)],[])).
% 13.70/13.89 tff(8116,plain,
% 13.70/13.89 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s11, s12)) | node3(c_bit2, s11, s12)),
% 13.70/13.89 inference(modus_ponens,[status(thm)],[8115, 8114])).
% 13.70/13.89 tff(8117,plain,
% 13.70/13.89 (node3(c_bit2, s11, s12)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8116, 59, 389])).
% 13.70/13.89 tff(8118,plain,
% 13.70/13.89 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s12) | node1(c_bit2, s11) | (~node3(c_bit2, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s12) | node1(c_bit2, s11) | (~node3(c_bit2, s11, s12)))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8119,plain,
% 13.70/13.89 ((node1(c_bit2, s11) | (~node3(c_bit2, s11, s12)) | m_counter_cell_v_value(c_bit2, s12)) <=> (m_counter_cell_v_value(c_bit2, s12) | node1(c_bit2, s11) | (~node3(c_bit2, s11, s12)))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8120,plain,
% 13.70/13.89 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s11) | (~node3(c_bit2, s11, s12)) | m_counter_cell_v_value(c_bit2, s12))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s12) | node1(c_bit2, s11) | (~node3(c_bit2, s11, s12))))),
% 13.70/13.89 inference(monotonicity,[status(thm)],[8119])).
% 13.70/13.89 tff(8121,plain,
% 13.70/13.89 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s11) | (~node3(c_bit2, s11, s12)) | m_counter_cell_v_value(c_bit2, s12))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s12) | node1(c_bit2, s11) | (~node3(c_bit2, s11, s12)))),
% 13.70/13.89 inference(transitivity,[status(thm)],[8120, 8118])).
% 13.70/13.89 tff(8122,plain,
% 13.70/13.89 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s11) | (~node3(c_bit2, s11, s12)) | m_counter_cell_v_value(c_bit2, s12))),
% 13.70/13.89 inference(quant_inst,[status(thm)],[])).
% 13.70/13.89 tff(8123,plain,
% 13.70/13.89 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s12) | node1(c_bit2, s11) | (~node3(c_bit2, s11, s12))),
% 13.70/13.89 inference(modus_ponens,[status(thm)],[8122, 8121])).
% 13.70/13.89 tff(8124,plain,
% 13.70/13.89 (m_counter_cell_v_value(c_bit2, s12) | node1(c_bit2, s11)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8123, 73, 8117])).
% 13.70/13.89 tff(8125,plain,
% 13.70/13.89 (m_counter_cell_v_value(c_bit2, s12)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8124, 8113])).
% 13.70/13.89 tff(8126,plain,
% 13.70/13.89 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s12) | (~node4(c_bit1, s12)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s12) | (~node4(c_bit1, s12)))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8127,plain,
% 13.70/13.89 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s12) | (~node4(c_bit1, s12)))),
% 13.70/13.89 inference(quant_inst,[status(thm)],[])).
% 13.70/13.89 tff(8128,plain,
% 13.70/13.89 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s12) | (~node4(c_bit1, s12))),
% 13.70/13.89 inference(modus_ponens,[status(thm)],[8127, 8126])).
% 13.70/13.89 tff(8129,plain,
% 13.70/13.89 (~node4(c_bit1, s12)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8128, 2941, 1862])).
% 13.70/13.89 tff(8130,plain,
% 13.70/13.89 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s12)) | node4(c_bit1, s12))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s12)) | node4(c_bit1, s12))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8131,plain,
% 13.70/13.89 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s12)) | node4(c_bit1, s12))),
% 13.70/13.89 inference(quant_inst,[status(thm)],[])).
% 13.70/13.89 tff(8132,plain,
% 13.70/13.89 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s12)) | node4(c_bit1, s12)),
% 13.70/13.89 inference(modus_ponens,[status(thm)],[8131, 8130])).
% 13.70/13.89 tff(8133,plain,
% 13.70/13.89 (~m_counter_cell_v_carry_out(c_bit1, s12)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8132, 1359, 8129])).
% 13.70/13.89 tff(8134,plain,
% 13.70/13.89 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s12)) | m_counter_cell_v_carry_out(c_bit1, s12))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s12)) | m_counter_cell_v_carry_out(c_bit1, s12))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8135,plain,
% 13.70/13.89 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s12)) | m_counter_cell_v_carry_out(c_bit1, s12))),
% 13.70/13.89 inference(quant_inst,[status(thm)],[])).
% 13.70/13.89 tff(8136,plain,
% 13.70/13.89 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s12)) | m_counter_cell_v_carry_out(c_bit1, s12)),
% 13.70/13.89 inference(modus_ponens,[status(thm)],[8135, 8134])).
% 13.70/13.89 tff(8137,plain,
% 13.70/13.89 (~m_counter_cell_v_carry_in(c_bit2, s12)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8136, 3675, 8133])).
% 13.70/13.89 tff(8138,plain,
% 13.70/13.89 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s12) | (~m_counter_cell_v_value(c_bit2, s12)) | (~node1(c_bit2, s12)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s12) | (~m_counter_cell_v_value(c_bit2, s12)) | (~node1(c_bit2, s12)))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8139,plain,
% 13.70/13.89 (((~node1(c_bit2, s12)) | m_counter_cell_v_carry_in(c_bit2, s12) | (~m_counter_cell_v_value(c_bit2, s12))) <=> (m_counter_cell_v_carry_in(c_bit2, s12) | (~m_counter_cell_v_value(c_bit2, s12)) | (~node1(c_bit2, s12)))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8140,plain,
% 13.70/13.89 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s12)) | m_counter_cell_v_carry_in(c_bit2, s12) | (~m_counter_cell_v_value(c_bit2, s12)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s12) | (~m_counter_cell_v_value(c_bit2, s12)) | (~node1(c_bit2, s12))))),
% 13.70/13.89 inference(monotonicity,[status(thm)],[8139])).
% 13.70/13.89 tff(8141,plain,
% 13.70/13.89 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s12)) | m_counter_cell_v_carry_in(c_bit2, s12) | (~m_counter_cell_v_value(c_bit2, s12)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s12) | (~m_counter_cell_v_value(c_bit2, s12)) | (~node1(c_bit2, s12)))),
% 13.70/13.89 inference(transitivity,[status(thm)],[8140, 8138])).
% 13.70/13.89 tff(8142,plain,
% 13.70/13.89 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s12)) | m_counter_cell_v_carry_in(c_bit2, s12) | (~m_counter_cell_v_value(c_bit2, s12)))),
% 13.70/13.89 inference(quant_inst,[status(thm)],[])).
% 13.70/13.89 tff(8143,plain,
% 13.70/13.89 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s12) | (~m_counter_cell_v_value(c_bit2, s12)) | (~node1(c_bit2, s12))),
% 13.70/13.89 inference(modus_ponens,[status(thm)],[8142, 8141])).
% 13.70/13.89 tff(8144,plain,
% 13.70/13.89 ((~m_counter_cell_v_value(c_bit2, s12)) | (~node1(c_bit2, s12))),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8143, 1569, 8137])).
% 13.70/13.89 tff(8145,plain,
% 13.70/13.89 (~node1(c_bit2, s12)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8144, 8125])).
% 13.70/13.89 tff(8146,plain,
% 13.70/13.89 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s13) | node1(c_bit2, s12) | (~node3(c_bit2, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s13) | node1(c_bit2, s12) | (~node3(c_bit2, s12, s13)))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8147,plain,
% 13.70/13.89 ((node1(c_bit2, s12) | (~node3(c_bit2, s12, s13)) | m_counter_cell_v_value(c_bit2, s13)) <=> (m_counter_cell_v_value(c_bit2, s13) | node1(c_bit2, s12) | (~node3(c_bit2, s12, s13)))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8148,plain,
% 13.70/13.89 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s12) | (~node3(c_bit2, s12, s13)) | m_counter_cell_v_value(c_bit2, s13))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s13) | node1(c_bit2, s12) | (~node3(c_bit2, s12, s13))))),
% 13.70/13.89 inference(monotonicity,[status(thm)],[8147])).
% 13.70/13.89 tff(8149,plain,
% 13.70/13.89 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s12) | (~node3(c_bit2, s12, s13)) | m_counter_cell_v_value(c_bit2, s13))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s13) | node1(c_bit2, s12) | (~node3(c_bit2, s12, s13)))),
% 13.70/13.89 inference(transitivity,[status(thm)],[8148, 8146])).
% 13.70/13.89 tff(8150,plain,
% 13.70/13.89 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s12) | (~node3(c_bit2, s12, s13)) | m_counter_cell_v_value(c_bit2, s13))),
% 13.70/13.89 inference(quant_inst,[status(thm)],[])).
% 13.70/13.89 tff(8151,plain,
% 13.70/13.89 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s13) | node1(c_bit2, s12) | (~node3(c_bit2, s12, s13))),
% 13.70/13.89 inference(modus_ponens,[status(thm)],[8150, 8149])).
% 13.70/13.89 tff(8152,plain,
% 13.70/13.89 (m_counter_cell_v_value(c_bit2, s13)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8151, 73, 8145, 8006])).
% 13.70/13.89 tff(8153,plain,
% 13.70/13.89 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s13) | (~node4(c_bit1, s13)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s13) | (~node4(c_bit1, s13)))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8154,plain,
% 13.70/13.89 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s13) | (~node4(c_bit1, s13)))),
% 13.70/13.89 inference(quant_inst,[status(thm)],[])).
% 13.70/13.89 tff(8155,plain,
% 13.70/13.89 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s13) | (~node4(c_bit1, s13))),
% 13.70/13.89 inference(modus_ponens,[status(thm)],[8154, 8153])).
% 13.70/13.89 tff(8156,plain,
% 13.70/13.89 (~node4(c_bit1, s13)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8155, 1344, 1879])).
% 13.70/13.89 tff(8157,plain,
% 13.70/13.89 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s13)) | node4(c_bit1, s13))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s13)) | node4(c_bit1, s13))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8158,plain,
% 13.70/13.89 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s13)) | node4(c_bit1, s13))),
% 13.70/13.89 inference(quant_inst,[status(thm)],[])).
% 13.70/13.89 tff(8159,plain,
% 13.70/13.89 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s13)) | node4(c_bit1, s13)),
% 13.70/13.89 inference(modus_ponens,[status(thm)],[8158, 8157])).
% 13.70/13.89 tff(8160,plain,
% 13.70/13.89 (~m_counter_cell_v_carry_out(c_bit1, s13)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8159, 1359, 8156])).
% 13.70/13.89 tff(8161,plain,
% 13.70/13.89 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s13)) | m_counter_cell_v_carry_out(c_bit1, s13))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s13)) | m_counter_cell_v_carry_out(c_bit1, s13))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8162,plain,
% 13.70/13.89 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s13)) | m_counter_cell_v_carry_out(c_bit1, s13))),
% 13.70/13.89 inference(quant_inst,[status(thm)],[])).
% 13.70/13.89 tff(8163,plain,
% 13.70/13.89 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s13)) | m_counter_cell_v_carry_out(c_bit1, s13)),
% 13.70/13.89 inference(modus_ponens,[status(thm)],[8162, 8161])).
% 13.70/13.89 tff(8164,plain,
% 13.70/13.89 (~m_counter_cell_v_carry_in(c_bit2, s13)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8163, 3675, 8160])).
% 13.70/13.89 tff(8165,plain,
% 13.70/13.89 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s13) | (~m_counter_cell_v_value(c_bit2, s13)) | (~node1(c_bit2, s13)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s13) | (~m_counter_cell_v_value(c_bit2, s13)) | (~node1(c_bit2, s13)))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8166,plain,
% 13.70/13.89 (((~node1(c_bit2, s13)) | m_counter_cell_v_carry_in(c_bit2, s13) | (~m_counter_cell_v_value(c_bit2, s13))) <=> (m_counter_cell_v_carry_in(c_bit2, s13) | (~m_counter_cell_v_value(c_bit2, s13)) | (~node1(c_bit2, s13)))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8167,plain,
% 13.70/13.89 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s13)) | m_counter_cell_v_carry_in(c_bit2, s13) | (~m_counter_cell_v_value(c_bit2, s13)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s13) | (~m_counter_cell_v_value(c_bit2, s13)) | (~node1(c_bit2, s13))))),
% 13.70/13.89 inference(monotonicity,[status(thm)],[8166])).
% 13.70/13.89 tff(8168,plain,
% 13.70/13.89 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s13)) | m_counter_cell_v_carry_in(c_bit2, s13) | (~m_counter_cell_v_value(c_bit2, s13)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s13) | (~m_counter_cell_v_value(c_bit2, s13)) | (~node1(c_bit2, s13)))),
% 13.70/13.89 inference(transitivity,[status(thm)],[8167, 8165])).
% 13.70/13.89 tff(8169,plain,
% 13.70/13.89 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s13)) | m_counter_cell_v_carry_in(c_bit2, s13) | (~m_counter_cell_v_value(c_bit2, s13)))),
% 13.70/13.89 inference(quant_inst,[status(thm)],[])).
% 13.70/13.89 tff(8170,plain,
% 13.70/13.89 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s13) | (~m_counter_cell_v_value(c_bit2, s13)) | (~node1(c_bit2, s13))),
% 13.70/13.89 inference(modus_ponens,[status(thm)],[8169, 8168])).
% 13.70/13.89 tff(8171,plain,
% 13.70/13.89 ((~m_counter_cell_v_value(c_bit2, s13)) | (~node1(c_bit2, s13))),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8170, 1569, 8164])).
% 13.70/13.89 tff(8172,plain,
% 13.70/13.89 (~node1(c_bit2, s13)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8171, 8152])).
% 13.70/13.89 tff(8173,plain,
% 13.70/13.89 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s13, s14)) | node3(c_bit2, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s13, s14)) | node3(c_bit2, s13, s14))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8174,plain,
% 13.70/13.89 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s13, s14)) | node3(c_bit2, s13, s14))),
% 13.70/13.89 inference(quant_inst,[status(thm)],[])).
% 13.70/13.89 tff(8175,plain,
% 13.70/13.89 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s13, s14)) | node3(c_bit2, s13, s14)),
% 13.70/13.89 inference(modus_ponens,[status(thm)],[8174, 8173])).
% 13.70/13.89 tff(8176,plain,
% 13.70/13.89 (node3(c_bit2, s13, s14)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8175, 59, 444])).
% 13.70/13.89 tff(8177,plain,
% 13.70/13.89 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s14) | node1(c_bit2, s13) | (~node3(c_bit2, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s14) | node1(c_bit2, s13) | (~node3(c_bit2, s13, s14)))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8178,plain,
% 13.70/13.89 ((node1(c_bit2, s13) | (~node3(c_bit2, s13, s14)) | m_counter_cell_v_value(c_bit2, s14)) <=> (m_counter_cell_v_value(c_bit2, s14) | node1(c_bit2, s13) | (~node3(c_bit2, s13, s14)))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8179,plain,
% 13.70/13.89 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s13) | (~node3(c_bit2, s13, s14)) | m_counter_cell_v_value(c_bit2, s14))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s14) | node1(c_bit2, s13) | (~node3(c_bit2, s13, s14))))),
% 13.70/13.89 inference(monotonicity,[status(thm)],[8178])).
% 13.70/13.89 tff(8180,plain,
% 13.70/13.89 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s13) | (~node3(c_bit2, s13, s14)) | m_counter_cell_v_value(c_bit2, s14))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s14) | node1(c_bit2, s13) | (~node3(c_bit2, s13, s14)))),
% 13.70/13.89 inference(transitivity,[status(thm)],[8179, 8177])).
% 13.70/13.89 tff(8181,plain,
% 13.70/13.89 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s13) | (~node3(c_bit2, s13, s14)) | m_counter_cell_v_value(c_bit2, s14))),
% 13.70/13.89 inference(quant_inst,[status(thm)],[])).
% 13.70/13.89 tff(8182,plain,
% 13.70/13.89 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s14) | node1(c_bit2, s13) | (~node3(c_bit2, s13, s14))),
% 13.70/13.89 inference(modus_ponens,[status(thm)],[8181, 8180])).
% 13.70/13.89 tff(8183,plain,
% 13.70/13.89 (m_counter_cell_v_value(c_bit2, s14) | node1(c_bit2, s13)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8182, 73, 8176])).
% 13.70/13.89 tff(8184,plain,
% 13.70/13.89 (m_counter_cell_v_value(c_bit2, s14)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8183, 8172])).
% 13.70/13.89 tff(8185,plain,
% 13.70/13.89 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s14) | (~node4(c_bit1, s14)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s14) | (~node4(c_bit1, s14)))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8186,plain,
% 13.70/13.89 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s14) | (~node4(c_bit1, s14)))),
% 13.70/13.89 inference(quant_inst,[status(thm)],[])).
% 13.70/13.89 tff(8187,plain,
% 13.70/13.89 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s14) | (~node4(c_bit1, s14))),
% 13.70/13.89 inference(modus_ponens,[status(thm)],[8186, 8185])).
% 13.70/13.89 tff(8188,plain,
% 13.70/13.89 (~node4(c_bit1, s14)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8187, 2941, 1920])).
% 13.70/13.89 tff(8189,plain,
% 13.70/13.89 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s14)) | node4(c_bit1, s14))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s14)) | node4(c_bit1, s14))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8190,plain,
% 13.70/13.89 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s14)) | node4(c_bit1, s14))),
% 13.70/13.89 inference(quant_inst,[status(thm)],[])).
% 13.70/13.89 tff(8191,plain,
% 13.70/13.89 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s14)) | node4(c_bit1, s14)),
% 13.70/13.89 inference(modus_ponens,[status(thm)],[8190, 8189])).
% 13.70/13.89 tff(8192,plain,
% 13.70/13.89 (~m_counter_cell_v_carry_out(c_bit1, s14)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8191, 1359, 8188])).
% 13.70/13.89 tff(8193,plain,
% 13.70/13.89 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s14)) | m_counter_cell_v_carry_out(c_bit1, s14))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s14)) | m_counter_cell_v_carry_out(c_bit1, s14))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8194,plain,
% 13.70/13.89 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s14)) | m_counter_cell_v_carry_out(c_bit1, s14))),
% 13.70/13.89 inference(quant_inst,[status(thm)],[])).
% 13.70/13.89 tff(8195,plain,
% 13.70/13.89 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s14)) | m_counter_cell_v_carry_out(c_bit1, s14)),
% 13.70/13.89 inference(modus_ponens,[status(thm)],[8194, 8193])).
% 13.70/13.89 tff(8196,plain,
% 13.70/13.89 (~m_counter_cell_v_carry_in(c_bit2, s14)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8195, 3675, 8192])).
% 13.70/13.89 tff(8197,plain,
% 13.70/13.89 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s14) | (~m_counter_cell_v_value(c_bit2, s14)) | (~node1(c_bit2, s14)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s14) | (~m_counter_cell_v_value(c_bit2, s14)) | (~node1(c_bit2, s14)))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8198,plain,
% 13.70/13.89 (((~node1(c_bit2, s14)) | m_counter_cell_v_carry_in(c_bit2, s14) | (~m_counter_cell_v_value(c_bit2, s14))) <=> (m_counter_cell_v_carry_in(c_bit2, s14) | (~m_counter_cell_v_value(c_bit2, s14)) | (~node1(c_bit2, s14)))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8199,plain,
% 13.70/13.89 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s14)) | m_counter_cell_v_carry_in(c_bit2, s14) | (~m_counter_cell_v_value(c_bit2, s14)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s14) | (~m_counter_cell_v_value(c_bit2, s14)) | (~node1(c_bit2, s14))))),
% 13.70/13.89 inference(monotonicity,[status(thm)],[8198])).
% 13.70/13.89 tff(8200,plain,
% 13.70/13.89 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s14)) | m_counter_cell_v_carry_in(c_bit2, s14) | (~m_counter_cell_v_value(c_bit2, s14)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s14) | (~m_counter_cell_v_value(c_bit2, s14)) | (~node1(c_bit2, s14)))),
% 13.70/13.89 inference(transitivity,[status(thm)],[8199, 8197])).
% 13.70/13.89 tff(8201,plain,
% 13.70/13.89 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s14)) | m_counter_cell_v_carry_in(c_bit2, s14) | (~m_counter_cell_v_value(c_bit2, s14)))),
% 13.70/13.89 inference(quant_inst,[status(thm)],[])).
% 13.70/13.89 tff(8202,plain,
% 13.70/13.89 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s14) | (~m_counter_cell_v_value(c_bit2, s14)) | (~node1(c_bit2, s14))),
% 13.70/13.89 inference(modus_ponens,[status(thm)],[8201, 8200])).
% 13.70/13.89 tff(8203,plain,
% 13.70/13.89 ((~m_counter_cell_v_value(c_bit2, s14)) | (~node1(c_bit2, s14))),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8202, 1569, 8196])).
% 13.70/13.89 tff(8204,plain,
% 13.70/13.89 (~node1(c_bit2, s14)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8203, 8184])).
% 13.70/13.89 tff(8205,plain,
% 13.70/13.89 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s14, s15)) | node3(c_bit2, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s14, s15)) | node3(c_bit2, s14, s15))),
% 13.70/13.89 inference(rewrite,[status(thm)],[])).
% 13.70/13.89 tff(8206,plain,
% 13.70/13.89 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s14, s15)) | node3(c_bit2, s14, s15))),
% 13.70/13.89 inference(quant_inst,[status(thm)],[])).
% 13.70/13.89 tff(8207,plain,
% 13.70/13.89 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s14, s15)) | node3(c_bit2, s14, s15)),
% 13.70/13.89 inference(modus_ponens,[status(thm)],[8206, 8205])).
% 13.70/13.89 tff(8208,plain,
% 13.70/13.89 (node3(c_bit2, s14, s15)),
% 13.70/13.89 inference(unit_resolution,[status(thm)],[8207, 59, 473])).
% 13.70/13.89 tff(8209,plain,
% 13.70/13.89 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s15) | node1(c_bit2, s14) | (~node3(c_bit2, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s15) | node1(c_bit2, s14) | (~node3(c_bit2, s14, s15)))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8210,plain,
% 13.70/13.90 ((node1(c_bit2, s14) | (~node3(c_bit2, s14, s15)) | m_counter_cell_v_value(c_bit2, s15)) <=> (m_counter_cell_v_value(c_bit2, s15) | node1(c_bit2, s14) | (~node3(c_bit2, s14, s15)))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8211,plain,
% 13.70/13.90 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s14) | (~node3(c_bit2, s14, s15)) | m_counter_cell_v_value(c_bit2, s15))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s15) | node1(c_bit2, s14) | (~node3(c_bit2, s14, s15))))),
% 13.70/13.90 inference(monotonicity,[status(thm)],[8210])).
% 13.70/13.90 tff(8212,plain,
% 13.70/13.90 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s14) | (~node3(c_bit2, s14, s15)) | m_counter_cell_v_value(c_bit2, s15))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s15) | node1(c_bit2, s14) | (~node3(c_bit2, s14, s15)))),
% 13.70/13.90 inference(transitivity,[status(thm)],[8211, 8209])).
% 13.70/13.90 tff(8213,plain,
% 13.70/13.90 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s14) | (~node3(c_bit2, s14, s15)) | m_counter_cell_v_value(c_bit2, s15))),
% 13.70/13.90 inference(quant_inst,[status(thm)],[])).
% 13.70/13.90 tff(8214,plain,
% 13.70/13.90 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s15) | node1(c_bit2, s14) | (~node3(c_bit2, s14, s15))),
% 13.70/13.90 inference(modus_ponens,[status(thm)],[8213, 8212])).
% 13.70/13.90 tff(8215,plain,
% 13.70/13.90 (m_counter_cell_v_value(c_bit2, s15) | node1(c_bit2, s14)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8214, 73, 8208])).
% 13.70/13.90 tff(8216,plain,
% 13.70/13.90 (m_counter_cell_v_value(c_bit2, s15)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8215, 8204])).
% 13.70/13.90 tff(8217,plain,
% 13.70/13.90 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s15)) | (~m_counter_cell_v_value(c_bit1, s15)) | m_counter_cell_v_carry_out(c_bit1, s15))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s15)) | (~m_counter_cell_v_value(c_bit1, s15)) | m_counter_cell_v_carry_out(c_bit1, s15))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8218,plain,
% 13.70/13.90 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s15)) | (~m_counter_cell_v_value(c_bit1, s15)) | m_counter_cell_v_carry_out(c_bit1, s15))),
% 13.70/13.90 inference(quant_inst,[status(thm)],[])).
% 13.70/13.90 tff(8219,plain,
% 13.70/13.90 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s15)) | (~m_counter_cell_v_value(c_bit1, s15)) | m_counter_cell_v_carry_out(c_bit1, s15)),
% 13.70/13.90 inference(modus_ponens,[status(thm)],[8218, 8217])).
% 13.70/13.90 tff(8220,plain,
% 13.70/13.90 ((~m_counter_cell_v_value(c_bit1, s15)) | m_counter_cell_v_carry_out(c_bit1, s15)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8219, 1390, 1949])).
% 13.70/13.90 tff(8221,plain,
% 13.70/13.90 (m_counter_cell_v_carry_out(c_bit1, s15)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8220, 1940])).
% 13.70/13.90 tff(8222,plain,
% 13.70/13.90 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s15)) | m_counter_cell_v_carry_in(c_bit2, s15))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s15)) | m_counter_cell_v_carry_in(c_bit2, s15))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8223,plain,
% 13.70/13.90 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s15)) | m_counter_cell_v_carry_in(c_bit2, s15))),
% 13.70/13.90 inference(quant_inst,[status(thm)],[])).
% 13.70/13.90 tff(8224,plain,
% 13.70/13.90 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s15)) | m_counter_cell_v_carry_in(c_bit2, s15)),
% 13.70/13.90 inference(modus_ponens,[status(thm)],[8223, 8222])).
% 13.70/13.90 tff(8225,plain,
% 13.70/13.90 (m_counter_cell_v_carry_in(c_bit2, s15)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8224, 3305, 8221])).
% 13.70/13.90 tff(8226,plain,
% 13.70/13.90 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit2, s15)) | (~m_counter_cell_v_value(c_bit2, s15)) | (~node2(c_bit2, s15)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit2, s15)) | (~m_counter_cell_v_value(c_bit2, s15)) | (~node2(c_bit2, s15)))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8227,plain,
% 13.70/13.90 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit2, s15)) | (~m_counter_cell_v_value(c_bit2, s15)) | (~node2(c_bit2, s15)))),
% 13.70/13.90 inference(quant_inst,[status(thm)],[])).
% 13.70/13.90 tff(8228,plain,
% 13.70/13.90 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit2, s15)) | (~m_counter_cell_v_value(c_bit2, s15)) | (~node2(c_bit2, s15))),
% 13.70/13.90 inference(modus_ponens,[status(thm)],[8227, 8226])).
% 13.70/13.90 tff(8229,plain,
% 13.70/13.90 ((~m_counter_cell_v_value(c_bit2, s15)) | (~node2(c_bit2, s15))),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8228, 93, 8225])).
% 13.70/13.90 tff(8230,plain,
% 13.70/13.90 (~node2(c_bit2, s15)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8229, 8216])).
% 13.70/13.90 tff(8231,plain,
% 13.70/13.90 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s15, s16)) | node3(c_bit2, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s15, s16)) | node3(c_bit2, s15, s16))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8232,plain,
% 13.70/13.90 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s15, s16)) | node3(c_bit2, s15, s16))),
% 13.70/13.90 inference(quant_inst,[status(thm)],[])).
% 13.70/13.90 tff(8233,plain,
% 13.70/13.90 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s15, s16)) | node3(c_bit2, s15, s16)),
% 13.70/13.90 inference(modus_ponens,[status(thm)],[8232, 8231])).
% 13.70/13.90 tff(8234,plain,
% 13.70/13.90 (node3(c_bit2, s15, s16)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8233, 59, 499])).
% 13.70/13.90 tff(8235,plain,
% 13.70/13.90 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s16)) | node2(c_bit2, s15) | (~node3(c_bit2, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s16)) | node2(c_bit2, s15) | (~node3(c_bit2, s15, s16)))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8236,plain,
% 13.70/13.90 ((node2(c_bit2, s15) | (~node3(c_bit2, s15, s16)) | (~m_counter_cell_v_value(c_bit2, s16))) <=> ((~m_counter_cell_v_value(c_bit2, s16)) | node2(c_bit2, s15) | (~node3(c_bit2, s15, s16)))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8237,plain,
% 13.70/13.90 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s15) | (~node3(c_bit2, s15, s16)) | (~m_counter_cell_v_value(c_bit2, s16)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s16)) | node2(c_bit2, s15) | (~node3(c_bit2, s15, s16))))),
% 13.70/13.90 inference(monotonicity,[status(thm)],[8236])).
% 13.70/13.90 tff(8238,plain,
% 13.70/13.90 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s15) | (~node3(c_bit2, s15, s16)) | (~m_counter_cell_v_value(c_bit2, s16)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s16)) | node2(c_bit2, s15) | (~node3(c_bit2, s15, s16)))),
% 13.70/13.90 inference(transitivity,[status(thm)],[8237, 8235])).
% 13.70/13.90 tff(8239,plain,
% 13.70/13.90 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s15) | (~node3(c_bit2, s15, s16)) | (~m_counter_cell_v_value(c_bit2, s16)))),
% 13.70/13.90 inference(quant_inst,[status(thm)],[])).
% 13.70/13.90 tff(8240,plain,
% 13.70/13.90 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s16)) | node2(c_bit2, s15) | (~node3(c_bit2, s15, s16))),
% 13.70/13.90 inference(modus_ponens,[status(thm)],[8239, 8238])).
% 13.70/13.90 tff(8241,plain,
% 13.70/13.90 ((~m_counter_cell_v_value(c_bit2, s16)) | node2(c_bit2, s15)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8240, 121, 8234])).
% 13.70/13.90 tff(8242,plain,
% 13.70/13.90 (~m_counter_cell_v_value(c_bit2, s16)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8241, 8230])).
% 13.70/13.90 tff(8243,plain,
% 13.70/13.90 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s16) | (~node4(c_bit1, s16)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s16) | (~node4(c_bit1, s16)))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8244,plain,
% 13.70/13.90 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s16) | (~node4(c_bit1, s16)))),
% 13.70/13.90 inference(quant_inst,[status(thm)],[])).
% 13.70/13.90 tff(8245,plain,
% 13.70/13.90 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s16) | (~node4(c_bit1, s16))),
% 13.70/13.90 inference(modus_ponens,[status(thm)],[8244, 8243])).
% 13.70/13.90 tff(8246,plain,
% 13.70/13.90 (~node4(c_bit1, s16)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8245, 2941, 1978])).
% 13.70/13.90 tff(8247,plain,
% 13.70/13.90 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s16)) | node4(c_bit1, s16))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s16)) | node4(c_bit1, s16))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8248,plain,
% 13.70/13.90 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s16)) | node4(c_bit1, s16))),
% 13.70/13.90 inference(quant_inst,[status(thm)],[])).
% 13.70/13.90 tff(8249,plain,
% 13.70/13.90 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s16)) | node4(c_bit1, s16)),
% 13.70/13.90 inference(modus_ponens,[status(thm)],[8248, 8247])).
% 13.70/13.90 tff(8250,plain,
% 13.70/13.90 (~m_counter_cell_v_carry_out(c_bit1, s16)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8249, 1359, 8246])).
% 13.70/13.90 tff(8251,plain,
% 13.70/13.90 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s16)) | m_counter_cell_v_carry_out(c_bit1, s16))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s16)) | m_counter_cell_v_carry_out(c_bit1, s16))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8252,plain,
% 13.70/13.90 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s16)) | m_counter_cell_v_carry_out(c_bit1, s16))),
% 13.70/13.90 inference(quant_inst,[status(thm)],[])).
% 13.70/13.90 tff(8253,plain,
% 13.70/13.90 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s16)) | m_counter_cell_v_carry_out(c_bit1, s16)),
% 13.70/13.90 inference(modus_ponens,[status(thm)],[8252, 8251])).
% 13.70/13.90 tff(8254,plain,
% 13.70/13.90 (~m_counter_cell_v_carry_in(c_bit2, s16)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8253, 3675, 8250])).
% 13.70/13.90 tff(8255,plain,
% 13.70/13.90 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s16) | m_counter_cell_v_value(c_bit2, s16) | (~node2(c_bit2, s16)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s16) | m_counter_cell_v_value(c_bit2, s16) | (~node2(c_bit2, s16)))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8256,plain,
% 13.70/13.90 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s16) | m_counter_cell_v_value(c_bit2, s16) | (~node2(c_bit2, s16)))),
% 13.70/13.90 inference(quant_inst,[status(thm)],[])).
% 13.70/13.90 tff(8257,plain,
% 13.70/13.90 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s16) | m_counter_cell_v_value(c_bit2, s16) | (~node2(c_bit2, s16))),
% 13.70/13.90 inference(modus_ponens,[status(thm)],[8256, 8255])).
% 13.70/13.90 tff(8258,plain,
% 13.70/13.90 (m_counter_cell_v_value(c_bit2, s16) | (~node2(c_bit2, s16))),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8257, 1498, 8254])).
% 13.70/13.90 tff(8259,plain,
% 13.70/13.90 (~node2(c_bit2, s16)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8258, 8242])).
% 13.70/13.90 tff(8260,plain,
% 13.70/13.90 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s16, s17)) | node3(c_bit2, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s16, s17)) | node3(c_bit2, s16, s17))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8261,plain,
% 13.70/13.90 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s16, s17)) | node3(c_bit2, s16, s17))),
% 13.70/13.90 inference(quant_inst,[status(thm)],[])).
% 13.70/13.90 tff(8262,plain,
% 13.70/13.90 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s16, s17)) | node3(c_bit2, s16, s17)),
% 13.70/13.90 inference(modus_ponens,[status(thm)],[8261, 8260])).
% 13.70/13.90 tff(8263,plain,
% 13.70/13.90 (node3(c_bit2, s16, s17)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8262, 59, 528])).
% 13.70/13.90 tff(8264,plain,
% 13.70/13.90 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s17)) | node2(c_bit2, s16) | (~node3(c_bit2, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s17)) | node2(c_bit2, s16) | (~node3(c_bit2, s16, s17)))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8265,plain,
% 13.70/13.90 ((node2(c_bit2, s16) | (~node3(c_bit2, s16, s17)) | (~m_counter_cell_v_value(c_bit2, s17))) <=> ((~m_counter_cell_v_value(c_bit2, s17)) | node2(c_bit2, s16) | (~node3(c_bit2, s16, s17)))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8266,plain,
% 13.70/13.90 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s16) | (~node3(c_bit2, s16, s17)) | (~m_counter_cell_v_value(c_bit2, s17)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s17)) | node2(c_bit2, s16) | (~node3(c_bit2, s16, s17))))),
% 13.70/13.90 inference(monotonicity,[status(thm)],[8265])).
% 13.70/13.90 tff(8267,plain,
% 13.70/13.90 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s16) | (~node3(c_bit2, s16, s17)) | (~m_counter_cell_v_value(c_bit2, s17)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s17)) | node2(c_bit2, s16) | (~node3(c_bit2, s16, s17)))),
% 13.70/13.90 inference(transitivity,[status(thm)],[8266, 8264])).
% 13.70/13.90 tff(8268,plain,
% 13.70/13.90 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s16) | (~node3(c_bit2, s16, s17)) | (~m_counter_cell_v_value(c_bit2, s17)))),
% 13.70/13.90 inference(quant_inst,[status(thm)],[])).
% 13.70/13.90 tff(8269,plain,
% 13.70/13.90 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s17)) | node2(c_bit2, s16) | (~node3(c_bit2, s16, s17))),
% 13.70/13.90 inference(modus_ponens,[status(thm)],[8268, 8267])).
% 13.70/13.90 tff(8270,plain,
% 13.70/13.90 ((~m_counter_cell_v_value(c_bit2, s17)) | node2(c_bit2, s16)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8269, 121, 8263])).
% 13.70/13.90 tff(8271,plain,
% 13.70/13.90 (~m_counter_cell_v_value(c_bit2, s17)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8270, 8259])).
% 13.70/13.90 tff(8272,plain,
% 13.70/13.90 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s17) | (~node4(c_bit1, s17)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s17) | (~node4(c_bit1, s17)))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8273,plain,
% 13.70/13.90 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s17) | (~node4(c_bit1, s17)))),
% 13.70/13.90 inference(quant_inst,[status(thm)],[])).
% 13.70/13.90 tff(8274,plain,
% 13.70/13.90 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s17) | (~node4(c_bit1, s17))),
% 13.70/13.90 inference(modus_ponens,[status(thm)],[8273, 8272])).
% 13.70/13.90 tff(8275,plain,
% 13.70/13.90 (~node4(c_bit1, s17)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8274, 1344, 1995])).
% 13.70/13.90 tff(8276,plain,
% 13.70/13.90 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s17)) | node4(c_bit1, s17))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s17)) | node4(c_bit1, s17))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8277,plain,
% 13.70/13.90 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s17)) | node4(c_bit1, s17))),
% 13.70/13.90 inference(quant_inst,[status(thm)],[])).
% 13.70/13.90 tff(8278,plain,
% 13.70/13.90 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s17)) | node4(c_bit1, s17)),
% 13.70/13.90 inference(modus_ponens,[status(thm)],[8277, 8276])).
% 13.70/13.90 tff(8279,plain,
% 13.70/13.90 (~m_counter_cell_v_carry_out(c_bit1, s17)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8278, 1359, 8275])).
% 13.70/13.90 tff(8280,plain,
% 13.70/13.90 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s17)) | m_counter_cell_v_carry_out(c_bit1, s17))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s17)) | m_counter_cell_v_carry_out(c_bit1, s17))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8281,plain,
% 13.70/13.90 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s17)) | m_counter_cell_v_carry_out(c_bit1, s17))),
% 13.70/13.90 inference(quant_inst,[status(thm)],[])).
% 13.70/13.90 tff(8282,plain,
% 13.70/13.90 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s17)) | m_counter_cell_v_carry_out(c_bit1, s17)),
% 13.70/13.90 inference(modus_ponens,[status(thm)],[8281, 8280])).
% 13.70/13.90 tff(8283,plain,
% 13.70/13.90 (~m_counter_cell_v_carry_in(c_bit2, s17)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8282, 3675, 8279])).
% 13.70/13.90 tff(8284,plain,
% 13.70/13.90 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s17) | m_counter_cell_v_value(c_bit2, s17) | (~node2(c_bit2, s17)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s17) | m_counter_cell_v_value(c_bit2, s17) | (~node2(c_bit2, s17)))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8285,plain,
% 13.70/13.90 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s17) | m_counter_cell_v_value(c_bit2, s17) | (~node2(c_bit2, s17)))),
% 13.70/13.90 inference(quant_inst,[status(thm)],[])).
% 13.70/13.90 tff(8286,plain,
% 13.70/13.90 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s17) | m_counter_cell_v_value(c_bit2, s17) | (~node2(c_bit2, s17))),
% 13.70/13.90 inference(modus_ponens,[status(thm)],[8285, 8284])).
% 13.70/13.90 tff(8287,plain,
% 13.70/13.90 (m_counter_cell_v_value(c_bit2, s17) | (~node2(c_bit2, s17))),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8286, 1498, 8283])).
% 13.70/13.90 tff(8288,plain,
% 13.70/13.90 (~node2(c_bit2, s17)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8287, 8271])).
% 13.70/13.90 tff(8289,plain,
% 13.70/13.90 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s17, s18)) | node3(c_bit2, s17, s18))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s17, s18)) | node3(c_bit2, s17, s18))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8290,plain,
% 13.70/13.90 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s17, s18)) | node3(c_bit2, s17, s18))),
% 13.70/13.90 inference(quant_inst,[status(thm)],[])).
% 13.70/13.90 tff(8291,plain,
% 13.70/13.90 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s17, s18)) | node3(c_bit2, s17, s18)),
% 13.70/13.90 inference(modus_ponens,[status(thm)],[8290, 8289])).
% 13.70/13.90 tff(8292,plain,
% 13.70/13.90 (node3(c_bit2, s17, s18)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8291, 59, 556])).
% 13.70/13.90 tff(8293,plain,
% 13.70/13.90 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s18)) | node2(c_bit2, s17) | (~node3(c_bit2, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s18)) | node2(c_bit2, s17) | (~node3(c_bit2, s17, s18)))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8294,plain,
% 13.70/13.90 ((node2(c_bit2, s17) | (~node3(c_bit2, s17, s18)) | (~m_counter_cell_v_value(c_bit2, s18))) <=> ((~m_counter_cell_v_value(c_bit2, s18)) | node2(c_bit2, s17) | (~node3(c_bit2, s17, s18)))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8295,plain,
% 13.70/13.90 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s17) | (~node3(c_bit2, s17, s18)) | (~m_counter_cell_v_value(c_bit2, s18)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s18)) | node2(c_bit2, s17) | (~node3(c_bit2, s17, s18))))),
% 13.70/13.90 inference(monotonicity,[status(thm)],[8294])).
% 13.70/13.90 tff(8296,plain,
% 13.70/13.90 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s17) | (~node3(c_bit2, s17, s18)) | (~m_counter_cell_v_value(c_bit2, s18)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s18)) | node2(c_bit2, s17) | (~node3(c_bit2, s17, s18)))),
% 13.70/13.90 inference(transitivity,[status(thm)],[8295, 8293])).
% 13.70/13.90 tff(8297,plain,
% 13.70/13.90 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s17) | (~node3(c_bit2, s17, s18)) | (~m_counter_cell_v_value(c_bit2, s18)))),
% 13.70/13.90 inference(quant_inst,[status(thm)],[])).
% 13.70/13.90 tff(8298,plain,
% 13.70/13.90 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s18)) | node2(c_bit2, s17) | (~node3(c_bit2, s17, s18))),
% 13.70/13.90 inference(modus_ponens,[status(thm)],[8297, 8296])).
% 13.70/13.90 tff(8299,plain,
% 13.70/13.90 ((~m_counter_cell_v_value(c_bit2, s18)) | node2(c_bit2, s17)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8298, 121, 8292])).
% 13.70/13.90 tff(8300,plain,
% 13.70/13.90 (~m_counter_cell_v_value(c_bit2, s18)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8299, 8288])).
% 13.70/13.90 tff(8301,plain,
% 13.70/13.90 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s18) | m_counter_cell_v_value(c_bit2, s18) | (~node2(c_bit2, s18)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s18) | m_counter_cell_v_value(c_bit2, s18) | (~node2(c_bit2, s18)))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8302,plain,
% 13.70/13.90 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s18) | m_counter_cell_v_value(c_bit2, s18) | (~node2(c_bit2, s18)))),
% 13.70/13.90 inference(quant_inst,[status(thm)],[])).
% 13.70/13.90 tff(8303,plain,
% 13.70/13.90 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s18) | m_counter_cell_v_value(c_bit2, s18) | (~node2(c_bit2, s18))),
% 13.70/13.90 inference(modus_ponens,[status(thm)],[8302, 8301])).
% 13.70/13.90 tff(8304,plain,
% 13.70/13.90 (m_counter_cell_v_carry_in(c_bit2, s18) | (~node2(c_bit2, s18))),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8303, 1498, 8300])).
% 13.70/13.90 tff(8305,plain,
% 13.70/13.90 (~node2(c_bit2, s18)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8304, 8002])).
% 13.70/13.90 tff(8306,plain,
% 13.70/13.90 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s18, s19)) | node3(c_bit2, s18, s19))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s18, s19)) | node3(c_bit2, s18, s19))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8307,plain,
% 13.70/13.90 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s18, s19)) | node3(c_bit2, s18, s19))),
% 13.70/13.90 inference(quant_inst,[status(thm)],[])).
% 13.70/13.90 tff(8308,plain,
% 13.70/13.90 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s18, s19)) | node3(c_bit2, s18, s19)),
% 13.70/13.90 inference(modus_ponens,[status(thm)],[8307, 8306])).
% 13.70/13.90 tff(8309,plain,
% 13.70/13.90 (node3(c_bit2, s18, s19)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8308, 59, 587])).
% 13.70/13.90 tff(8310,plain,
% 13.70/13.90 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s19)) | node2(c_bit2, s18) | (~node3(c_bit2, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s19)) | node2(c_bit2, s18) | (~node3(c_bit2, s18, s19)))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8311,plain,
% 13.70/13.90 ((node2(c_bit2, s18) | (~node3(c_bit2, s18, s19)) | (~m_counter_cell_v_value(c_bit2, s19))) <=> ((~m_counter_cell_v_value(c_bit2, s19)) | node2(c_bit2, s18) | (~node3(c_bit2, s18, s19)))),
% 13.70/13.90 inference(rewrite,[status(thm)],[])).
% 13.70/13.90 tff(8312,plain,
% 13.70/13.90 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s18) | (~node3(c_bit2, s18, s19)) | (~m_counter_cell_v_value(c_bit2, s19)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s19)) | node2(c_bit2, s18) | (~node3(c_bit2, s18, s19))))),
% 13.70/13.90 inference(monotonicity,[status(thm)],[8311])).
% 13.70/13.90 tff(8313,plain,
% 13.70/13.90 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s18) | (~node3(c_bit2, s18, s19)) | (~m_counter_cell_v_value(c_bit2, s19)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s19)) | node2(c_bit2, s18) | (~node3(c_bit2, s18, s19)))),
% 13.70/13.90 inference(transitivity,[status(thm)],[8312, 8310])).
% 13.70/13.90 tff(8314,plain,
% 13.70/13.90 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s18) | (~node3(c_bit2, s18, s19)) | (~m_counter_cell_v_value(c_bit2, s19)))),
% 13.70/13.90 inference(quant_inst,[status(thm)],[])).
% 13.70/13.90 tff(8315,plain,
% 13.70/13.90 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s19)) | node2(c_bit2, s18) | (~node3(c_bit2, s18, s19))),
% 13.70/13.90 inference(modus_ponens,[status(thm)],[8314, 8313])).
% 13.70/13.90 tff(8316,plain,
% 13.70/13.90 ((~m_counter_cell_v_value(c_bit2, s19)) | node2(c_bit2, s18)),
% 13.70/13.90 inference(unit_resolution,[status(thm)],[8315, 121, 8309])).
% 13.70/13.90 tff(8317,plain,
% 13.70/13.90 (~m_counter_cell_v_value(c_bit2, s19)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8316, 8305])).
% 13.70/13.91 tff(8318,plain,
% 13.70/13.91 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s19)) | m_counter_cell_v_value(c_bit2, s19) | (~node1(c_bit2, s19)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s19)) | m_counter_cell_v_value(c_bit2, s19) | (~node1(c_bit2, s19)))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8319,plain,
% 13.70/13.91 (((~node1(c_bit2, s19)) | (~m_counter_cell_v_carry_in(c_bit2, s19)) | m_counter_cell_v_value(c_bit2, s19)) <=> ((~m_counter_cell_v_carry_in(c_bit2, s19)) | m_counter_cell_v_value(c_bit2, s19) | (~node1(c_bit2, s19)))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8320,plain,
% 13.70/13.91 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s19)) | (~m_counter_cell_v_carry_in(c_bit2, s19)) | m_counter_cell_v_value(c_bit2, s19))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s19)) | m_counter_cell_v_value(c_bit2, s19) | (~node1(c_bit2, s19))))),
% 13.70/13.91 inference(monotonicity,[status(thm)],[8319])).
% 13.70/13.91 tff(8321,plain,
% 13.70/13.91 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s19)) | (~m_counter_cell_v_carry_in(c_bit2, s19)) | m_counter_cell_v_value(c_bit2, s19))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s19)) | m_counter_cell_v_value(c_bit2, s19) | (~node1(c_bit2, s19)))),
% 13.70/13.91 inference(transitivity,[status(thm)],[8320, 8318])).
% 13.70/13.91 tff(8322,plain,
% 13.70/13.91 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s19)) | (~m_counter_cell_v_carry_in(c_bit2, s19)) | m_counter_cell_v_value(c_bit2, s19))),
% 13.70/13.91 inference(quant_inst,[status(thm)],[])).
% 13.70/13.91 tff(8323,plain,
% 13.70/13.91 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s19)) | m_counter_cell_v_value(c_bit2, s19) | (~node1(c_bit2, s19))),
% 13.70/13.91 inference(modus_ponens,[status(thm)],[8322, 8321])).
% 13.70/13.91 tff(8324,plain,
% 13.70/13.91 (~node1(c_bit2, s19)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8323, 30, 8317, 7988])).
% 13.70/13.91 tff(8325,plain,
% 13.70/13.91 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s19, s20)) | node3(c_bit2, s19, s20))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s19, s20)) | node3(c_bit2, s19, s20))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8326,plain,
% 13.70/13.91 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s19, s20)) | node3(c_bit2, s19, s20))),
% 13.70/13.91 inference(quant_inst,[status(thm)],[])).
% 13.70/13.91 tff(8327,plain,
% 13.70/13.91 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s19, s20)) | node3(c_bit2, s19, s20)),
% 13.70/13.91 inference(modus_ponens,[status(thm)],[8326, 8325])).
% 13.70/13.91 tff(8328,plain,
% 13.70/13.91 (node3(c_bit2, s19, s20)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8327, 59, 615])).
% 13.70/13.91 tff(8329,plain,
% 13.70/13.91 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s20) | node1(c_bit2, s19) | (~node3(c_bit2, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s20) | node1(c_bit2, s19) | (~node3(c_bit2, s19, s20)))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8330,plain,
% 13.70/13.91 ((node1(c_bit2, s19) | (~node3(c_bit2, s19, s20)) | m_counter_cell_v_value(c_bit2, s20)) <=> (m_counter_cell_v_value(c_bit2, s20) | node1(c_bit2, s19) | (~node3(c_bit2, s19, s20)))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8331,plain,
% 13.70/13.91 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s19) | (~node3(c_bit2, s19, s20)) | m_counter_cell_v_value(c_bit2, s20))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s20) | node1(c_bit2, s19) | (~node3(c_bit2, s19, s20))))),
% 13.70/13.91 inference(monotonicity,[status(thm)],[8330])).
% 13.70/13.91 tff(8332,plain,
% 13.70/13.91 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s19) | (~node3(c_bit2, s19, s20)) | m_counter_cell_v_value(c_bit2, s20))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s20) | node1(c_bit2, s19) | (~node3(c_bit2, s19, s20)))),
% 13.70/13.91 inference(transitivity,[status(thm)],[8331, 8329])).
% 13.70/13.91 tff(8333,plain,
% 13.70/13.91 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s19) | (~node3(c_bit2, s19, s20)) | m_counter_cell_v_value(c_bit2, s20))),
% 13.70/13.91 inference(quant_inst,[status(thm)],[])).
% 13.70/13.91 tff(8334,plain,
% 13.70/13.91 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s20) | node1(c_bit2, s19) | (~node3(c_bit2, s19, s20))),
% 13.70/13.91 inference(modus_ponens,[status(thm)],[8333, 8332])).
% 13.70/13.91 tff(8335,plain,
% 13.70/13.91 (m_counter_cell_v_value(c_bit2, s20) | node1(c_bit2, s19)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8334, 73, 8328])).
% 13.70/13.91 tff(8336,plain,
% 13.70/13.91 (m_counter_cell_v_value(c_bit2, s20)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8335, 8324])).
% 13.70/13.91 tff(8337,plain,
% 13.70/13.91 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s20) | (~node4(c_bit1, s20)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s20) | (~node4(c_bit1, s20)))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8338,plain,
% 13.70/13.91 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s20) | (~node4(c_bit1, s20)))),
% 13.70/13.91 inference(quant_inst,[status(thm)],[])).
% 13.70/13.91 tff(8339,plain,
% 13.70/13.91 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s20) | (~node4(c_bit1, s20))),
% 13.70/13.91 inference(modus_ponens,[status(thm)],[8338, 8337])).
% 13.70/13.91 tff(8340,plain,
% 13.70/13.91 (~node4(c_bit1, s20)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8339, 1344, 2081])).
% 13.70/13.91 tff(8341,plain,
% 13.70/13.91 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s20)) | node4(c_bit1, s20))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s20)) | node4(c_bit1, s20))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8342,plain,
% 13.70/13.91 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s20)) | node4(c_bit1, s20))),
% 13.70/13.91 inference(quant_inst,[status(thm)],[])).
% 13.70/13.91 tff(8343,plain,
% 13.70/13.91 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s20)) | node4(c_bit1, s20)),
% 13.70/13.91 inference(modus_ponens,[status(thm)],[8342, 8341])).
% 13.70/13.91 tff(8344,plain,
% 13.70/13.91 (~m_counter_cell_v_carry_out(c_bit1, s20)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8343, 1359, 8340])).
% 13.70/13.91 tff(8345,plain,
% 13.70/13.91 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s20)) | m_counter_cell_v_carry_out(c_bit1, s20))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s20)) | m_counter_cell_v_carry_out(c_bit1, s20))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8346,plain,
% 13.70/13.91 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s20)) | m_counter_cell_v_carry_out(c_bit1, s20))),
% 13.70/13.91 inference(quant_inst,[status(thm)],[])).
% 13.70/13.91 tff(8347,plain,
% 13.70/13.91 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s20)) | m_counter_cell_v_carry_out(c_bit1, s20)),
% 13.70/13.91 inference(modus_ponens,[status(thm)],[8346, 8345])).
% 13.70/13.91 tff(8348,plain,
% 13.70/13.91 (~m_counter_cell_v_carry_in(c_bit2, s20)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8347, 3675, 8344])).
% 13.70/13.91 tff(8349,plain,
% 13.70/13.91 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s20) | (~m_counter_cell_v_value(c_bit2, s20)) | (~node1(c_bit2, s20)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s20) | (~m_counter_cell_v_value(c_bit2, s20)) | (~node1(c_bit2, s20)))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8350,plain,
% 13.70/13.91 (((~node1(c_bit2, s20)) | m_counter_cell_v_carry_in(c_bit2, s20) | (~m_counter_cell_v_value(c_bit2, s20))) <=> (m_counter_cell_v_carry_in(c_bit2, s20) | (~m_counter_cell_v_value(c_bit2, s20)) | (~node1(c_bit2, s20)))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8351,plain,
% 13.70/13.91 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s20)) | m_counter_cell_v_carry_in(c_bit2, s20) | (~m_counter_cell_v_value(c_bit2, s20)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s20) | (~m_counter_cell_v_value(c_bit2, s20)) | (~node1(c_bit2, s20))))),
% 13.70/13.91 inference(monotonicity,[status(thm)],[8350])).
% 13.70/13.91 tff(8352,plain,
% 13.70/13.91 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s20)) | m_counter_cell_v_carry_in(c_bit2, s20) | (~m_counter_cell_v_value(c_bit2, s20)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s20) | (~m_counter_cell_v_value(c_bit2, s20)) | (~node1(c_bit2, s20)))),
% 13.70/13.91 inference(transitivity,[status(thm)],[8351, 8349])).
% 13.70/13.91 tff(8353,plain,
% 13.70/13.91 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s20)) | m_counter_cell_v_carry_in(c_bit2, s20) | (~m_counter_cell_v_value(c_bit2, s20)))),
% 13.70/13.91 inference(quant_inst,[status(thm)],[])).
% 13.70/13.91 tff(8354,plain,
% 13.70/13.91 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s20) | (~m_counter_cell_v_value(c_bit2, s20)) | (~node1(c_bit2, s20))),
% 13.70/13.91 inference(modus_ponens,[status(thm)],[8353, 8352])).
% 13.70/13.91 tff(8355,plain,
% 13.70/13.91 ((~m_counter_cell_v_value(c_bit2, s20)) | (~node1(c_bit2, s20))),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8354, 1569, 8348])).
% 13.70/13.91 tff(8356,plain,
% 13.70/13.91 (~node1(c_bit2, s20)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8355, 8336])).
% 13.70/13.91 tff(8357,plain,
% 13.70/13.91 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s20, s21)) | node3(c_bit2, s20, s21))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s20, s21)) | node3(c_bit2, s20, s21))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8358,plain,
% 13.70/13.91 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s20, s21)) | node3(c_bit2, s20, s21))),
% 13.70/13.91 inference(quant_inst,[status(thm)],[])).
% 13.70/13.91 tff(8359,plain,
% 13.70/13.91 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s20, s21)) | node3(c_bit2, s20, s21)),
% 13.70/13.91 inference(modus_ponens,[status(thm)],[8358, 8357])).
% 13.70/13.91 tff(8360,plain,
% 13.70/13.91 (node3(c_bit2, s20, s21)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8359, 59, 646])).
% 13.70/13.91 tff(8361,plain,
% 13.70/13.91 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s21) | node1(c_bit2, s20) | (~node3(c_bit2, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s21) | node1(c_bit2, s20) | (~node3(c_bit2, s20, s21)))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8362,plain,
% 13.70/13.91 ((node1(c_bit2, s20) | (~node3(c_bit2, s20, s21)) | m_counter_cell_v_value(c_bit2, s21)) <=> (m_counter_cell_v_value(c_bit2, s21) | node1(c_bit2, s20) | (~node3(c_bit2, s20, s21)))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8363,plain,
% 13.70/13.91 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s20) | (~node3(c_bit2, s20, s21)) | m_counter_cell_v_value(c_bit2, s21))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s21) | node1(c_bit2, s20) | (~node3(c_bit2, s20, s21))))),
% 13.70/13.91 inference(monotonicity,[status(thm)],[8362])).
% 13.70/13.91 tff(8364,plain,
% 13.70/13.91 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s20) | (~node3(c_bit2, s20, s21)) | m_counter_cell_v_value(c_bit2, s21))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s21) | node1(c_bit2, s20) | (~node3(c_bit2, s20, s21)))),
% 13.70/13.91 inference(transitivity,[status(thm)],[8363, 8361])).
% 13.70/13.91 tff(8365,plain,
% 13.70/13.91 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s20) | (~node3(c_bit2, s20, s21)) | m_counter_cell_v_value(c_bit2, s21))),
% 13.70/13.91 inference(quant_inst,[status(thm)],[])).
% 13.70/13.91 tff(8366,plain,
% 13.70/13.91 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s21) | node1(c_bit2, s20) | (~node3(c_bit2, s20, s21))),
% 13.70/13.91 inference(modus_ponens,[status(thm)],[8365, 8364])).
% 13.70/13.91 tff(8367,plain,
% 13.70/13.91 (m_counter_cell_v_value(c_bit2, s21) | node1(c_bit2, s20)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8366, 73, 8360])).
% 13.70/13.91 tff(8368,plain,
% 13.70/13.91 (m_counter_cell_v_value(c_bit2, s21)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8367, 8356])).
% 13.70/13.91 tff(8369,plain,
% 13.70/13.91 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s21)) | (~m_counter_cell_v_value(c_bit2, s21)) | m_counter_cell_v_carry_out(c_bit2, s21))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s21)) | (~m_counter_cell_v_value(c_bit2, s21)) | m_counter_cell_v_carry_out(c_bit2, s21))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8370,plain,
% 13.70/13.91 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s21)) | (~m_counter_cell_v_value(c_bit2, s21)) | m_counter_cell_v_carry_out(c_bit2, s21))),
% 13.70/13.91 inference(quant_inst,[status(thm)],[])).
% 13.70/13.91 tff(8371,plain,
% 13.70/13.91 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s21)) | (~m_counter_cell_v_value(c_bit2, s21)) | m_counter_cell_v_carry_out(c_bit2, s21)),
% 13.70/13.91 inference(modus_ponens,[status(thm)],[8370, 8369])).
% 13.70/13.91 tff(8372,plain,
% 13.70/13.91 ((~m_counter_cell_v_carry_in(c_bit2, s21)) | m_counter_cell_v_carry_out(c_bit2, s21)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8371, 1390, 8368])).
% 13.70/13.91 tff(8373,plain,
% 13.70/13.91 (~m_counter_cell_v_carry_in(c_bit2, s21)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8372, 7971])).
% 13.70/13.91 tff(8374,plain,
% 13.70/13.91 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s21) | (~m_counter_cell_v_value(c_bit2, s21)) | (~node1(c_bit2, s21)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s21) | (~m_counter_cell_v_value(c_bit2, s21)) | (~node1(c_bit2, s21)))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8375,plain,
% 13.70/13.91 (((~node1(c_bit2, s21)) | m_counter_cell_v_carry_in(c_bit2, s21) | (~m_counter_cell_v_value(c_bit2, s21))) <=> (m_counter_cell_v_carry_in(c_bit2, s21) | (~m_counter_cell_v_value(c_bit2, s21)) | (~node1(c_bit2, s21)))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8376,plain,
% 13.70/13.91 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s21)) | m_counter_cell_v_carry_in(c_bit2, s21) | (~m_counter_cell_v_value(c_bit2, s21)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s21) | (~m_counter_cell_v_value(c_bit2, s21)) | (~node1(c_bit2, s21))))),
% 13.70/13.91 inference(monotonicity,[status(thm)],[8375])).
% 13.70/13.91 tff(8377,plain,
% 13.70/13.91 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s21)) | m_counter_cell_v_carry_in(c_bit2, s21) | (~m_counter_cell_v_value(c_bit2, s21)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s21) | (~m_counter_cell_v_value(c_bit2, s21)) | (~node1(c_bit2, s21)))),
% 13.70/13.91 inference(transitivity,[status(thm)],[8376, 8374])).
% 13.70/13.91 tff(8378,plain,
% 13.70/13.91 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s21)) | m_counter_cell_v_carry_in(c_bit2, s21) | (~m_counter_cell_v_value(c_bit2, s21)))),
% 13.70/13.91 inference(quant_inst,[status(thm)],[])).
% 13.70/13.91 tff(8379,plain,
% 13.70/13.91 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s21) | (~m_counter_cell_v_value(c_bit2, s21)) | (~node1(c_bit2, s21))),
% 13.70/13.91 inference(modus_ponens,[status(thm)],[8378, 8377])).
% 13.70/13.91 tff(8380,plain,
% 13.70/13.91 (m_counter_cell_v_carry_in(c_bit2, s21) | (~node1(c_bit2, s21))),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8379, 1569, 8368])).
% 13.70/13.91 tff(8381,plain,
% 13.70/13.91 (~node1(c_bit2, s21)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8380, 8373])).
% 13.70/13.91 tff(8382,plain,
% 13.70/13.91 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s21, s22)) | node3(c_bit2, s21, s22))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s21, s22)) | node3(c_bit2, s21, s22))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8383,plain,
% 13.70/13.91 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s21, s22)) | node3(c_bit2, s21, s22))),
% 13.70/13.91 inference(quant_inst,[status(thm)],[])).
% 13.70/13.91 tff(8384,plain,
% 13.70/13.91 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s21, s22)) | node3(c_bit2, s21, s22)),
% 13.70/13.91 inference(modus_ponens,[status(thm)],[8383, 8382])).
% 13.70/13.91 tff(8385,plain,
% 13.70/13.91 (node3(c_bit2, s21, s22)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8384, 59, 674])).
% 13.70/13.91 tff(8386,plain,
% 13.70/13.91 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s22) | node1(c_bit2, s21) | (~node3(c_bit2, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s22) | node1(c_bit2, s21) | (~node3(c_bit2, s21, s22)))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8387,plain,
% 13.70/13.91 ((node1(c_bit2, s21) | (~node3(c_bit2, s21, s22)) | m_counter_cell_v_value(c_bit2, s22)) <=> (m_counter_cell_v_value(c_bit2, s22) | node1(c_bit2, s21) | (~node3(c_bit2, s21, s22)))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8388,plain,
% 13.70/13.91 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s21) | (~node3(c_bit2, s21, s22)) | m_counter_cell_v_value(c_bit2, s22))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s22) | node1(c_bit2, s21) | (~node3(c_bit2, s21, s22))))),
% 13.70/13.91 inference(monotonicity,[status(thm)],[8387])).
% 13.70/13.91 tff(8389,plain,
% 13.70/13.91 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s21) | (~node3(c_bit2, s21, s22)) | m_counter_cell_v_value(c_bit2, s22))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s22) | node1(c_bit2, s21) | (~node3(c_bit2, s21, s22)))),
% 13.70/13.91 inference(transitivity,[status(thm)],[8388, 8386])).
% 13.70/13.91 tff(8390,plain,
% 13.70/13.91 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s21) | (~node3(c_bit2, s21, s22)) | m_counter_cell_v_value(c_bit2, s22))),
% 13.70/13.91 inference(quant_inst,[status(thm)],[])).
% 13.70/13.91 tff(8391,plain,
% 13.70/13.91 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s22) | node1(c_bit2, s21) | (~node3(c_bit2, s21, s22))),
% 13.70/13.91 inference(modus_ponens,[status(thm)],[8390, 8389])).
% 13.70/13.91 tff(8392,plain,
% 13.70/13.91 (m_counter_cell_v_value(c_bit2, s22) | node1(c_bit2, s21)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8391, 73, 8385])).
% 13.70/13.91 tff(8393,plain,
% 13.70/13.91 (m_counter_cell_v_value(c_bit2, s22)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8392, 8381])).
% 13.70/13.91 tff(8394,assumption,(node4(c_bit1, s22)), introduced(assumption)).
% 13.70/13.91 tff(8395,assumption,(~m_counter_cell_v_carry_in(c_bit1, s22)), introduced(assumption)).
% 13.70/13.91 tff(8396,plain,
% 13.70/13.91 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s22) | (~node4(c_bit1, s22)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s22) | (~node4(c_bit1, s22)))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8397,plain,
% 13.70/13.91 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s22) | (~node4(c_bit1, s22)))),
% 13.70/13.91 inference(quant_inst,[status(thm)],[])).
% 13.70/13.91 tff(8398,plain,
% 13.70/13.91 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s22) | (~node4(c_bit1, s22))),
% 13.70/13.91 inference(modus_ponens,[status(thm)],[8397, 8396])).
% 13.70/13.91 tff(8399,plain,
% 13.70/13.91 ($false),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8398, 2941, 8395, 8394])).
% 13.70/13.91 tff(8400,plain,((~node4(c_bit1, s22)) | m_counter_cell_v_carry_in(c_bit1, s22)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.91 tff(8401,plain,
% 13.70/13.91 (~node4(c_bit1, s22)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8400, 2151])).
% 13.70/13.91 tff(8402,assumption,(m_counter_cell_v_carry_out(c_bit1, s22)), introduced(assumption)).
% 13.70/13.91 tff(8403,assumption,(~node4(c_bit1, s22)), introduced(assumption)).
% 13.70/13.91 tff(8404,plain,
% 13.70/13.91 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s22)) | node4(c_bit1, s22))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s22)) | node4(c_bit1, s22))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8405,plain,
% 13.70/13.91 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s22)) | node4(c_bit1, s22))),
% 13.70/13.91 inference(quant_inst,[status(thm)],[])).
% 13.70/13.91 tff(8406,plain,
% 13.70/13.91 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s22)) | node4(c_bit1, s22)),
% 13.70/13.91 inference(modus_ponens,[status(thm)],[8405, 8404])).
% 13.70/13.91 tff(8407,plain,
% 13.70/13.91 ($false),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8406, 1359, 8403, 8402])).
% 13.70/13.91 tff(8408,plain,((~m_counter_cell_v_carry_out(c_bit1, s22)) | node4(c_bit1, s22)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.91 tff(8409,plain,
% 13.70/13.91 (~m_counter_cell_v_carry_out(c_bit1, s22)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8408, 8401])).
% 13.70/13.91 tff(8410,assumption,(m_counter_cell_v_carry_in(c_bit2, s22)), introduced(assumption)).
% 13.70/13.91 tff(8411,assumption,(~m_counter_cell_v_carry_out(c_bit1, s22)), introduced(assumption)).
% 13.70/13.91 tff(8412,plain,
% 13.70/13.91 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s22)) | m_counter_cell_v_carry_out(c_bit1, s22))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s22)) | m_counter_cell_v_carry_out(c_bit1, s22))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8413,plain,
% 13.70/13.91 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s22)) | m_counter_cell_v_carry_out(c_bit1, s22))),
% 13.70/13.91 inference(quant_inst,[status(thm)],[])).
% 13.70/13.91 tff(8414,plain,
% 13.70/13.91 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s22)) | m_counter_cell_v_carry_out(c_bit1, s22)),
% 13.70/13.91 inference(modus_ponens,[status(thm)],[8413, 8412])).
% 13.70/13.91 tff(8415,plain,
% 13.70/13.91 ($false),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8414, 3675, 8411, 8410])).
% 13.70/13.91 tff(8416,plain,((~m_counter_cell_v_carry_in(c_bit2, s22)) | m_counter_cell_v_carry_out(c_bit1, s22)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.91 tff(8417,plain,
% 13.70/13.91 (~m_counter_cell_v_carry_in(c_bit2, s22)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8416, 8409])).
% 13.70/13.91 tff(8418,plain,
% 13.70/13.91 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s22) | (~m_counter_cell_v_value(c_bit2, s22)) | (~node1(c_bit2, s22)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s22) | (~m_counter_cell_v_value(c_bit2, s22)) | (~node1(c_bit2, s22)))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8419,plain,
% 13.70/13.91 (((~node1(c_bit2, s22)) | m_counter_cell_v_carry_in(c_bit2, s22) | (~m_counter_cell_v_value(c_bit2, s22))) <=> (m_counter_cell_v_carry_in(c_bit2, s22) | (~m_counter_cell_v_value(c_bit2, s22)) | (~node1(c_bit2, s22)))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8420,plain,
% 13.70/13.91 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s22)) | m_counter_cell_v_carry_in(c_bit2, s22) | (~m_counter_cell_v_value(c_bit2, s22)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s22) | (~m_counter_cell_v_value(c_bit2, s22)) | (~node1(c_bit2, s22))))),
% 13.70/13.91 inference(monotonicity,[status(thm)],[8419])).
% 13.70/13.91 tff(8421,plain,
% 13.70/13.91 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s22)) | m_counter_cell_v_carry_in(c_bit2, s22) | (~m_counter_cell_v_value(c_bit2, s22)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s22) | (~m_counter_cell_v_value(c_bit2, s22)) | (~node1(c_bit2, s22)))),
% 13.70/13.91 inference(transitivity,[status(thm)],[8420, 8418])).
% 13.70/13.91 tff(8422,plain,
% 13.70/13.91 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s22)) | m_counter_cell_v_carry_in(c_bit2, s22) | (~m_counter_cell_v_value(c_bit2, s22)))),
% 13.70/13.91 inference(quant_inst,[status(thm)],[])).
% 13.70/13.91 tff(8423,plain,
% 13.70/13.91 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s22) | (~m_counter_cell_v_value(c_bit2, s22)) | (~node1(c_bit2, s22))),
% 13.70/13.91 inference(modus_ponens,[status(thm)],[8422, 8421])).
% 13.70/13.91 tff(8424,plain,
% 13.70/13.91 ((~m_counter_cell_v_value(c_bit2, s22)) | (~node1(c_bit2, s22))),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8423, 1569, 8417])).
% 13.70/13.91 tff(8425,plain,
% 13.70/13.91 ($false),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8424, 8393, 7967])).
% 13.70/13.91 tff(8426,plain,(~always5(s21)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.91 tff(8427,plain,
% 13.70/13.91 (~always5(s20)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[4201, 8426])).
% 13.70/13.91 tff(8428,assumption,(~always5(s20)), introduced(assumption)).
% 13.70/13.91 tff(8429,plain,
% 13.70/13.91 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s20) | (~trans(s59, s20)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s20) | (~trans(s59, s20)))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8430,plain,
% 13.70/13.91 (((~always5(s59)) | (~trans(s59, s20)) | always5(s20)) <=> ((~always5(s59)) | always5(s20) | (~trans(s59, s20)))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8431,plain,
% 13.70/13.91 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s20)) | always5(s20))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s20) | (~trans(s59, s20))))),
% 13.70/13.91 inference(monotonicity,[status(thm)],[8430])).
% 13.70/13.91 tff(8432,plain,
% 13.70/13.91 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s20)) | always5(s20))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s20) | (~trans(s59, s20)))),
% 13.70/13.91 inference(transitivity,[status(thm)],[8431, 8429])).
% 13.70/13.91 tff(8433,plain,
% 13.70/13.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s20)) | always5(s20))),
% 13.70/13.91 inference(quant_inst,[status(thm)],[])).
% 13.70/13.91 tff(8434,plain,
% 13.70/13.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s20) | (~trans(s59, s20))),
% 13.70/13.91 inference(modus_ponens,[status(thm)],[8433, 8432])).
% 13.70/13.91 tff(8435,plain,
% 13.70/13.91 ($false),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8434, 6019, 3890, 6915, 8428])).
% 13.70/13.91 tff(8436,plain,((~trans(s59, s20)) | always5(s20)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.91 tff(8437,plain,
% 13.70/13.91 (~trans(s59, s20)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8436, 8427])).
% 13.70/13.91 tff(8438,plain,
% 13.70/13.91 (~always5(s24)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[4169, 7503])).
% 13.70/13.91 tff(8439,plain,
% 13.70/13.91 (~always5(s23)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[4177, 8438])).
% 13.70/13.91 tff(8440,plain,
% 13.70/13.91 (~always5(s22)),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[4185, 8439])).
% 13.70/13.91 tff(8441,assumption,(~always5(s22)), introduced(assumption)).
% 13.70/13.91 tff(8442,plain,
% 13.70/13.91 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s22) | (~trans(s59, s22)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s22) | (~trans(s59, s22)))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8443,plain,
% 13.70/13.91 (((~always5(s59)) | (~trans(s59, s22)) | always5(s22)) <=> ((~always5(s59)) | always5(s22) | (~trans(s59, s22)))),
% 13.70/13.91 inference(rewrite,[status(thm)],[])).
% 13.70/13.91 tff(8444,plain,
% 13.70/13.91 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s22)) | always5(s22))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s22) | (~trans(s59, s22))))),
% 13.70/13.91 inference(monotonicity,[status(thm)],[8443])).
% 13.70/13.91 tff(8445,plain,
% 13.70/13.91 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s22)) | always5(s22))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s22) | (~trans(s59, s22)))),
% 13.70/13.91 inference(transitivity,[status(thm)],[8444, 8442])).
% 13.70/13.91 tff(8446,plain,
% 13.70/13.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s22)) | always5(s22))),
% 13.70/13.91 inference(quant_inst,[status(thm)],[])).
% 13.70/13.91 tff(8447,plain,
% 13.70/13.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s22) | (~trans(s59, s22))),
% 13.70/13.91 inference(modus_ponens,[status(thm)],[8446, 8445])).
% 13.70/13.91 tff(8448,plain,
% 13.70/13.91 ($false),
% 13.70/13.91 inference(unit_resolution,[status(thm)],[8447, 6030, 3890, 6915, 8441])).
% 13.70/13.91 tff(8449,plain,((~trans(s59, s22)) | always5(s22)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.91 tff(8450,plain,
% 13.70/13.91 (~trans(s59, s22)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8449, 8440])).
% 13.70/13.92 tff(8451,assumption,(~always5(s30)), introduced(assumption)).
% 13.70/13.92 tff(8452,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s30) | (~trans(s59, s30)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s30) | (~trans(s59, s30)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8453,plain,
% 13.70/13.92 (((~always5(s59)) | (~trans(s59, s30)) | always5(s30)) <=> ((~always5(s59)) | always5(s30) | (~trans(s59, s30)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8454,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s30)) | always5(s30))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s30) | (~trans(s59, s30))))),
% 13.70/13.92 inference(monotonicity,[status(thm)],[8453])).
% 13.70/13.92 tff(8455,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s30)) | always5(s30))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s30) | (~trans(s59, s30)))),
% 13.70/13.92 inference(transitivity,[status(thm)],[8454, 8452])).
% 13.70/13.92 tff(8456,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s30)) | always5(s30))),
% 13.70/13.92 inference(quant_inst,[status(thm)],[])).
% 13.70/13.92 tff(8457,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s30) | (~trans(s59, s30))),
% 13.70/13.92 inference(modus_ponens,[status(thm)],[8456, 8455])).
% 13.70/13.92 tff(8458,plain,
% 13.70/13.92 ($false),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8457, 6052, 3890, 6915, 8451])).
% 13.70/13.92 tff(8459,plain,((~trans(s59, s30)) | always5(s30)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.92 tff(8460,plain,
% 13.70/13.92 (~trans(s59, s30)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8459, 7464])).
% 13.70/13.92 tff(8461,plain,
% 13.70/13.92 (~always5(s19)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[4209, 8427])).
% 13.70/13.92 tff(8462,plain,
% 13.70/13.92 (~always5(s18)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[4217, 8461])).
% 13.70/13.92 tff(8463,assumption,(~always5(s18)), introduced(assumption)).
% 13.70/13.92 tff(8464,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s18) | (~trans(s59, s18)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s18) | (~trans(s59, s18)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8465,plain,
% 13.70/13.92 (((~always5(s59)) | (~trans(s59, s18)) | always5(s18)) <=> ((~always5(s59)) | always5(s18) | (~trans(s59, s18)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8466,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s18)) | always5(s18))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s18) | (~trans(s59, s18))))),
% 13.70/13.92 inference(monotonicity,[status(thm)],[8465])).
% 13.70/13.92 tff(8467,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s18)) | always5(s18))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s18) | (~trans(s59, s18)))),
% 13.70/13.92 inference(transitivity,[status(thm)],[8466, 8464])).
% 13.70/13.92 tff(8468,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s18)) | always5(s18))),
% 13.70/13.92 inference(quant_inst,[status(thm)],[])).
% 13.70/13.92 tff(8469,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s18) | (~trans(s59, s18))),
% 13.70/13.92 inference(modus_ponens,[status(thm)],[8468, 8467])).
% 13.70/13.92 tff(8470,plain,
% 13.70/13.92 ($false),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8469, 6063, 3890, 6915, 8463])).
% 13.70/13.92 tff(8471,plain,((~trans(s59, s18)) | always5(s18)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.92 tff(8472,plain,
% 13.70/13.92 (~trans(s59, s18)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8471, 8462])).
% 13.70/13.92 tff(8473,assumption,(~always5(s28)), introduced(assumption)).
% 13.70/13.92 tff(8474,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s28) | (~trans(s59, s28)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s28) | (~trans(s59, s28)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8475,plain,
% 13.70/13.92 (((~always5(s59)) | (~trans(s59, s28)) | always5(s28)) <=> ((~always5(s59)) | always5(s28) | (~trans(s59, s28)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8476,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s28)) | always5(s28))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s28) | (~trans(s59, s28))))),
% 13.70/13.92 inference(monotonicity,[status(thm)],[8475])).
% 13.70/13.92 tff(8477,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s28)) | always5(s28))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s28) | (~trans(s59, s28)))),
% 13.70/13.92 inference(transitivity,[status(thm)],[8476, 8474])).
% 13.70/13.92 tff(8478,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s28)) | always5(s28))),
% 13.70/13.92 inference(quant_inst,[status(thm)],[])).
% 13.70/13.92 tff(8479,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s28) | (~trans(s59, s28))),
% 13.70/13.92 inference(modus_ponens,[status(thm)],[8478, 8477])).
% 13.70/13.92 tff(8480,plain,
% 13.70/13.92 ($false),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8479, 6074, 3890, 6915, 8473])).
% 13.70/13.92 tff(8481,plain,((~trans(s59, s28)) | always5(s28)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.92 tff(8482,plain,
% 13.70/13.92 (~trans(s59, s28)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8481, 7466])).
% 13.70/13.92 tff(8483,plain,
% 13.70/13.92 (~always5(s17)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[4225, 8462])).
% 13.70/13.92 tff(8484,assumption,(~always5(s17)), introduced(assumption)).
% 13.70/13.92 tff(8485,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s17) | (~trans(s59, s17)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s17) | (~trans(s59, s17)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8486,plain,
% 13.70/13.92 (((~always5(s59)) | (~trans(s59, s17)) | always5(s17)) <=> ((~always5(s59)) | always5(s17) | (~trans(s59, s17)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8487,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s17)) | always5(s17))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s17) | (~trans(s59, s17))))),
% 13.70/13.92 inference(monotonicity,[status(thm)],[8486])).
% 13.70/13.92 tff(8488,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s17)) | always5(s17))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s17) | (~trans(s59, s17)))),
% 13.70/13.92 inference(transitivity,[status(thm)],[8487, 8485])).
% 13.70/13.92 tff(8489,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s17)) | always5(s17))),
% 13.70/13.92 inference(quant_inst,[status(thm)],[])).
% 13.70/13.92 tff(8490,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s17) | (~trans(s59, s17))),
% 13.70/13.92 inference(modus_ponens,[status(thm)],[8489, 8488])).
% 13.70/13.92 tff(8491,plain,
% 13.70/13.92 ($false),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8490, 6184, 3890, 6915, 8484])).
% 13.70/13.92 tff(8492,plain,((~trans(s59, s17)) | always5(s17)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.92 tff(8493,plain,
% 13.70/13.92 (~trans(s59, s17)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8492, 8483])).
% 13.70/13.92 tff(8494,assumption,(~always5(s24)), introduced(assumption)).
% 13.70/13.92 tff(8495,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s24) | (~trans(s59, s24)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s24) | (~trans(s59, s24)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8496,plain,
% 13.70/13.92 (((~always5(s59)) | (~trans(s59, s24)) | always5(s24)) <=> ((~always5(s59)) | always5(s24) | (~trans(s59, s24)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8497,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s24)) | always5(s24))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s24) | (~trans(s59, s24))))),
% 13.70/13.92 inference(monotonicity,[status(thm)],[8496])).
% 13.70/13.92 tff(8498,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s24)) | always5(s24))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s24) | (~trans(s59, s24)))),
% 13.70/13.92 inference(transitivity,[status(thm)],[8497, 8495])).
% 13.70/13.92 tff(8499,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s24)) | always5(s24))),
% 13.70/13.92 inference(quant_inst,[status(thm)],[])).
% 13.70/13.92 tff(8500,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s24) | (~trans(s59, s24))),
% 13.70/13.92 inference(modus_ponens,[status(thm)],[8499, 8498])).
% 13.70/13.92 tff(8501,plain,
% 13.70/13.92 ($false),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8500, 6140, 3890, 6915, 8494])).
% 13.70/13.92 tff(8502,plain,((~trans(s59, s24)) | always5(s24)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.92 tff(8503,plain,
% 13.70/13.92 (~trans(s59, s24)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8502, 8438])).
% 13.70/13.92 tff(8504,assumption,(~always5(s35)), introduced(assumption)).
% 13.70/13.92 tff(8505,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s35) | (~trans(s59, s35)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s35) | (~trans(s59, s35)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8506,plain,
% 13.70/13.92 (((~always5(s59)) | (~trans(s59, s35)) | always5(s35)) <=> ((~always5(s59)) | always5(s35) | (~trans(s59, s35)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8507,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s35)) | always5(s35))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s35) | (~trans(s59, s35))))),
% 13.70/13.92 inference(monotonicity,[status(thm)],[8506])).
% 13.70/13.92 tff(8508,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s35)) | always5(s35))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s35) | (~trans(s59, s35)))),
% 13.70/13.92 inference(transitivity,[status(thm)],[8507, 8505])).
% 13.70/13.92 tff(8509,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s35)) | always5(s35))),
% 13.70/13.92 inference(quant_inst,[status(thm)],[])).
% 13.70/13.92 tff(8510,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s35) | (~trans(s59, s35))),
% 13.70/13.92 inference(modus_ponens,[status(thm)],[8509, 8508])).
% 13.70/13.92 tff(8511,plain,
% 13.70/13.92 ($false),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8510, 6129, 3890, 6915, 8504])).
% 13.70/13.92 tff(8512,plain,((~trans(s59, s35)) | always5(s35)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.92 tff(8513,plain,
% 13.70/13.92 (~trans(s59, s35)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8512, 7459])).
% 13.70/13.92 tff(8514,assumption,(~always5(s29)), introduced(assumption)).
% 13.70/13.92 tff(8515,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s29) | (~trans(s59, s29)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s29) | (~trans(s59, s29)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8516,plain,
% 13.70/13.92 (((~always5(s59)) | (~trans(s59, s29)) | always5(s29)) <=> ((~always5(s59)) | always5(s29) | (~trans(s59, s29)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8517,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s29)) | always5(s29))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s29) | (~trans(s59, s29))))),
% 13.70/13.92 inference(monotonicity,[status(thm)],[8516])).
% 13.70/13.92 tff(8518,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s29)) | always5(s29))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s29) | (~trans(s59, s29)))),
% 13.70/13.92 inference(transitivity,[status(thm)],[8517, 8515])).
% 13.70/13.92 tff(8519,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s29)) | always5(s29))),
% 13.70/13.92 inference(quant_inst,[status(thm)],[])).
% 13.70/13.92 tff(8520,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s29) | (~trans(s59, s29))),
% 13.70/13.92 inference(modus_ponens,[status(thm)],[8519, 8518])).
% 13.70/13.92 tff(8521,plain,
% 13.70/13.92 ($false),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8520, 5920, 3890, 6915, 8514])).
% 13.70/13.92 tff(8522,plain,((~trans(s59, s29)) | always5(s29)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.92 tff(8523,plain,
% 13.70/13.92 (~trans(s59, s29)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8522, 7465])).
% 13.70/13.92 tff(8524,assumption,(~always5(s32)), introduced(assumption)).
% 13.70/13.92 tff(8525,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s32) | (~trans(s59, s32)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s32) | (~trans(s59, s32)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8526,plain,
% 13.70/13.92 (((~always5(s59)) | (~trans(s59, s32)) | always5(s32)) <=> ((~always5(s59)) | always5(s32) | (~trans(s59, s32)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8527,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s32)) | always5(s32))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s32) | (~trans(s59, s32))))),
% 13.70/13.92 inference(monotonicity,[status(thm)],[8526])).
% 13.70/13.92 tff(8528,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s32)) | always5(s32))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s32) | (~trans(s59, s32)))),
% 13.70/13.92 inference(transitivity,[status(thm)],[8527, 8525])).
% 13.70/13.92 tff(8529,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s32)) | always5(s32))),
% 13.70/13.92 inference(quant_inst,[status(thm)],[])).
% 13.70/13.92 tff(8530,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s32) | (~trans(s59, s32))),
% 13.70/13.92 inference(modus_ponens,[status(thm)],[8529, 8528])).
% 13.70/13.92 tff(8531,plain,
% 13.70/13.92 ($false),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8530, 5909, 3890, 6915, 8524])).
% 13.70/13.92 tff(8532,plain,((~trans(s59, s32)) | always5(s32)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.92 tff(8533,plain,
% 13.70/13.92 (~trans(s59, s32)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8532, 7462])).
% 13.70/13.92 tff(8534,assumption,(~always5(s46)), introduced(assumption)).
% 13.70/13.92 tff(8535,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s46) | (~trans(s59, s46)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s46) | (~trans(s59, s46)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8536,plain,
% 13.70/13.92 (((~always5(s59)) | (~trans(s59, s46)) | always5(s46)) <=> ((~always5(s59)) | always5(s46) | (~trans(s59, s46)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8537,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s46)) | always5(s46))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s46) | (~trans(s59, s46))))),
% 13.70/13.92 inference(monotonicity,[status(thm)],[8536])).
% 13.70/13.92 tff(8538,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s46)) | always5(s46))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s46) | (~trans(s59, s46)))),
% 13.70/13.92 inference(transitivity,[status(thm)],[8537, 8535])).
% 13.70/13.92 tff(8539,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s46)) | always5(s46))),
% 13.70/13.92 inference(quant_inst,[status(thm)],[])).
% 13.70/13.92 tff(8540,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s46) | (~trans(s59, s46))),
% 13.70/13.92 inference(modus_ponens,[status(thm)],[8539, 8538])).
% 13.70/13.92 tff(8541,plain,
% 13.70/13.92 ($false),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8540, 6305, 3890, 6915, 8534])).
% 13.70/13.92 tff(8542,plain,((~trans(s59, s46)) | always5(s46)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.92 tff(8543,plain,
% 13.70/13.92 (~trans(s59, s46)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8542, 7440])).
% 13.70/13.92 tff(8544,plain,
% 13.70/13.92 (~always5(s16)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[4233, 8483])).
% 13.70/13.92 tff(8545,assumption,(~always5(s16)), introduced(assumption)).
% 13.70/13.92 tff(8546,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s16) | (~trans(s59, s16)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s16) | (~trans(s59, s16)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8547,plain,
% 13.70/13.92 (((~always5(s59)) | (~trans(s59, s16)) | always5(s16)) <=> ((~always5(s59)) | always5(s16) | (~trans(s59, s16)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8548,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s16)) | always5(s16))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s16) | (~trans(s59, s16))))),
% 13.70/13.92 inference(monotonicity,[status(thm)],[8547])).
% 13.70/13.92 tff(8549,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s16)) | always5(s16))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s16) | (~trans(s59, s16)))),
% 13.70/13.92 inference(transitivity,[status(thm)],[8548, 8546])).
% 13.70/13.92 tff(8550,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s16)) | always5(s16))),
% 13.70/13.92 inference(quant_inst,[status(thm)],[])).
% 13.70/13.92 tff(8551,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s16) | (~trans(s59, s16))),
% 13.70/13.92 inference(modus_ponens,[status(thm)],[8550, 8549])).
% 13.70/13.92 tff(8552,plain,
% 13.70/13.92 ($false),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8551, 6371, 3890, 6915, 8545])).
% 13.70/13.92 tff(8553,plain,((~trans(s59, s16)) | always5(s16)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.92 tff(8554,plain,
% 13.70/13.92 (~trans(s59, s16)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8553, 8544])).
% 13.70/13.92 tff(8555,assumption,(~always5(s19)), introduced(assumption)).
% 13.70/13.92 tff(8556,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s19) | (~trans(s59, s19)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s19) | (~trans(s59, s19)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8557,plain,
% 13.70/13.92 (((~always5(s59)) | (~trans(s59, s19)) | always5(s19)) <=> ((~always5(s59)) | always5(s19) | (~trans(s59, s19)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8558,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s19)) | always5(s19))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s19) | (~trans(s59, s19))))),
% 13.70/13.92 inference(monotonicity,[status(thm)],[8557])).
% 13.70/13.92 tff(8559,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s19)) | always5(s19))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s19) | (~trans(s59, s19)))),
% 13.70/13.92 inference(transitivity,[status(thm)],[8558, 8556])).
% 13.70/13.92 tff(8560,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s19)) | always5(s19))),
% 13.70/13.92 inference(quant_inst,[status(thm)],[])).
% 13.70/13.92 tff(8561,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s19) | (~trans(s59, s19))),
% 13.70/13.92 inference(modus_ponens,[status(thm)],[8560, 8559])).
% 13.70/13.92 tff(8562,plain,
% 13.70/13.92 ($false),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8561, 6327, 3890, 6915, 8555])).
% 13.70/13.92 tff(8563,plain,((~trans(s59, s19)) | always5(s19)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.92 tff(8564,plain,
% 13.70/13.92 (~trans(s59, s19)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8563, 8461])).
% 13.70/13.92 tff(8565,assumption,(node3(c_bit0, s59, s57)), introduced(assumption)).
% 13.70/13.92 tff(8566,plain,
% 13.70/13.92 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s59)) | (~m_counter_cell_v_value(c_bit0, s59)) | (~node2(c_bit0, s59)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s59)) | (~m_counter_cell_v_value(c_bit0, s59)) | (~node2(c_bit0, s59)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8567,plain,
% 13.70/13.92 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s59)) | (~m_counter_cell_v_value(c_bit0, s59)) | (~node2(c_bit0, s59)))),
% 13.70/13.92 inference(quant_inst,[status(thm)],[])).
% 13.70/13.92 tff(8568,plain,
% 13.70/13.92 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s59)) | (~m_counter_cell_v_value(c_bit0, s59)) | (~node2(c_bit0, s59))),
% 13.70/13.92 inference(modus_ponens,[status(thm)],[8567, 8566])).
% 13.70/13.92 tff(8569,plain,
% 13.70/13.92 ((~m_counter_cell_v_value(c_bit0, s59)) | (~node2(c_bit0, s59))),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8568, 93, 3857])).
% 13.70/13.92 tff(8570,plain,
% 13.70/13.92 (~node2(c_bit0, s59)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8569, 3853])).
% 13.70/13.92 tff(8571,plain,
% 13.70/13.92 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s57)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s57)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s57)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s57)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8572,plain,
% 13.70/13.92 ((node2(c_bit0, s59) | (~node3(c_bit0, s59, s57)) | (~m_counter_cell_v_value(c_bit0, s57))) <=> ((~m_counter_cell_v_value(c_bit0, s57)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s57)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8573,plain,
% 13.70/13.92 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s57)) | (~m_counter_cell_v_value(c_bit0, s57)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s57)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s57))))),
% 13.70/13.92 inference(monotonicity,[status(thm)],[8572])).
% 13.70/13.92 tff(8574,plain,
% 13.70/13.92 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s57)) | (~m_counter_cell_v_value(c_bit0, s57)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s57)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s57)))),
% 13.70/13.92 inference(transitivity,[status(thm)],[8573, 8571])).
% 13.70/13.92 tff(8575,plain,
% 13.70/13.92 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s57)) | (~m_counter_cell_v_value(c_bit0, s57)))),
% 13.70/13.92 inference(quant_inst,[status(thm)],[])).
% 13.70/13.92 tff(8576,plain,
% 13.70/13.92 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s57)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s57))),
% 13.70/13.92 inference(modus_ponens,[status(thm)],[8575, 8574])).
% 13.70/13.92 tff(8577,plain,
% 13.70/13.92 ($false),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8576, 121, 8570, 3705, 8565])).
% 13.70/13.92 tff(8578,plain,(~node3(c_bit0, s59, s57)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.92 tff(8579,plain,
% 13.70/13.92 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s57)) | node3(c_bit0, s59, s57))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s57)) | node3(c_bit0, s59, s57))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8580,plain,
% 13.70/13.92 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s57)) | node3(c_bit0, s59, s57))),
% 13.70/13.92 inference(quant_inst,[status(thm)],[])).
% 13.70/13.92 tff(8581,plain,
% 13.70/13.92 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s57)) | node3(c_bit0, s59, s57)),
% 13.70/13.92 inference(modus_ponens,[status(thm)],[8580, 8579])).
% 13.70/13.92 tff(8582,plain,
% 13.70/13.92 ((~trans(s59, s57)) | node3(c_bit0, s59, s57)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8581, 59])).
% 13.70/13.92 tff(8583,plain,
% 13.70/13.92 (~trans(s59, s57)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8582, 8578])).
% 13.70/13.92 tff(8584,plain,
% 13.70/13.92 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s15)) | (~m_counter_cell_v_value(c_bit2, s15)) | m_counter_cell_v_carry_out(c_bit2, s15))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s15)) | (~m_counter_cell_v_value(c_bit2, s15)) | m_counter_cell_v_carry_out(c_bit2, s15))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8585,plain,
% 13.70/13.92 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s15)) | (~m_counter_cell_v_value(c_bit2, s15)) | m_counter_cell_v_carry_out(c_bit2, s15))),
% 13.70/13.92 inference(quant_inst,[status(thm)],[])).
% 13.70/13.92 tff(8586,plain,
% 13.70/13.92 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s15)) | (~m_counter_cell_v_value(c_bit2, s15)) | m_counter_cell_v_carry_out(c_bit2, s15)),
% 13.70/13.92 inference(modus_ponens,[status(thm)],[8585, 8584])).
% 13.70/13.92 tff(8587,plain,
% 13.70/13.92 ((~m_counter_cell_v_value(c_bit2, s15)) | m_counter_cell_v_carry_out(c_bit2, s15)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8586, 1390, 8225])).
% 13.70/13.92 tff(8588,plain,
% 13.70/13.92 (m_counter_cell_v_carry_out(c_bit2, s15)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8587, 8216])).
% 13.70/13.92 tff(8589,plain,
% 13.70/13.92 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s15)) | (~m_counter_cell_v_carry_out(c_bit2, s15)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s15)) | (~m_counter_cell_v_carry_out(c_bit2, s15)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8590,plain,
% 13.70/13.92 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s15)) | (~m_counter_cell_v_carry_out(c_bit2, s15)))),
% 13.70/13.92 inference(quant_inst,[status(thm)],[])).
% 13.70/13.92 tff(8591,plain,
% 13.70/13.92 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s15)) | (~m_counter_cell_v_carry_out(c_bit2, s15))),
% 13.70/13.92 inference(modus_ponens,[status(thm)],[8590, 8589])).
% 13.70/13.92 tff(8592,plain,
% 13.70/13.92 (~always5(s15)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8591, 6925, 8588])).
% 13.70/13.92 tff(8593,plain,
% 13.70/13.92 (~always5(s14)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[4249, 8592])).
% 13.70/13.92 tff(8594,plain,
% 13.70/13.92 (~always5(s13)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[4257, 8593])).
% 13.70/13.92 tff(8595,plain,
% 13.70/13.92 (~always5(s12)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[4265, 8594])).
% 13.70/13.92 tff(8596,plain,
% 13.70/13.92 (~always5(s11)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[4273, 8595])).
% 13.70/13.92 tff(8597,plain,
% 13.70/13.92 (~always5(s10)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[4281, 8596])).
% 13.70/13.92 tff(8598,plain,
% 13.70/13.92 (~always5(s9)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[4289, 8597])).
% 13.70/13.92 tff(8599,plain,
% 13.70/13.92 (~always5(s8)),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[4297, 8598])).
% 13.70/13.92 tff(8600,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s8) | (~trans(s59, s8)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s8) | (~trans(s59, s8)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8601,plain,
% 13.70/13.92 (((~always5(s59)) | (~trans(s59, s8)) | always5(s8)) <=> ((~always5(s59)) | always5(s8) | (~trans(s59, s8)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8602,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s8)) | always5(s8))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s8) | (~trans(s59, s8))))),
% 13.70/13.92 inference(monotonicity,[status(thm)],[8601])).
% 13.70/13.92 tff(8603,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s8)) | always5(s8))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s8) | (~trans(s59, s8)))),
% 13.70/13.92 inference(transitivity,[status(thm)],[8602, 8600])).
% 13.70/13.92 tff(8604,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s8)) | always5(s8))),
% 13.70/13.92 inference(quant_inst,[status(thm)],[])).
% 13.70/13.92 tff(8605,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s8) | (~trans(s59, s8))),
% 13.70/13.92 inference(modus_ponens,[status(thm)],[8604, 8603])).
% 13.70/13.92 tff(8606,plain,
% 13.70/13.92 ($false),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8605, 6261, 3890, 6915, 8599])).
% 13.70/13.92 tff(8607,plain,(~trans(s59, s8)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.92 tff(8608,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s10) | (~trans(s59, s10)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s10) | (~trans(s59, s10)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8609,plain,
% 13.70/13.92 (((~always5(s59)) | (~trans(s59, s10)) | always5(s10)) <=> ((~always5(s59)) | always5(s10) | (~trans(s59, s10)))),
% 13.70/13.92 inference(rewrite,[status(thm)],[])).
% 13.70/13.92 tff(8610,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s10)) | always5(s10))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s10) | (~trans(s59, s10))))),
% 13.70/13.92 inference(monotonicity,[status(thm)],[8609])).
% 13.70/13.92 tff(8611,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s10)) | always5(s10))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s10) | (~trans(s59, s10)))),
% 13.70/13.92 inference(transitivity,[status(thm)],[8610, 8608])).
% 13.70/13.92 tff(8612,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s10)) | always5(s10))),
% 13.70/13.92 inference(quant_inst,[status(thm)],[])).
% 13.70/13.92 tff(8613,plain,
% 13.70/13.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s10) | (~trans(s59, s10))),
% 13.70/13.92 inference(modus_ponens,[status(thm)],[8612, 8611])).
% 13.70/13.92 tff(8614,plain,
% 13.70/13.92 ($false),
% 13.70/13.92 inference(unit_resolution,[status(thm)],[8613, 5898, 3890, 6915, 8597])).
% 13.70/13.92 tff(8615,plain,(~trans(s59, s10)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.92 tff(8616,plain,
% 13.70/13.92 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s12) | (~trans(s59, s12)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s12) | (~trans(s59, s12)))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8617,plain,
% 13.70/13.93 (((~always5(s59)) | (~trans(s59, s12)) | always5(s12)) <=> ((~always5(s59)) | always5(s12) | (~trans(s59, s12)))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8618,plain,
% 13.70/13.93 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s12)) | always5(s12))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s12) | (~trans(s59, s12))))),
% 13.70/13.93 inference(monotonicity,[status(thm)],[8617])).
% 13.70/13.93 tff(8619,plain,
% 13.70/13.93 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s12)) | always5(s12))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s12) | (~trans(s59, s12)))),
% 13.70/13.93 inference(transitivity,[status(thm)],[8618, 8616])).
% 13.70/13.93 tff(8620,plain,
% 13.70/13.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s12)) | always5(s12))),
% 13.70/13.93 inference(quant_inst,[status(thm)],[])).
% 13.70/13.93 tff(8621,plain,
% 13.70/13.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s12) | (~trans(s59, s12))),
% 13.70/13.93 inference(modus_ponens,[status(thm)],[8620, 8619])).
% 13.70/13.93 tff(8622,plain,
% 13.70/13.93 ($false),
% 13.70/13.93 inference(unit_resolution,[status(thm)],[8621, 5975, 3890, 6915, 8595])).
% 13.70/13.93 tff(8623,plain,(~trans(s59, s12)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.93 tff(8624,plain,
% 13.70/13.93 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s14) | (~trans(s59, s14)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s14) | (~trans(s59, s14)))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8625,plain,
% 13.70/13.93 (((~always5(s59)) | (~trans(s59, s14)) | always5(s14)) <=> ((~always5(s59)) | always5(s14) | (~trans(s59, s14)))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8626,plain,
% 13.70/13.93 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s14)) | always5(s14))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s14) | (~trans(s59, s14))))),
% 13.70/13.93 inference(monotonicity,[status(thm)],[8625])).
% 13.70/13.93 tff(8627,plain,
% 13.70/13.93 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s14)) | always5(s14))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s14) | (~trans(s59, s14)))),
% 13.70/13.93 inference(transitivity,[status(thm)],[8626, 8624])).
% 13.70/13.93 tff(8628,plain,
% 13.70/13.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s14)) | always5(s14))),
% 13.70/13.93 inference(quant_inst,[status(thm)],[])).
% 13.70/13.93 tff(8629,plain,
% 13.70/13.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s14) | (~trans(s59, s14))),
% 13.70/13.93 inference(modus_ponens,[status(thm)],[8628, 8627])).
% 13.70/13.93 tff(8630,plain,
% 13.70/13.93 ($false),
% 13.70/13.93 inference(unit_resolution,[status(thm)],[8629, 6085, 3890, 6915, 8593])).
% 13.70/13.93 tff(8631,plain,(~trans(s59, s14)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.93 tff(8632,plain,
% 13.70/13.93 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s7) | (~trans(s59, s7)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s7) | (~trans(s59, s7)))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8633,plain,
% 13.70/13.93 (((~always5(s59)) | (~trans(s59, s7)) | always5(s7)) <=> ((~always5(s59)) | always5(s7) | (~trans(s59, s7)))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8634,plain,
% 13.70/13.93 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s7)) | always5(s7))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s7) | (~trans(s59, s7))))),
% 13.70/13.93 inference(monotonicity,[status(thm)],[8633])).
% 13.70/13.93 tff(8635,plain,
% 13.70/13.93 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s7)) | always5(s7))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s7) | (~trans(s59, s7)))),
% 13.70/13.93 inference(transitivity,[status(thm)],[8634, 8632])).
% 13.70/13.93 tff(8636,plain,
% 13.70/13.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s7)) | always5(s7))),
% 13.70/13.93 inference(quant_inst,[status(thm)],[])).
% 13.70/13.93 tff(8637,plain,
% 13.70/13.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s7) | (~trans(s59, s7))),
% 13.70/13.93 inference(modus_ponens,[status(thm)],[8636, 8635])).
% 13.70/13.93 tff(8638,plain,
% 13.70/13.93 ($false),
% 13.70/13.93 inference(unit_resolution,[status(thm)],[8637, 6096, 3890, 6915, 7848])).
% 13.70/13.93 tff(8639,plain,(~trans(s59, s7)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.93 tff(8640,plain,
% 13.70/13.93 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s6) | (~trans(s59, s6)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s6) | (~trans(s59, s6)))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8641,plain,
% 13.70/13.93 (((~always5(s59)) | (~trans(s59, s6)) | always5(s6)) <=> ((~always5(s59)) | always5(s6) | (~trans(s59, s6)))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8642,plain,
% 13.70/13.93 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s6)) | always5(s6))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s6) | (~trans(s59, s6))))),
% 13.70/13.93 inference(monotonicity,[status(thm)],[8641])).
% 13.70/13.93 tff(8643,plain,
% 13.70/13.93 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s6)) | always5(s6))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s6) | (~trans(s59, s6)))),
% 13.70/13.93 inference(transitivity,[status(thm)],[8642, 8640])).
% 13.70/13.93 tff(8644,plain,
% 13.70/13.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s6)) | always5(s6))),
% 13.70/13.93 inference(quant_inst,[status(thm)],[])).
% 13.70/13.93 tff(8645,plain,
% 13.70/13.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s6) | (~trans(s59, s6))),
% 13.70/13.93 inference(modus_ponens,[status(thm)],[8644, 8643])).
% 13.70/13.93 tff(8646,plain,
% 13.70/13.93 ($false),
% 13.70/13.93 inference(unit_resolution,[status(thm)],[8645, 6162, 3890, 6915, 7849])).
% 13.70/13.93 tff(8647,plain,(~trans(s59, s6)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.93 tff(8648,plain,
% 13.70/13.93 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s13) | (~trans(s59, s13)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s13) | (~trans(s59, s13)))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8649,plain,
% 13.70/13.93 (((~always5(s59)) | (~trans(s59, s13)) | always5(s13)) <=> ((~always5(s59)) | always5(s13) | (~trans(s59, s13)))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8650,plain,
% 13.70/13.93 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s13)) | always5(s13))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s13) | (~trans(s59, s13))))),
% 13.70/13.93 inference(monotonicity,[status(thm)],[8649])).
% 13.70/13.93 tff(8651,plain,
% 13.70/13.93 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s13)) | always5(s13))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s13) | (~trans(s59, s13)))),
% 13.70/13.93 inference(transitivity,[status(thm)],[8650, 8648])).
% 13.70/13.93 tff(8652,plain,
% 13.70/13.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s13)) | always5(s13))),
% 13.70/13.93 inference(quant_inst,[status(thm)],[])).
% 13.70/13.93 tff(8653,plain,
% 13.70/13.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s13) | (~trans(s59, s13))),
% 13.70/13.93 inference(modus_ponens,[status(thm)],[8652, 8651])).
% 13.70/13.93 tff(8654,plain,
% 13.70/13.93 ($false),
% 13.70/13.93 inference(unit_resolution,[status(thm)],[8653, 6173, 3890, 6915, 8594])).
% 13.70/13.93 tff(8655,plain,(~trans(s59, s13)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.93 tff(8656,plain,
% 13.70/13.93 (~always5(s1)),
% 13.70/13.93 inference(unit_resolution,[status(thm)],[4353, 7853])).
% 13.70/13.93 tff(8657,plain,
% 13.70/13.93 (~always5(s0)),
% 13.70/13.93 inference(unit_resolution,[status(thm)],[4361, 8656])).
% 13.70/13.93 tff(8658,assumption,(~always5(s0)), introduced(assumption)).
% 13.70/13.93 tff(8659,plain,
% 13.70/13.93 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s0) | (~trans(s59, s0)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s0) | (~trans(s59, s0)))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8660,plain,
% 13.70/13.93 (((~always5(s59)) | (~trans(s59, s0)) | always5(s0)) <=> ((~always5(s59)) | always5(s0) | (~trans(s59, s0)))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8661,plain,
% 13.70/13.93 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s0)) | always5(s0))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s0) | (~trans(s59, s0))))),
% 13.70/13.93 inference(monotonicity,[status(thm)],[8660])).
% 13.70/13.93 tff(8662,plain,
% 13.70/13.93 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s0)) | always5(s0))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s0) | (~trans(s59, s0)))),
% 13.70/13.93 inference(transitivity,[status(thm)],[8661, 8659])).
% 13.70/13.93 tff(8663,plain,
% 13.70/13.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s0)) | always5(s0))),
% 13.70/13.93 inference(quant_inst,[status(thm)],[])).
% 13.70/13.93 tff(8664,plain,
% 13.70/13.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s0) | (~trans(s59, s0))),
% 13.70/13.93 inference(modus_ponens,[status(thm)],[8663, 8662])).
% 13.70/13.93 tff(8665,plain,
% 13.70/13.93 ($false),
% 13.70/13.93 inference(unit_resolution,[status(thm)],[8664, 6436, 3890, 6915, 8658])).
% 13.70/13.93 tff(8666,plain,((~trans(s59, s0)) | always5(s0)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.93 tff(8667,plain,
% 13.70/13.93 (~trans(s59, s0)),
% 13.70/13.93 inference(unit_resolution,[status(thm)],[8666, 8657])).
% 13.70/13.93 tff(8668,assumption,(~always5(s4)), introduced(assumption)).
% 13.70/13.93 tff(8669,assumption,(always5(s59)), introduced(assumption)).
% 13.70/13.93 tff(8670,assumption,(trans(s59, s4)), introduced(assumption)).
% 13.70/13.93 tff(8671,plain,
% 13.70/13.93 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s4) | (~trans(s59, s4)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s4) | (~trans(s59, s4)))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8672,plain,
% 13.70/13.93 (((~always5(s59)) | (~trans(s59, s4)) | always5(s4)) <=> ((~always5(s59)) | always5(s4) | (~trans(s59, s4)))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8673,plain,
% 13.70/13.93 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s4)) | always5(s4))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s4) | (~trans(s59, s4))))),
% 13.70/13.93 inference(monotonicity,[status(thm)],[8672])).
% 13.70/13.93 tff(8674,plain,
% 13.70/13.93 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s4)) | always5(s4))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s4) | (~trans(s59, s4)))),
% 13.70/13.93 inference(transitivity,[status(thm)],[8673, 8671])).
% 13.70/13.93 tff(8675,plain,
% 13.70/13.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s4)) | always5(s4))),
% 13.70/13.93 inference(quant_inst,[status(thm)],[])).
% 13.70/13.93 tff(8676,plain,
% 13.70/13.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s4) | (~trans(s59, s4))),
% 13.70/13.93 inference(modus_ponens,[status(thm)],[8675, 8674])).
% 13.70/13.93 tff(8677,plain,
% 13.70/13.93 ($false),
% 13.70/13.93 inference(unit_resolution,[status(thm)],[8676, 8670, 3890, 8669, 8668])).
% 13.70/13.93 tff(8678,plain,((~trans(s59, s4)) | (~always5(s59)) | always5(s4)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.93 tff(8679,plain,
% 13.70/13.93 ((~trans(s59, s4)) | always5(s4)),
% 13.70/13.93 inference(unit_resolution,[status(thm)],[8678, 6915])).
% 13.70/13.93 tff(8680,plain,
% 13.70/13.93 (~trans(s59, s4)),
% 13.70/13.93 inference(unit_resolution,[status(thm)],[8679, 7851])).
% 13.70/13.93 tff(8681,plain,
% 13.70/13.93 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s5) | (~trans(s59, s5)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s5) | (~trans(s59, s5)))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8682,plain,
% 13.70/13.93 (((~always5(s59)) | (~trans(s59, s5)) | always5(s5)) <=> ((~always5(s59)) | always5(s5) | (~trans(s59, s5)))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8683,plain,
% 13.70/13.93 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s5)) | always5(s5))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s5) | (~trans(s59, s5))))),
% 13.70/13.93 inference(monotonicity,[status(thm)],[8682])).
% 13.70/13.93 tff(8684,plain,
% 13.70/13.93 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s5)) | always5(s5))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s5) | (~trans(s59, s5)))),
% 13.70/13.93 inference(transitivity,[status(thm)],[8683, 8681])).
% 13.70/13.93 tff(8685,plain,
% 13.70/13.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s5)) | always5(s5))),
% 13.70/13.93 inference(quant_inst,[status(thm)],[])).
% 13.70/13.93 tff(8686,plain,
% 13.70/13.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s5) | (~trans(s59, s5))),
% 13.70/13.93 inference(modus_ponens,[status(thm)],[8685, 8684])).
% 13.70/13.93 tff(8687,plain,
% 13.70/13.93 (always5(s5) | (~trans(s59, s5))),
% 13.70/13.93 inference(unit_resolution,[status(thm)],[8686, 3890, 6915])).
% 13.70/13.93 tff(8688,plain,
% 13.70/13.93 (~trans(s59, s5)),
% 13.70/13.93 inference(unit_resolution,[status(thm)],[8687, 7850])).
% 13.70/13.93 tff(8689,assumption,(node3(c_bit0, s59, s23)), introduced(assumption)).
% 13.70/13.93 tff(8690,plain,
% 13.70/13.93 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s23)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s23)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s23)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s23)))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8691,plain,
% 13.70/13.93 ((node2(c_bit0, s59) | (~node3(c_bit0, s59, s23)) | (~m_counter_cell_v_value(c_bit0, s23))) <=> ((~m_counter_cell_v_value(c_bit0, s23)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s23)))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8692,plain,
% 13.70/13.93 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s23)) | (~m_counter_cell_v_value(c_bit0, s23)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s23)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s23))))),
% 13.70/13.93 inference(monotonicity,[status(thm)],[8691])).
% 13.70/13.93 tff(8693,plain,
% 13.70/13.93 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s23)) | (~m_counter_cell_v_value(c_bit0, s23)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s23)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s23)))),
% 13.70/13.93 inference(transitivity,[status(thm)],[8692, 8690])).
% 13.70/13.93 tff(8694,plain,
% 13.70/13.93 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s23)) | (~m_counter_cell_v_value(c_bit0, s23)))),
% 13.70/13.93 inference(quant_inst,[status(thm)],[])).
% 13.70/13.93 tff(8695,plain,
% 13.70/13.93 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s23)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s23))),
% 13.70/13.93 inference(modus_ponens,[status(thm)],[8694, 8693])).
% 13.70/13.93 tff(8696,plain,
% 13.70/13.93 ($false),
% 13.70/13.93 inference(unit_resolution,[status(thm)],[8695, 121, 8570, 717, 8689])).
% 13.70/13.93 tff(8697,plain,(~node3(c_bit0, s59, s23)), inference(lemma,lemma(discharge,[]))).
% 13.70/13.93 tff(8698,plain,
% 13.70/13.93 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s23)) | node3(c_bit0, s59, s23))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s23)) | node3(c_bit0, s59, s23))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8699,plain,
% 13.70/13.93 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s23)) | node3(c_bit0, s59, s23))),
% 13.70/13.93 inference(quant_inst,[status(thm)],[])).
% 13.70/13.93 tff(8700,plain,
% 13.70/13.93 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s23)) | node3(c_bit0, s59, s23)),
% 13.70/13.93 inference(modus_ponens,[status(thm)],[8699, 8698])).
% 13.70/13.93 tff(8701,plain,
% 13.70/13.93 ((~trans(s59, s23)) | node3(c_bit0, s59, s23)),
% 13.70/13.93 inference(unit_resolution,[status(thm)],[8700, 59])).
% 13.70/13.93 tff(8702,plain,
% 13.70/13.93 (~trans(s59, s23)),
% 13.70/13.93 inference(unit_resolution,[status(thm)],[8701, 8697])).
% 13.70/13.93 tff(8703,plain,
% 13.70/13.93 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s37)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s37)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s37)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s37)))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8704,plain,
% 13.70/13.93 ((node2(c_bit0, s59) | (~node3(c_bit0, s59, s37)) | (~m_counter_cell_v_value(c_bit0, s37))) <=> ((~m_counter_cell_v_value(c_bit0, s37)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s37)))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8705,plain,
% 13.70/13.93 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s37)) | (~m_counter_cell_v_value(c_bit0, s37)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s37)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s37))))),
% 13.70/13.93 inference(monotonicity,[status(thm)],[8704])).
% 13.70/13.93 tff(8706,plain,
% 13.70/13.93 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s37)) | (~m_counter_cell_v_value(c_bit0, s37)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s37)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s37)))),
% 13.70/13.93 inference(transitivity,[status(thm)],[8705, 8703])).
% 13.70/13.93 tff(8707,plain,
% 13.70/13.93 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s37)) | (~m_counter_cell_v_value(c_bit0, s37)))),
% 13.70/13.93 inference(quant_inst,[status(thm)],[])).
% 13.70/13.93 tff(8708,plain,
% 13.70/13.93 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s37)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s37))),
% 13.70/13.93 inference(modus_ponens,[status(thm)],[8707, 8706])).
% 13.70/13.93 tff(8709,plain,
% 13.70/13.93 (~node3(c_bit0, s59, s37)),
% 13.70/13.93 inference(unit_resolution,[status(thm)],[8708, 121, 8570, 1130])).
% 13.70/13.93 tff(8710,plain,
% 13.70/13.93 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s37)) | node3(c_bit0, s59, s37))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s37)) | node3(c_bit0, s59, s37))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8711,plain,
% 13.70/13.93 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s37)) | node3(c_bit0, s59, s37))),
% 13.70/13.93 inference(quant_inst,[status(thm)],[])).
% 13.70/13.93 tff(8712,plain,
% 13.70/13.93 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s37)) | node3(c_bit0, s59, s37)),
% 13.70/13.93 inference(modus_ponens,[status(thm)],[8711, 8710])).
% 13.70/13.93 tff(8713,plain,
% 13.70/13.93 (~trans(s59, s37)),
% 13.70/13.93 inference(unit_resolution,[status(thm)],[8712, 59, 8709])).
% 13.70/13.93 tff(8714,plain,
% 13.70/13.93 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s41)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s41)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s41)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s41)))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8715,plain,
% 13.70/13.93 ((node2(c_bit0, s59) | (~node3(c_bit0, s59, s41)) | (~m_counter_cell_v_value(c_bit0, s41))) <=> ((~m_counter_cell_v_value(c_bit0, s41)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s41)))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8716,plain,
% 13.70/13.93 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s41)) | (~m_counter_cell_v_value(c_bit0, s41)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s41)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s41))))),
% 13.70/13.93 inference(monotonicity,[status(thm)],[8715])).
% 13.70/13.93 tff(8717,plain,
% 13.70/13.93 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s41)) | (~m_counter_cell_v_value(c_bit0, s41)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s41)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s41)))),
% 13.70/13.93 inference(transitivity,[status(thm)],[8716, 8714])).
% 13.70/13.93 tff(8718,plain,
% 13.70/13.93 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s41)) | (~m_counter_cell_v_value(c_bit0, s41)))),
% 13.70/13.93 inference(quant_inst,[status(thm)],[])).
% 13.70/13.93 tff(8719,plain,
% 13.70/13.93 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s41)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s41))),
% 13.70/13.93 inference(modus_ponens,[status(thm)],[8718, 8717])).
% 13.70/13.93 tff(8720,plain,
% 13.70/13.93 (~node3(c_bit0, s59, s41)),
% 13.70/13.93 inference(unit_resolution,[status(thm)],[8719, 121, 8570, 1248])).
% 13.70/13.93 tff(8721,plain,
% 13.70/13.93 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s41)) | node3(c_bit0, s59, s41))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s41)) | node3(c_bit0, s59, s41))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8722,plain,
% 13.70/13.93 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s41)) | node3(c_bit0, s59, s41))),
% 13.70/13.93 inference(quant_inst,[status(thm)],[])).
% 13.70/13.93 tff(8723,plain,
% 13.70/13.93 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s41)) | node3(c_bit0, s59, s41)),
% 13.70/13.93 inference(modus_ponens,[status(thm)],[8722, 8721])).
% 13.70/13.93 tff(8724,plain,
% 13.70/13.93 (~trans(s59, s41)),
% 13.70/13.93 inference(unit_resolution,[status(thm)],[8723, 59, 8720])).
% 13.70/13.93 tff(8725,plain,
% 13.70/13.93 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s33)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s33)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s33)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s33)))),
% 13.70/13.93 inference(rewrite,[status(thm)],[])).
% 13.70/13.93 tff(8726,plain,
% 13.70/13.93 ((node2(c_bit0, s59) | (~node3(c_bit0, s59, s33)) | (~m_counter_cell_v_value(c_bit0, s33))) <=> ((~m_counter_cell_v_value(c_bit0, s33)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s33)))),
% 13.70/13.94 inference(rewrite,[status(thm)],[])).
% 13.70/13.94 tff(8727,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s33)) | (~m_counter_cell_v_value(c_bit0, s33)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s33)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s33))))),
% 13.70/13.94 inference(monotonicity,[status(thm)],[8726])).
% 13.70/13.94 tff(8728,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s33)) | (~m_counter_cell_v_value(c_bit0, s33)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s33)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s33)))),
% 13.70/13.94 inference(transitivity,[status(thm)],[8727, 8725])).
% 13.70/13.94 tff(8729,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s33)) | (~m_counter_cell_v_value(c_bit0, s33)))),
% 13.70/13.94 inference(quant_inst,[status(thm)],[])).
% 13.70/13.94 tff(8730,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s33)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s33))),
% 13.70/13.94 inference(modus_ponens,[status(thm)],[8729, 8728])).
% 13.70/13.94 tff(8731,plain,
% 13.70/13.94 (~node3(c_bit0, s59, s33)),
% 13.70/13.94 inference(unit_resolution,[status(thm)],[8730, 121, 8570, 1012])).
% 13.70/13.94 tff(8732,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s33)) | node3(c_bit0, s59, s33))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s33)) | node3(c_bit0, s59, s33))),
% 13.70/13.94 inference(rewrite,[status(thm)],[])).
% 13.70/13.94 tff(8733,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s33)) | node3(c_bit0, s59, s33))),
% 13.70/13.94 inference(quant_inst,[status(thm)],[])).
% 13.70/13.94 tff(8734,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s33)) | node3(c_bit0, s59, s33)),
% 13.70/13.94 inference(modus_ponens,[status(thm)],[8733, 8732])).
% 13.70/13.94 tff(8735,plain,
% 13.70/13.94 (~trans(s59, s33)),
% 13.70/13.94 inference(unit_resolution,[status(thm)],[8734, 59, 8731])).
% 13.70/13.94 tff(8736,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s45)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s45)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s45)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s45)))),
% 13.70/13.94 inference(rewrite,[status(thm)],[])).
% 13.70/13.94 tff(8737,plain,
% 13.70/13.94 ((node2(c_bit0, s59) | (~node3(c_bit0, s59, s45)) | (~m_counter_cell_v_value(c_bit0, s45))) <=> ((~m_counter_cell_v_value(c_bit0, s45)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s45)))),
% 13.70/13.94 inference(rewrite,[status(thm)],[])).
% 13.70/13.94 tff(8738,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s45)) | (~m_counter_cell_v_value(c_bit0, s45)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s45)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s45))))),
% 13.70/13.94 inference(monotonicity,[status(thm)],[8737])).
% 13.70/13.94 tff(8739,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s45)) | (~m_counter_cell_v_value(c_bit0, s45)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s45)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s45)))),
% 13.70/13.94 inference(transitivity,[status(thm)],[8738, 8736])).
% 13.70/13.94 tff(8740,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s45)) | (~m_counter_cell_v_value(c_bit0, s45)))),
% 13.70/13.94 inference(quant_inst,[status(thm)],[])).
% 13.70/13.94 tff(8741,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s45)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s45))),
% 13.70/13.94 inference(modus_ponens,[status(thm)],[8740, 8739])).
% 13.70/13.94 tff(8742,plain,
% 13.70/13.94 (~node3(c_bit0, s59, s45)),
% 13.70/13.94 inference(unit_resolution,[status(thm)],[8741, 121, 8570, 2857])).
% 13.70/13.94 tff(8743,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s45)) | node3(c_bit0, s59, s45))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s45)) | node3(c_bit0, s59, s45))),
% 13.70/13.94 inference(rewrite,[status(thm)],[])).
% 13.70/13.94 tff(8744,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s45)) | node3(c_bit0, s59, s45))),
% 13.70/13.94 inference(quant_inst,[status(thm)],[])).
% 13.70/13.94 tff(8745,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s45)) | node3(c_bit0, s59, s45)),
% 13.70/13.94 inference(modus_ponens,[status(thm)],[8744, 8743])).
% 13.70/13.94 tff(8746,plain,
% 13.70/13.94 (~trans(s59, s45)),
% 13.70/13.94 inference(unit_resolution,[status(thm)],[8745, 59, 8742])).
% 13.70/13.94 tff(8747,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s59)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s59)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s59)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s59)))),
% 13.70/13.94 inference(rewrite,[status(thm)],[])).
% 13.70/13.94 tff(8748,plain,
% 13.70/13.94 ((node2(c_bit0, s59) | (~node3(c_bit0, s59, s59)) | (~m_counter_cell_v_value(c_bit0, s59))) <=> ((~m_counter_cell_v_value(c_bit0, s59)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s59)))),
% 13.70/13.94 inference(rewrite,[status(thm)],[])).
% 13.70/13.94 tff(8749,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s59)) | (~m_counter_cell_v_value(c_bit0, s59)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s59)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s59))))),
% 13.70/13.94 inference(monotonicity,[status(thm)],[8748])).
% 13.70/13.94 tff(8750,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s59)) | (~m_counter_cell_v_value(c_bit0, s59)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s59)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s59)))),
% 13.70/13.94 inference(transitivity,[status(thm)],[8749, 8747])).
% 13.70/13.94 tff(8751,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s59)) | (~m_counter_cell_v_value(c_bit0, s59)))),
% 13.70/13.94 inference(quant_inst,[status(thm)],[])).
% 13.70/13.94 tff(8752,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s59)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s59))),
% 13.70/13.94 inference(modus_ponens,[status(thm)],[8751, 8750])).
% 13.70/13.94 tff(8753,plain,
% 13.70/13.94 (~node3(c_bit0, s59, s59)),
% 13.70/13.94 inference(unit_resolution,[status(thm)],[8752, 121, 3853, 8570])).
% 13.70/13.94 tff(8754,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s59)) | node3(c_bit0, s59, s59))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s59)) | node3(c_bit0, s59, s59))),
% 13.70/13.94 inference(rewrite,[status(thm)],[])).
% 13.70/13.94 tff(8755,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s59)) | node3(c_bit0, s59, s59))),
% 13.70/13.94 inference(quant_inst,[status(thm)],[])).
% 13.70/13.94 tff(8756,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s59)) | node3(c_bit0, s59, s59)),
% 13.70/13.94 inference(modus_ponens,[status(thm)],[8755, 8754])).
% 13.70/13.94 tff(8757,plain,
% 13.70/13.94 (~trans(s59, s59)),
% 13.70/13.94 inference(unit_resolution,[status(thm)],[8756, 59, 8753])).
% 13.70/13.94 tff(8758,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s49)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s49)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s49)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s49)))),
% 13.70/13.94 inference(rewrite,[status(thm)],[])).
% 13.70/13.94 tff(8759,plain,
% 13.70/13.94 ((node2(c_bit0, s59) | (~node3(c_bit0, s59, s49)) | (~m_counter_cell_v_value(c_bit0, s49))) <=> ((~m_counter_cell_v_value(c_bit0, s49)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s49)))),
% 13.70/13.94 inference(rewrite,[status(thm)],[])).
% 13.70/13.94 tff(8760,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s49)) | (~m_counter_cell_v_value(c_bit0, s49)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s49)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s49))))),
% 13.70/13.94 inference(monotonicity,[status(thm)],[8759])).
% 13.70/13.94 tff(8761,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s49)) | (~m_counter_cell_v_value(c_bit0, s49)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s49)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s49)))),
% 13.70/13.94 inference(transitivity,[status(thm)],[8760, 8758])).
% 13.70/13.94 tff(8762,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s49)) | (~m_counter_cell_v_value(c_bit0, s49)))),
% 13.70/13.94 inference(quant_inst,[status(thm)],[])).
% 13.70/13.94 tff(8763,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s49)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s49))),
% 13.70/13.94 inference(modus_ponens,[status(thm)],[8762, 8761])).
% 13.70/13.94 tff(8764,plain,
% 13.70/13.94 (~node3(c_bit0, s59, s49)),
% 13.70/13.94 inference(unit_resolution,[status(thm)],[8763, 121, 8570, 3133])).
% 13.70/13.94 tff(8765,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s49)) | node3(c_bit0, s59, s49))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s49)) | node3(c_bit0, s59, s49))),
% 13.70/13.94 inference(rewrite,[status(thm)],[])).
% 13.70/13.94 tff(8766,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s49)) | node3(c_bit0, s59, s49))),
% 13.70/13.94 inference(quant_inst,[status(thm)],[])).
% 13.70/13.94 tff(8767,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s49)) | node3(c_bit0, s59, s49)),
% 13.70/13.94 inference(modus_ponens,[status(thm)],[8766, 8765])).
% 13.70/13.94 tff(8768,plain,
% 13.70/13.94 (~trans(s59, s49)),
% 13.70/13.94 inference(unit_resolution,[status(thm)],[8767, 59, 8764])).
% 13.70/13.94 tff(8769,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s21)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s21)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s21)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s21)))),
% 13.70/13.94 inference(rewrite,[status(thm)],[])).
% 13.70/13.94 tff(8770,plain,
% 13.70/13.94 ((node2(c_bit0, s59) | (~node3(c_bit0, s59, s21)) | (~m_counter_cell_v_value(c_bit0, s21))) <=> ((~m_counter_cell_v_value(c_bit0, s21)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s21)))),
% 13.70/13.94 inference(rewrite,[status(thm)],[])).
% 13.70/13.94 tff(8771,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s21)) | (~m_counter_cell_v_value(c_bit0, s21)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s21)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s21))))),
% 13.70/13.94 inference(monotonicity,[status(thm)],[8770])).
% 13.70/13.94 tff(8772,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s21)) | (~m_counter_cell_v_value(c_bit0, s21)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s21)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s21)))),
% 13.70/13.94 inference(transitivity,[status(thm)],[8771, 8769])).
% 13.70/13.94 tff(8773,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s21)) | (~m_counter_cell_v_value(c_bit0, s21)))),
% 13.70/13.94 inference(quant_inst,[status(thm)],[])).
% 13.70/13.94 tff(8774,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s21)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s21))),
% 13.70/13.94 inference(modus_ponens,[status(thm)],[8773, 8772])).
% 13.70/13.94 tff(8775,plain,
% 13.70/13.94 (~node3(c_bit0, s59, s21)),
% 13.70/13.94 inference(unit_resolution,[status(thm)],[8774, 121, 8570, 658])).
% 13.70/13.94 tff(8776,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s21)) | node3(c_bit0, s59, s21))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s21)) | node3(c_bit0, s59, s21))),
% 13.70/13.94 inference(rewrite,[status(thm)],[])).
% 13.70/13.94 tff(8777,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s21)) | node3(c_bit0, s59, s21))),
% 13.70/13.94 inference(quant_inst,[status(thm)],[])).
% 13.70/13.94 tff(8778,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s21)) | node3(c_bit0, s59, s21)),
% 13.70/13.94 inference(modus_ponens,[status(thm)],[8777, 8776])).
% 13.70/13.94 tff(8779,plain,
% 13.70/13.94 (~trans(s59, s21)),
% 13.70/13.94 inference(unit_resolution,[status(thm)],[8778, 59, 8775])).
% 13.70/13.94 tff(8780,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s51)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s51)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s51)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s51)))),
% 13.70/13.94 inference(rewrite,[status(thm)],[])).
% 13.70/13.94 tff(8781,plain,
% 13.70/13.94 ((node2(c_bit0, s59) | (~node3(c_bit0, s59, s51)) | (~m_counter_cell_v_value(c_bit0, s51))) <=> ((~m_counter_cell_v_value(c_bit0, s51)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s51)))),
% 13.70/13.94 inference(rewrite,[status(thm)],[])).
% 13.70/13.94 tff(8782,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s51)) | (~m_counter_cell_v_value(c_bit0, s51)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s51)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s51))))),
% 13.70/13.94 inference(monotonicity,[status(thm)],[8781])).
% 13.70/13.94 tff(8783,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s51)) | (~m_counter_cell_v_value(c_bit0, s51)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s51)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s51)))),
% 13.70/13.94 inference(transitivity,[status(thm)],[8782, 8780])).
% 13.70/13.94 tff(8784,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s51)) | (~m_counter_cell_v_value(c_bit0, s51)))),
% 13.70/13.94 inference(quant_inst,[status(thm)],[])).
% 13.70/13.94 tff(8785,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s51)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s51))),
% 13.70/13.94 inference(modus_ponens,[status(thm)],[8784, 8783])).
% 13.70/13.94 tff(8786,plain,
% 13.70/13.94 ((~m_counter_cell_v_value(c_bit0, s51)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s51))),
% 13.70/13.94 inference(unit_resolution,[status(thm)],[8785, 121])).
% 13.70/13.94 tff(8787,plain,
% 13.70/13.94 (~node3(c_bit0, s59, s51)),
% 13.70/13.94 inference(unit_resolution,[status(thm)],[8786, 8570, 3270])).
% 13.70/13.94 tff(8788,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s51)) | node3(c_bit0, s59, s51))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s51)) | node3(c_bit0, s59, s51))),
% 13.70/13.94 inference(rewrite,[status(thm)],[])).
% 13.70/13.94 tff(8789,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s51)) | node3(c_bit0, s59, s51))),
% 13.70/13.94 inference(quant_inst,[status(thm)],[])).
% 13.70/13.94 tff(8790,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s51)) | node3(c_bit0, s59, s51)),
% 13.70/13.94 inference(modus_ponens,[status(thm)],[8789, 8788])).
% 13.70/13.94 tff(8791,plain,
% 13.70/13.94 (~trans(s59, s51)),
% 13.70/13.94 inference(unit_resolution,[status(thm)],[8790, 59, 8787])).
% 13.70/13.94 tff(8792,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~m_counter_cell_v_value(c_bit0, s1)) | (~node3(c_bit0, s59, s1)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s59) | (~m_counter_cell_v_value(c_bit0, s1)) | (~node3(c_bit0, s59, s1)))),
% 13.70/13.94 inference(rewrite,[status(thm)],[])).
% 13.70/13.94 tff(8793,plain,
% 13.70/13.94 ((node2(c_bit0, s59) | (~node3(c_bit0, s59, s1)) | (~m_counter_cell_v_value(c_bit0, s1))) <=> (node2(c_bit0, s59) | (~m_counter_cell_v_value(c_bit0, s1)) | (~node3(c_bit0, s59, s1)))),
% 13.70/13.94 inference(rewrite,[status(thm)],[])).
% 13.70/13.94 tff(8794,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s1)) | (~m_counter_cell_v_value(c_bit0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~m_counter_cell_v_value(c_bit0, s1)) | (~node3(c_bit0, s59, s1))))),
% 13.70/13.94 inference(monotonicity,[status(thm)],[8793])).
% 13.70/13.94 tff(8795,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s1)) | (~m_counter_cell_v_value(c_bit0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s59) | (~m_counter_cell_v_value(c_bit0, s1)) | (~node3(c_bit0, s59, s1)))),
% 13.70/13.94 inference(transitivity,[status(thm)],[8794, 8792])).
% 13.70/13.94 tff(8796,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s1)) | (~m_counter_cell_v_value(c_bit0, s1)))),
% 13.70/13.94 inference(quant_inst,[status(thm)],[])).
% 13.70/13.94 tff(8797,plain,
% 13.70/13.94 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s59) | (~m_counter_cell_v_value(c_bit0, s1)) | (~node3(c_bit0, s59, s1))),
% 13.70/13.94 inference(modus_ponens,[status(thm)],[8796, 8795])).
% 13.70/13.94 tff(8798,plain,
% 13.70/13.94 (node2(c_bit0, s59) | (~m_counter_cell_v_value(c_bit0, s1)) | (~node3(c_bit0, s59, s1))),
% 13.70/13.94 inference(unit_resolution,[status(thm)],[8797, 121])).
% 13.70/13.94 tff(8799,plain,
% 13.70/13.94 (~node3(c_bit0, s59, s1)),
% 13.70/13.94 inference(unit_resolution,[status(thm)],[8798, 8570, 81])).
% 13.70/13.94 tff(8800,plain,
% 13.70/13.94 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s1)) | node3(c_bit0, s59, s1))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s1)) | node3(c_bit0, s59, s1))),
% 13.80/13.94 inference(rewrite,[status(thm)],[])).
% 13.80/13.94 tff(8801,plain,
% 13.80/13.94 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s1)) | node3(c_bit0, s59, s1))),
% 13.80/13.94 inference(quant_inst,[status(thm)],[])).
% 13.80/13.94 tff(8802,plain,
% 13.80/13.94 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s1)) | node3(c_bit0, s59, s1)),
% 13.80/13.94 inference(modus_ponens,[status(thm)],[8801, 8800])).
% 13.80/13.94 tff(8803,plain,
% 13.80/13.94 (~trans(s59, s1)),
% 13.80/13.94 inference(unit_resolution,[status(thm)],[8802, 59, 8799])).
% 13.80/13.94 tff(8804,plain,
% 13.80/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s9)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s9)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s9)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s9)))),
% 13.80/13.94 inference(rewrite,[status(thm)],[])).
% 13.80/13.94 tff(8805,plain,
% 13.80/13.94 ((node2(c_bit0, s59) | (~node3(c_bit0, s59, s9)) | (~m_counter_cell_v_value(c_bit0, s9))) <=> ((~m_counter_cell_v_value(c_bit0, s9)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s9)))),
% 13.80/13.94 inference(rewrite,[status(thm)],[])).
% 13.80/13.94 tff(8806,plain,
% 13.80/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s9)) | (~m_counter_cell_v_value(c_bit0, s9)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s9)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s9))))),
% 13.80/13.94 inference(monotonicity,[status(thm)],[8805])).
% 13.80/13.94 tff(8807,plain,
% 13.80/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s9)) | (~m_counter_cell_v_value(c_bit0, s9)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s9)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s9)))),
% 13.80/13.94 inference(transitivity,[status(thm)],[8806, 8804])).
% 13.80/13.94 tff(8808,plain,
% 13.80/13.94 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s9)) | (~m_counter_cell_v_value(c_bit0, s9)))),
% 13.80/13.94 inference(quant_inst,[status(thm)],[])).
% 13.80/13.94 tff(8809,plain,
% 13.80/13.94 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s9)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s9))),
% 13.80/13.94 inference(modus_ponens,[status(thm)],[8808, 8807])).
% 13.80/13.94 tff(8810,plain,
% 13.80/13.94 ((~m_counter_cell_v_value(c_bit0, s9)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s9))),
% 13.80/13.94 inference(unit_resolution,[status(thm)],[8809, 121])).
% 13.80/13.94 tff(8811,plain,
% 13.80/13.94 (~node3(c_bit0, s59, s9)),
% 13.80/13.94 inference(unit_resolution,[status(thm)],[8810, 8570, 320])).
% 13.80/13.94 tff(8812,plain,
% 13.80/13.94 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s9)) | node3(c_bit0, s59, s9))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s9)) | node3(c_bit0, s59, s9))),
% 13.80/13.94 inference(rewrite,[status(thm)],[])).
% 13.80/13.94 tff(8813,plain,
% 13.80/13.94 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s9)) | node3(c_bit0, s59, s9))),
% 13.80/13.94 inference(quant_inst,[status(thm)],[])).
% 13.80/13.94 tff(8814,plain,
% 13.80/13.94 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s9)) | node3(c_bit0, s59, s9)),
% 13.80/13.94 inference(modus_ponens,[status(thm)],[8813, 8812])).
% 13.80/13.94 tff(8815,plain,
% 13.80/13.94 (~trans(s59, s9)),
% 13.80/13.94 inference(unit_resolution,[status(thm)],[8814, 59, 8811])).
% 13.80/13.94 tff(8816,plain,
% 13.80/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s53)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s53)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s53)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s53)))),
% 13.80/13.94 inference(rewrite,[status(thm)],[])).
% 13.80/13.94 tff(8817,plain,
% 13.80/13.94 ((node2(c_bit0, s59) | (~node3(c_bit0, s59, s53)) | (~m_counter_cell_v_value(c_bit0, s53))) <=> ((~m_counter_cell_v_value(c_bit0, s53)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s53)))),
% 13.80/13.94 inference(rewrite,[status(thm)],[])).
% 13.80/13.94 tff(8818,plain,
% 13.80/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s53)) | (~m_counter_cell_v_value(c_bit0, s53)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s53)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s53))))),
% 13.80/13.94 inference(monotonicity,[status(thm)],[8817])).
% 13.80/13.94 tff(8819,plain,
% 13.80/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s53)) | (~m_counter_cell_v_value(c_bit0, s53)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s53)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s53)))),
% 13.80/13.94 inference(transitivity,[status(thm)],[8818, 8816])).
% 13.80/13.94 tff(8820,plain,
% 13.80/13.94 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s53)) | (~m_counter_cell_v_value(c_bit0, s53)))),
% 13.80/13.94 inference(quant_inst,[status(thm)],[])).
% 13.80/13.94 tff(8821,plain,
% 13.80/13.94 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s53)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s53))),
% 13.80/13.94 inference(modus_ponens,[status(thm)],[8820, 8819])).
% 13.80/13.94 tff(8822,plain,
% 13.80/13.94 ((~m_counter_cell_v_value(c_bit0, s53)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s53))),
% 13.80/13.94 inference(unit_resolution,[status(thm)],[8821, 121])).
% 13.80/13.94 tff(8823,plain,
% 13.80/13.94 (~node3(c_bit0, s59, s53)),
% 13.80/13.94 inference(unit_resolution,[status(thm)],[8822, 8570, 3420])).
% 13.80/13.94 tff(8824,plain,
% 13.80/13.94 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s53)) | node3(c_bit0, s59, s53))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s53)) | node3(c_bit0, s59, s53))),
% 13.80/13.94 inference(rewrite,[status(thm)],[])).
% 13.80/13.94 tff(8825,plain,
% 13.80/13.94 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s53)) | node3(c_bit0, s59, s53))),
% 13.80/13.94 inference(quant_inst,[status(thm)],[])).
% 13.80/13.94 tff(8826,plain,
% 13.80/13.94 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s53)) | node3(c_bit0, s59, s53)),
% 13.80/13.94 inference(modus_ponens,[status(thm)],[8825, 8824])).
% 13.80/13.94 tff(8827,plain,
% 13.80/13.94 (~trans(s59, s53)),
% 13.80/13.94 inference(unit_resolution,[status(thm)],[8826, 59, 8823])).
% 13.80/13.94 tff(8828,plain,
% 13.80/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s15)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s15)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s15)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s15)))),
% 13.80/13.94 inference(rewrite,[status(thm)],[])).
% 13.80/13.94 tff(8829,plain,
% 13.80/13.94 ((node2(c_bit0, s59) | (~node3(c_bit0, s59, s15)) | (~m_counter_cell_v_value(c_bit0, s15))) <=> ((~m_counter_cell_v_value(c_bit0, s15)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s15)))),
% 13.80/13.94 inference(rewrite,[status(thm)],[])).
% 13.80/13.94 tff(8830,plain,
% 13.80/13.94 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s15)) | (~m_counter_cell_v_value(c_bit0, s15)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s15)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s15))))),
% 13.80/13.95 inference(monotonicity,[status(thm)],[8829])).
% 13.80/13.95 tff(8831,plain,
% 13.80/13.95 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s15)) | (~m_counter_cell_v_value(c_bit0, s15)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s15)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s15)))),
% 13.80/13.95 inference(transitivity,[status(thm)],[8830, 8828])).
% 13.80/13.95 tff(8832,plain,
% 13.80/13.95 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s15)) | (~m_counter_cell_v_value(c_bit0, s15)))),
% 13.80/13.95 inference(quant_inst,[status(thm)],[])).
% 13.80/13.95 tff(8833,plain,
% 13.80/13.95 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s15)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s15))),
% 13.80/13.95 inference(modus_ponens,[status(thm)],[8832, 8831])).
% 13.80/13.95 tff(8834,plain,
% 13.80/13.95 ((~m_counter_cell_v_value(c_bit0, s15)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s15))),
% 13.80/13.95 inference(unit_resolution,[status(thm)],[8833, 121])).
% 13.80/13.95 tff(8835,plain,
% 13.80/13.95 (~node3(c_bit0, s59, s15)),
% 13.80/13.95 inference(unit_resolution,[status(thm)],[8834, 8570, 485])).
% 13.80/13.95 tff(8836,plain,
% 13.80/13.95 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s15)) | node3(c_bit0, s59, s15))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s15)) | node3(c_bit0, s59, s15))),
% 13.80/13.95 inference(rewrite,[status(thm)],[])).
% 13.80/13.95 tff(8837,plain,
% 13.80/13.95 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s15)) | node3(c_bit0, s59, s15))),
% 13.80/13.95 inference(quant_inst,[status(thm)],[])).
% 13.80/13.95 tff(8838,plain,
% 13.80/13.95 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s15)) | node3(c_bit0, s59, s15)),
% 13.80/13.95 inference(modus_ponens,[status(thm)],[8837, 8836])).
% 13.80/13.95 tff(8839,plain,
% 13.80/13.95 (~trans(s59, s15)),
% 13.80/13.95 inference(unit_resolution,[status(thm)],[8838, 59, 8835])).
% 13.80/13.95 tff(8840,plain,
% 13.80/13.95 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~m_counter_cell_v_value(c_bit0, s3)) | (~node3(c_bit0, s59, s3)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s59) | (~m_counter_cell_v_value(c_bit0, s3)) | (~node3(c_bit0, s59, s3)))),
% 13.80/13.95 inference(rewrite,[status(thm)],[])).
% 13.80/13.95 tff(8841,plain,
% 13.80/13.95 ((node2(c_bit0, s59) | (~node3(c_bit0, s59, s3)) | (~m_counter_cell_v_value(c_bit0, s3))) <=> (node2(c_bit0, s59) | (~m_counter_cell_v_value(c_bit0, s3)) | (~node3(c_bit0, s59, s3)))),
% 13.80/13.95 inference(rewrite,[status(thm)],[])).
% 13.80/13.95 tff(8842,plain,
% 13.80/13.95 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s3)) | (~m_counter_cell_v_value(c_bit0, s3)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~m_counter_cell_v_value(c_bit0, s3)) | (~node3(c_bit0, s59, s3))))),
% 13.80/13.95 inference(monotonicity,[status(thm)],[8841])).
% 13.80/13.95 tff(8843,plain,
% 13.80/13.95 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s3)) | (~m_counter_cell_v_value(c_bit0, s3)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s59) | (~m_counter_cell_v_value(c_bit0, s3)) | (~node3(c_bit0, s59, s3)))),
% 13.80/13.95 inference(transitivity,[status(thm)],[8842, 8840])).
% 13.80/13.95 tff(8844,plain,
% 13.80/13.95 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s3)) | (~m_counter_cell_v_value(c_bit0, s3)))),
% 13.80/13.95 inference(quant_inst,[status(thm)],[])).
% 13.80/13.95 tff(8845,plain,
% 13.80/13.95 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s59) | (~m_counter_cell_v_value(c_bit0, s3)) | (~node3(c_bit0, s59, s3))),
% 13.80/13.95 inference(modus_ponens,[status(thm)],[8844, 8843])).
% 13.80/13.95 tff(8846,plain,
% 13.80/13.95 (node2(c_bit0, s59) | (~m_counter_cell_v_value(c_bit0, s3)) | (~node3(c_bit0, s59, s3))),
% 13.80/13.95 inference(unit_resolution,[status(thm)],[8845, 121])).
% 13.80/13.95 tff(8847,plain,
% 13.80/13.95 (~node3(c_bit0, s59, s3)),
% 13.80/13.95 inference(unit_resolution,[status(thm)],[8846, 8570, 155])).
% 13.80/13.95 tff(8848,plain,
% 13.80/13.95 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s3)) | node3(c_bit0, s59, s3))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s3)) | node3(c_bit0, s59, s3))),
% 13.80/13.95 inference(rewrite,[status(thm)],[])).
% 13.80/13.95 tff(8849,plain,
% 13.80/13.95 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s3)) | node3(c_bit0, s59, s3))),
% 13.80/13.95 inference(quant_inst,[status(thm)],[])).
% 13.80/13.95 tff(8850,plain,
% 13.80/13.95 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s3)) | node3(c_bit0, s59, s3)),
% 13.80/13.95 inference(modus_ponens,[status(thm)],[8849, 8848])).
% 13.80/13.95 tff(8851,plain,
% 13.80/13.95 (~trans(s59, s3)),
% 13.80/13.95 inference(unit_resolution,[status(thm)],[8850, 59, 8847])).
% 13.80/13.95 tff(8852,plain,
% 13.80/13.95 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s31)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s31)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s31)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s31)))),
% 13.80/13.95 inference(rewrite,[status(thm)],[])).
% 13.80/13.95 tff(8853,plain,
% 13.80/13.95 ((node2(c_bit0, s59) | (~node3(c_bit0, s59, s31)) | (~m_counter_cell_v_value(c_bit0, s31))) <=> ((~m_counter_cell_v_value(c_bit0, s31)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s31)))),
% 13.80/13.95 inference(rewrite,[status(thm)],[])).
% 13.80/13.95 tff(8854,plain,
% 13.80/13.95 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s31)) | (~m_counter_cell_v_value(c_bit0, s31)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s31)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s31))))),
% 13.80/13.95 inference(monotonicity,[status(thm)],[8853])).
% 13.80/13.95 tff(8855,plain,
% 13.80/13.95 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s31)) | (~m_counter_cell_v_value(c_bit0, s31)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s31)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s31)))),
% 13.80/13.95 inference(transitivity,[status(thm)],[8854, 8852])).
% 13.80/13.95 tff(8856,plain,
% 13.80/13.95 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s31)) | (~m_counter_cell_v_value(c_bit0, s31)))),
% 13.80/13.95 inference(quant_inst,[status(thm)],[])).
% 13.80/13.95 tff(8857,plain,
% 13.80/13.95 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s31)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s31))),
% 13.80/13.95 inference(modus_ponens,[status(thm)],[8856, 8855])).
% 13.80/13.95 tff(8858,plain,
% 13.80/13.95 ((~m_counter_cell_v_value(c_bit0, s31)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s31))),
% 13.80/13.95 inference(unit_resolution,[status(thm)],[8857, 121])).
% 13.80/13.95 tff(8859,plain,
% 13.80/13.95 (~node3(c_bit0, s59, s31)),
% 13.80/13.95 inference(unit_resolution,[status(thm)],[8858, 8570, 953])).
% 13.80/13.95 tff(8860,plain,
% 13.80/13.95 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s31)) | node3(c_bit0, s59, s31))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s31)) | node3(c_bit0, s59, s31))),
% 13.80/13.95 inference(rewrite,[status(thm)],[])).
% 13.80/13.95 tff(8861,plain,
% 13.80/13.95 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s31)) | node3(c_bit0, s59, s31))),
% 13.80/13.95 inference(quant_inst,[status(thm)],[])).
% 13.80/13.95 tff(8862,plain,
% 13.80/13.95 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s31)) | node3(c_bit0, s59, s31)),
% 13.80/13.95 inference(modus_ponens,[status(thm)],[8861, 8860])).
% 13.80/13.95 tff(8863,plain,
% 13.80/13.95 (~trans(s59, s31)),
% 13.80/13.95 inference(unit_resolution,[status(thm)],[8862, 59, 8859])).
% 13.80/13.95 tff(8864,plain,
% 13.80/13.95 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s11)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s11)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s11)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s11)))),
% 13.80/13.95 inference(rewrite,[status(thm)],[])).
% 13.80/13.95 tff(8865,plain,
% 13.80/13.95 ((node2(c_bit0, s59) | (~node3(c_bit0, s59, s11)) | (~m_counter_cell_v_value(c_bit0, s11))) <=> ((~m_counter_cell_v_value(c_bit0, s11)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s11)))),
% 13.80/13.95 inference(rewrite,[status(thm)],[])).
% 13.80/13.95 tff(8866,plain,
% 13.80/13.95 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s11)) | (~m_counter_cell_v_value(c_bit0, s11)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s11)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s11))))),
% 13.80/13.95 inference(monotonicity,[status(thm)],[8865])).
% 13.80/13.95 tff(8867,plain,
% 13.80/13.95 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s11)) | (~m_counter_cell_v_value(c_bit0, s11)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s11)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s11)))),
% 13.80/13.95 inference(transitivity,[status(thm)],[8866, 8864])).
% 13.80/13.95 tff(8868,plain,
% 13.80/13.95 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s11)) | (~m_counter_cell_v_value(c_bit0, s11)))),
% 13.80/13.95 inference(quant_inst,[status(thm)],[])).
% 13.80/13.95 tff(8869,plain,
% 13.80/13.95 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s11)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s11))),
% 13.80/13.95 inference(modus_ponens,[status(thm)],[8868, 8867])).
% 13.80/13.95 tff(8870,plain,
% 13.80/13.95 ((~m_counter_cell_v_value(c_bit0, s11)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s11))),
% 13.80/13.95 inference(unit_resolution,[status(thm)],[8869, 121])).
% 13.80/13.95 tff(8871,plain,
% 13.80/13.95 (~node3(c_bit0, s59, s11)),
% 13.80/13.95 inference(unit_resolution,[status(thm)],[8870, 8570, 375])).
% 13.80/13.95 tff(8872,plain,
% 13.80/13.95 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s11)) | node3(c_bit0, s59, s11))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s11)) | node3(c_bit0, s59, s11))),
% 13.80/13.95 inference(rewrite,[status(thm)],[])).
% 13.80/13.95 tff(8873,plain,
% 13.80/13.95 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s11)) | node3(c_bit0, s59, s11))),
% 13.80/13.95 inference(quant_inst,[status(thm)],[])).
% 13.80/13.95 tff(8874,plain,
% 13.80/13.95 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s11)) | node3(c_bit0, s59, s11)),
% 13.80/13.95 inference(modus_ponens,[status(thm)],[8873, 8872])).
% 13.80/13.95 tff(8875,plain,
% 13.80/13.95 (~trans(s59, s11)),
% 13.80/13.95 inference(unit_resolution,[status(thm)],[8874, 59, 8871])).
% 13.80/13.95 tff(8876,plain,
% 13.80/13.95 (trans(s59, s0) | trans(s59, s2) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s10) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s52) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58) | trans(s59, s59)),
% 13.80/13.95 inference(unit_resolution,[status(thm)],[6906, 8875, 8863, 8851, 8839, 8827, 8815, 8803, 8791])).
% 13.80/13.95 tff(8877,plain,
% 13.80/13.95 (trans(s59, s0) | trans(s59, s2) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s10) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s32) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s50) | trans(s59, s52) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58)),
% 13.80/13.95 inference(unit_resolution,[status(thm)],[8876, 8779, 8768, 8757, 8746, 8735, 8724, 8713])).
% 13.80/13.95 tff(8878,plain,
% 13.80/13.95 (trans(s59, s0) | trans(s59, s2) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s10) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s22) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s32) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s50) | trans(s59, s52) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58)),
% 13.80/13.95 inference(unit_resolution,[status(thm)],[8877, 8702])).
% 13.80/13.95 tff(8879,plain,
% 13.80/13.95 (trans(s59, s2) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s10) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s22) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s32) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s50) | trans(s59, s52) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58)),
% 13.80/13.95 inference(unit_resolution,[status(thm)],[8878, 8688, 8680, 8667])).
% 13.80/13.95 tff(8880,plain,
% 13.80/13.95 (trans(s59, s2) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s10) | trans(s59, s12) | trans(s59, s14) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s22) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s32) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s50) | trans(s59, s52) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58)),
% 13.80/13.95 inference(unit_resolution,[status(thm)],[8879, 8655])).
% 13.80/13.95 tff(8881,plain,
% 13.80/13.95 (trans(s59, s2) | trans(s59, s8) | trans(s59, s10) | trans(s59, s12) | trans(s59, s14) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s22) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s32) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s50) | trans(s59, s52) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58)),
% 13.80/13.96 inference(unit_resolution,[status(thm)],[8880, 8647, 8639])).
% 13.80/13.96 tff(8882,plain,
% 13.80/13.96 (trans(s59, s2) | trans(s59, s8) | trans(s59, s10) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s22) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s32) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s50) | trans(s59, s52) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58)),
% 13.80/13.96 inference(unit_resolution,[status(thm)],[8881, 8631, 8623])).
% 13.80/13.96 tff(8883,plain,
% 13.80/13.96 (trans(s59, s2) | trans(s59, s8) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s22) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s32) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s50) | trans(s59, s52) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58)),
% 13.80/13.96 inference(unit_resolution,[status(thm)],[8882, 8615])).
% 13.80/13.96 tff(8884,plain,
% 13.80/13.96 (trans(s59, s2) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s22) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s32) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s50) | trans(s59, s52) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58)),
% 13.80/13.96 inference(unit_resolution,[status(thm)],[8883, 8607])).
% 13.80/13.96 tff(8885,plain,
% 13.80/13.96 (trans(s59, s26) | trans(s59, s42) | trans(s59, s50) | trans(s59, s52) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s58)),
% 13.80/13.96 inference(unit_resolution,[status(thm)],[8884, 8583, 8564, 8554, 8543, 8533, 8523, 8513, 8503, 8493, 8482, 8472, 8460, 8450, 8437, 7929, 7919, 7909, 7899, 7889, 7879, 7871, 7861, 7513, 7502, 7492, 7484])).
% 13.80/13.96 tff(8886,plain,
% 13.80/13.96 (trans(s59, s50) | trans(s59, s52) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56)),
% 13.80/13.96 inference(unit_resolution,[status(thm)],[8885, 7476, 7452, 7300])).
% 13.80/13.96 tff(8887,plain,
% 13.80/13.96 (trans(s59, s56)),
% 13.80/13.96 inference(unit_resolution,[status(thm)],[8886, 7243, 7231, 7221, 7187])).
% 13.80/13.96 tff(8888,plain,
% 13.80/13.96 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s56)) | node3(c_bit2, s59, s56))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s56)) | node3(c_bit2, s59, s56))),
% 13.80/13.96 inference(rewrite,[status(thm)],[])).
% 13.80/13.96 tff(8889,plain,
% 13.80/13.96 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s56)) | node3(c_bit2, s59, s56))),
% 13.80/13.96 inference(quant_inst,[status(thm)],[])).
% 13.80/13.96 tff(8890,plain,
% 13.80/13.96 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s56)) | node3(c_bit2, s59, s56)),
% 13.80/13.96 inference(modus_ponens,[status(thm)],[8889, 8888])).
% 13.80/13.96 tff(8891,plain,
% 13.80/13.96 ((~trans(s59, s56)) | node3(c_bit2, s59, s56)),
% 13.80/13.96 inference(unit_resolution,[status(thm)],[8890, 59])).
% 13.80/13.96 tff(8892,plain,
% 13.80/13.96 (node3(c_bit2, s59, s56)),
% 13.80/13.96 inference(unit_resolution,[status(thm)],[8891, 8887])).
% 13.80/13.96 tff(8893,plain,
% 13.80/13.96 (~node2(c_bit1, s56)),
% 13.80/13.96 inference(unit_resolution,[status(thm)],[3634, 3588])).
% 13.80/13.96 tff(8894,plain,
% 13.80/13.96 (~m_counter_cell_v_value(c_bit1, s57)),
% 13.80/13.96 inference(unit_resolution,[status(thm)],[3653, 8893])).
% 13.80/13.96 tff(8895,plain,
% 13.80/13.96 (~node1(c_bit1, s57)),
% 13.80/13.96 inference(unit_resolution,[status(thm)],[3725, 8894])).
% 13.80/13.96 tff(8896,plain,
% 13.80/13.96 (m_counter_cell_v_value(c_bit1, s58)),
% 13.80/13.96 inference(unit_resolution,[status(thm)],[3744, 8895])).
% 13.80/13.96 tff(8897,plain,
% 13.80/13.96 (~node1(c_bit1, s58)),
% 13.80/13.96 inference(unit_resolution,[status(thm)],[3809, 8896])).
% 13.80/13.96 tff(8898,plain,
% 13.80/13.96 (m_counter_cell_v_value(c_bit1, s59)),
% 13.80/13.96 inference(unit_resolution,[status(thm)],[3828, 8897])).
% 13.80/13.96 tff(8899,plain,
% 13.80/13.96 (m_counter_cell_v_carry_out(c_bit1, s59)),
% 13.80/13.96 inference(unit_resolution,[status(thm)],[3870, 8898])).
% 13.80/13.96 tff(8900,plain,
% 13.80/13.96 (m_counter_cell_v_carry_in(c_bit2, s59)),
% 13.80/13.96 inference(unit_resolution,[status(thm)],[3878, 8899])).
% 13.80/13.96 tff(8901,plain,
% 13.80/13.96 (~m_counter_cell_v_value(c_bit2, s59)),
% 13.80/13.96 inference(unit_resolution,[status(thm)],[6933, 8900])).
% 13.80/13.96 tff(8902,plain,
% 13.80/13.96 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s59)) | m_counter_cell_v_value(c_bit2, s59) | (~node1(c_bit2, s59)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s59)) | m_counter_cell_v_value(c_bit2, s59) | (~node1(c_bit2, s59)))),
% 13.80/13.96 inference(rewrite,[status(thm)],[])).
% 13.80/13.96 tff(8903,plain,
% 13.80/13.96 (((~node1(c_bit2, s59)) | (~m_counter_cell_v_carry_in(c_bit2, s59)) | m_counter_cell_v_value(c_bit2, s59)) <=> ((~m_counter_cell_v_carry_in(c_bit2, s59)) | m_counter_cell_v_value(c_bit2, s59) | (~node1(c_bit2, s59)))),
% 13.80/13.96 inference(rewrite,[status(thm)],[])).
% 13.80/13.96 tff(8904,plain,
% 13.80/13.96 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s59)) | (~m_counter_cell_v_carry_in(c_bit2, s59)) | m_counter_cell_v_value(c_bit2, s59))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s59)) | m_counter_cell_v_value(c_bit2, s59) | (~node1(c_bit2, s59))))),
% 13.80/13.96 inference(monotonicity,[status(thm)],[8903])).
% 13.80/13.96 tff(8905,plain,
% 13.80/13.96 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s59)) | (~m_counter_cell_v_carry_in(c_bit2, s59)) | m_counter_cell_v_value(c_bit2, s59))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s59)) | m_counter_cell_v_value(c_bit2, s59) | (~node1(c_bit2, s59)))),
% 13.80/13.96 inference(transitivity,[status(thm)],[8904, 8902])).
% 13.80/13.96 tff(8906,plain,
% 13.80/13.96 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s59)) | (~m_counter_cell_v_carry_in(c_bit2, s59)) | m_counter_cell_v_value(c_bit2, s59))),
% 13.80/13.96 inference(quant_inst,[status(thm)],[])).
% 13.80/13.96 tff(8907,plain,
% 13.80/13.96 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s59)) | m_counter_cell_v_value(c_bit2, s59) | (~node1(c_bit2, s59))),
% 13.80/13.96 inference(modus_ponens,[status(thm)],[8906, 8905])).
% 13.80/13.96 tff(8908,plain,
% 13.80/13.96 (~node1(c_bit2, s59)),
% 13.80/13.96 inference(unit_resolution,[status(thm)],[8907, 30, 8900, 8901])).
% 13.80/13.96 tff(8909,plain,
% 13.80/13.96 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s56) | node1(c_bit2, s59) | (~node3(c_bit2, s59, s56)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s56) | node1(c_bit2, s59) | (~node3(c_bit2, s59, s56)))),
% 13.80/13.97 inference(rewrite,[status(thm)],[])).
% 13.80/13.97 tff(8910,plain,
% 13.80/13.97 ((node1(c_bit2, s59) | (~node3(c_bit2, s59, s56)) | m_counter_cell_v_value(c_bit2, s56)) <=> (m_counter_cell_v_value(c_bit2, s56) | node1(c_bit2, s59) | (~node3(c_bit2, s59, s56)))),
% 13.80/13.97 inference(rewrite,[status(thm)],[])).
% 13.80/13.97 tff(8911,plain,
% 13.80/13.97 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s59) | (~node3(c_bit2, s59, s56)) | m_counter_cell_v_value(c_bit2, s56))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s56) | node1(c_bit2, s59) | (~node3(c_bit2, s59, s56))))),
% 13.80/13.97 inference(monotonicity,[status(thm)],[8910])).
% 13.80/13.97 tff(8912,plain,
% 13.80/13.97 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s59) | (~node3(c_bit2, s59, s56)) | m_counter_cell_v_value(c_bit2, s56))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s56) | node1(c_bit2, s59) | (~node3(c_bit2, s59, s56)))),
% 13.80/13.97 inference(transitivity,[status(thm)],[8911, 8909])).
% 13.80/13.97 tff(8913,plain,
% 13.80/13.97 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s59) | (~node3(c_bit2, s59, s56)) | m_counter_cell_v_value(c_bit2, s56))),
% 13.80/13.97 inference(quant_inst,[status(thm)],[])).
% 13.80/13.97 tff(8914,plain,
% 13.80/13.97 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s56) | node1(c_bit2, s59) | (~node3(c_bit2, s59, s56))),
% 13.80/13.97 inference(modus_ponens,[status(thm)],[8913, 8912])).
% 13.80/13.97 tff(8915,plain,
% 13.80/13.97 ($false),
% 13.80/13.97 inference(unit_resolution,[status(thm)],[8914, 73, 8908, 7005, 8892])).
% 13.80/13.97 % SZS output end Proof
% 13.80/13.97 % E exiting
%------------------------------------------------------------------------------